{"id":17110,"date":"2021-08-27T10:52:02","date_gmt":"2021-08-27T05:22:02","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=17110"},"modified":"2021-09-15T19:54:34","modified_gmt":"2021-09-15T14:24:34","slug":"ap-10th-class-maths-bits-chapter-6","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/ap-10th-class-maths-bits-chapter-6\/","title":{"rendered":"AP 10th Class Maths Bits Chapter 6 Progressions with Answers"},"content":{"rendered":"

Practice the AP 10th Class Maths Bits with Answers<\/a> Chapter 6 Progressions on a regular basis so that you can attempt exams with utmost confidence.<\/p>\n

AP State Syllabus 10th Class Maths Bits 6th Lesson Progressions with Answers<\/h2>\n

Question 1.
\nWhich term of the G.P. \\(\\frac{1}{3}, \\frac{1}{9}, \\frac{1}{27},\\) …………………… is \\(\\frac{1}{2187}\\)
\nA) 5th<\/sup>
\nB) 6th<\/sup>
\nC) 7th<\/sup>
\nD) 8th<\/sup>
\nAnswer:
\nC) 7th<\/sup><\/p>\n

Question 2.
\nThe 21st<\/sup> term of an A.P., whose first two terms are -3 and 4 is …………………
\nA) 143
\nB) -143
\nC) 137
\nD) 17
\nAnswer:
\nC) 137<\/p>\n

\"AP<\/p>\n

Question 3.
\nThe common difference of an A.P. for which a18<\/sub> – a14<\/sub> = 32 is ……………..
\nA) 8
\nB) -8
\nC) -4
\nD) 4
\nAnswer:
\nA) 8<\/p>\n

Question 4.
\nIn an A.P., if a = 1, an<\/sub> = 20 and Sn<\/sub> = 399, then n = ………………
\nA) 19
\nB) 42
\nC) 28
\nD) 38
\nAnswer:
\nD) 38<\/p>\n

Question 5.
\nWhich term of G.P. 3, 3\u221a3,9, …………….. equals to 243?
\nA) 6
\nB) 7
\nC) 8
\nD) 9
\nAnswer:
\nB) 7<\/p>\n

Question 6.
\nIf x, x + 2, x + 6 are three consecutive terms in G.P, find the value of ‘x’.
\nA) 3
\nC) 2
\nB) 4
\nD) 1
\nAnswer:
\nD) 1<\/p>\n

Question 7.
\nIf an<\/sub> = \\(\\frac{n(n+3)}{n+2}\\) , then find a17<\/sub> = ………………….
\nA) \\(\\frac{340}{20}\\)
\nB) \\(\\frac{341}{19}\\)
\nC) \\(\\frac{340}{19}\\)
\nD) \\(\\frac{341}{20}\\)
\nAnswer:
\nC) \\(\\frac{340}{19}\\)<\/p>\n

Question 8.
\nA famous book written by ancient mathematician Aryabhatta is …………………
\nA) Arya Tharkam
\nB) Aryabhatteeyam
\nC) Siddhantha Siromani
\nD) Karana Kuthuhalam
\nAnswer:
\nB) Aryabhatteeyam<\/p>\n

Question 9.
\nThe sum of first 100 natural numbers is ………………….
\nA) 4050
\nB) 4500
\nC) 5500
\nD) 5050
\nAnswer:
\nD) 5050<\/p>\n

\"AP<\/p>\n

Question 10.
\nIf a, b, c are in G.P., then b = ……………….
\nA) ac
\nB) \\(\\sqrt{\\mathrm{ac}}\\)
\nC) \\(\\frac{a+c}{2}\\)
\nD) a2<\/sup>c2<\/sup>
\nAnswer:
\nB) \\(\\sqrt{\\mathrm{ac}}\\)<\/p>\n

Question 11.
\nWhich term of the A.P -18, -16, -14, …………………. is first positive term ?
\nA) t9<\/sub>
\nB) t10<\/sub>
\nC) t11<\/sub>
\nD) t12<\/sub>
\nAnswer:
\nC) t11<\/sub><\/p>\n

Question 12.
\nIf 16, x, 36 are in G.P. then x =
\nA) 24
\nB) 26
\nC) 28
\nD) 30
\nAnswer:
\nA) 24<\/p>\n

Question 13.
\nThe next term of the A.P(a + 3d),(a + d). (a – d), ………………….. is
\nA) a + 2d
\nB) a – 2d
\nC) a – 4d
\nD) a – 3d
\nAnswer:
\nD) a – 3d<\/p>\n

Question 14.
\nIn an A.P the nth<\/sup> term an<\/sub> is ………………….
\nA) an<\/sub> = a + (n – 1)d
\nB) d + (n – 1)a
\nC) a + d
\nD) \\(\\frac{(n-1)}{d}\\) + a
\nAnswer:
\nA) an<\/sub> = a + (n – 1)d<\/p>\n

Question 15.
\nIn a G.P. the 3rd<\/sup> term is 24 and 6th<\/sup> term is 192 then 10th<\/sup> term is …………………….
\nA) 2062
\nB) 3072
\nC) 4072
\nD) 1072
\nAnswer:
\nB) 3072<\/p>\n

Question 16.
\nIn a G.P. aP + Q<\/sub> = m,a P – Q<\/sub> = n then
\naP<\/sub>= …………………..
\nA) mn
\nB) \\(\\sqrt{m n}\\)
\nC) \\(\\frac{\\mathrm{mn}}{2}\\)
\nD) \\(\\frac{\\mathrm{m}}{2}\\)
\nAnswer:
\nB) \\(\\sqrt{m n}\\)<\/p>\n

\"AP<\/p>\n

Question 17.
\nIf an<\/sub> = \\(\\frac{n(n+1)(2 n+1)}{6}\\) then a6<\/sub> = ……………….
\nA) \u00b11
\nB) n(n + 1)
\nC) 55
\nD) 91
\nAnswer:
\nD) 91<\/p>\n

Question 18.
\nIf the sum of first ‘n’ terms of an A.P. 2, 5, 8, ………………… is equal to the sum of first n
\nterms of the A.P. 57, 59, 61, …………………… then ‘n’ is equal to …………………..
\nA) 110
\nC) 112
\nB) 111
\nD) 113
\nAnswer:
\nB) 111<\/p>\n

Question 19.
\nIf p, q, r are in A.P. and x, y, z in G.P., then Xq – r<\/sup> \u00d7 Yr – p<\/sup> \u00d7 Zp – q<\/sup> is equal to …………………..
\nA) p + q + r
\nB) x \u00d7 y \u00d7 z
\nC) 1
\nD) px + qy + rz
\nAnswer:
\nC) 1<\/p>\n

Question 20.
\nIn an A.P., pth<\/sup> term is q and qth<\/sup> term is p, then its common difference is ………………….
\nA) 1
\nB) -1
\nC) 2
\nD) -2
\nAnswer:
\nB) -1<\/p>\n

Question 21.
\nThe next term of \u221a2, \u221a8, \u221a18, \u221a32, …………………. is …………………..
\nA) \\(\\sqrt{34}\\)
\nB) \\(\\sqrt{38}\\)
\nC) \\(\\sqrt{42}\\)
\nD) \\(\\sqrt{50}\\)
\nAnswer:
\nD) \\(\\sqrt{50}\\)<\/p>\n

Question 22.
\nThe common difference of an AP in which a25<\/sub> – a12<\/sub> = -52 is ………………….
\nA) 4
\nB) -4
\nC) -3
\nD) 3
\nAnswer:
\nB) -4<\/p>\n

Question 23.
\nWhat will be the value of x if 8x + 4 , 6x – 2 and 2x + 7 are in arithmetic progression?
\nA) \\(\\frac{-15}{2}\\)
\nB) \\(\\frac{15}{2}\\)
\nC) 15
\nD) -15
\nAnswer:
\nB) \\(\\frac{15}{2}\\)<\/p>\n

\"AP<\/p>\n

Question 24.
\nThe nth<\/sup> term of an arithmetic progression is -11 while sum of the first n terms is 66, when its first term is 22 then the value of n is
\nA) 12
\nB) 13
\nC) 14
\nD) 15
\nAnswer:
\nA) 12<\/p>\n

Question 25.
\nIf the first and fifth term’s sum is 10, then the third term of an arithmetic progression is………………
\nA) 3
\nB) 1
\nC) 5
\nD) 2
\nAnswer:
\nC) 5<\/p>\n

Question 26.
\nIf the 10th<\/sup> term of the sequence \\(\\sqrt{3}, \\sqrt{12}, \\sqrt{27}\\) ……………..is \\(\\sqrt{3 n^{2}}\\) then the value of \\(\\frac{\\mathbf{n}}{2}\\) is ………………..
\nA) 3
\nB) \u221a3
\nC) 5
\nD) \u221a5
\nAnswer:
\nC) 5<\/p>\n

Question 27.
\nIf the product of five numbers in GP is 1024, then the middle number is
\nA) 8
\nB) 4
\nC) 2
\nD) None
\nAnswer:
\nB) 4<\/p>\n

Question 28.
\nIf the second term of a GP is 2 and the sum of infinite terms is 8, then the first term is
\nA) 8
\nB) 6
\nC) 4
\nD) 3
\nAnswer:
\nB) 6<\/p>\n

Question 29.
\nIf a, b and c are in AP and also in GP, then
\nA) a = b \u2260 c
\nB) a \u2260 b = c
\nC) a \u2260 b \u2260 c
\nD) a = b = c
\nAnswer:
\nA) a = b \u2260 c<\/p>\n

Question 30.
\nThe least value of n for which 1 + 2 + 22<\/sup> + ……………….. (n terms) is greater than 1000 is
\nA) 7
\nB) 8
\nC) 9
\nD) 10
\nAnswer:
\nD) 10<\/p>\n

\"AP<\/p>\n

Question 31.
\nThe number of numbers between 100 and 1000 which are divisible by 7 is
\nA) 7
\nB) 128
\nC) 132
\nD) None
\nAnswer:
\nB) 128<\/p>\n

Question 32.
\nWhich is the three digit number divisible by 7 ?
\nA) 100
\nB) 133
\nC) 137
\nD) 143
\nAnswer:
\nB) 133<\/p>\n

Question 33.
\nThe 6th term in the GP 2, 8, 32, ……………….. is
\nA) 512
\nB) 128
\nC) 2048
\nD) 256
\nAnswer:
\nC) 2048<\/p>\n

Question 34.
\n1 + 1 + 1 + ………….. n terms =
\nA) \\(\\frac{\\mathrm{n}}{2}\\)
\nB) \\(\\frac{\\mathrm{n}-1}{2}\\)
\nC) n
\nD) \\(\\frac{n+1}{2}\\)
\nAnswer:
\nC) n<\/p>\n

Question 35.
\n1 + 3 + 6 + 10 + …………………. n terms =
\nA) \\(\\frac{n(n+1)(n+2)}{4}\\)
\nB) \\(\\frac{n(n+1)(n+2)}{8}\\)
\nC) \\(\\frac{n(n+1)(n+2)}{6}\\)
\nD) None
\nAnswer:
\nC) \\(\\frac{n(n+1)(n+2)}{6}\\)<\/p>\n

Question 36.
\nHow many two-digit numbers are divisible by 6 ?
\nA) 12
\nB) 15
\nC) 10
\nD) 17
\nAnswer:
\nB) 15<\/p>\n

Question 37.
\nIf the 2nd term of an AP is 4 and the 6th term is 16, then its 11th term is
\nA) 29
\nB) 33
\nC) 34
\nD) 31
\nAnswer:
\nA) 29<\/p>\n

\"AP<\/p>\n

Question 38.
\nWhich term of the AP 24, 21, 18,……………. is the first negative ?
\nA) 10th
\nB) 8th
\nC) 7th
\nD) 6th
\nAnswer:
\nC) 7th<\/p>\n

Question 39.
\nIf a = 2 and d = 2, then S15<\/sub> =
\nA) 220
\nB) 230
\nC) 240
\nD) 245
\nAnswer:
\nC) 240<\/p>\n

Question 40.
\nThe nth<\/sup> term of a Geometric Progression is an<\/sub> = arn – 1<\/sup>, where ‘ r ‘ represents
\nA) Common difference
\nB) Common ratio
\nC) First term
\nD) Radius
\nAnswer:
\nB) Common ratio<\/p>\n

Question 41.
\nIf the nth<\/sup> term of an A.P. is an<\/sub> = 3 + 2n, then the common difference d is ……………………
\nA) 2
\nB) 3
\nC) 4
\nD) 5
\nAnswer:
\nA) 2<\/p>\n

Question 42.
\nThe common difference of the AP, x – y, x, x + y,………… is ……………….
\nA) x
\nB) y
\nC) – x
\nD) -y
\nAnswer:
\nB) y<\/p>\n

Question 43.
\nCommon difference of an Arithmetic Progression, whose 3rd term is 5 and 7th term is 9, is
\nA) 1
\nB) 2
\nC) 3
\nD) 4
\nAnswer:
\nA) 1<\/p>\n

Question 44.
\nIf (i) -1.0, -1.5, -2.0, -2.5, …………………. and (ii) -1,-3, -9, -27,…………….. are two progressions, then which of them is a Geometric Progression ?
\nA) (i) only
\nB) (ii) only
\nC) (i) and (ii) both
\nD) None of them
\nAnswer:
\nB) (ii) only<\/p>\n

\"AP<\/p>\n

Question 45.
\nIf nth<\/sup> term of a series is \\(\\frac{3 n-4}{7}\\), then 6th<\/sup> term =
\nA) \\(\\frac{15}{7}\\)
\nB) 1
\nC) 2
\nD) \\(\\frac{18}{7}\\)
\nAnswer:
\nC) 2<\/p>\n

Question 46.
\nIf nth<\/sup> term of a series is \\(\\) then 7th<\/sup> term =
\nA) \\(\\frac{73}{90}\\)
\nB) \\(\\frac{5}{9}\\)
\nC) \\(\\frac{49}{9}\\)
\nD) \\(\\frac{7}{9}\\)
\nAnswer:
\nB) \\(\\frac{5}{9}\\)<\/p>\n

Question 47.
\nWhich of the following is an A.P ?
\nA) 1 + 8 +27 + ……………….
\nB) 1 + 4 + 9 + ……………….
\nC) 1 – 2 + 3 – 4 + …………….
\nD) 1 + 2 + 3 + ……………
\nAnswer:
\nD) 1 + 2 + 3 + ……………<\/p>\n

Question 48.
\n10th<\/sup> term of 4 + 6 + 8 + ………….. is
\nA) 26
\nB) 18
\nC) 22
\nD) 20
\nAnswer:
\nC) 22<\/p>\n

Question 49.
\n27th<\/sup> term of 5, 14, 23, ……………… is
\nA) 900
\nB) 101
\nC) 100
\nD) 239
\nAnswer:
\nD) 239<\/p>\n

Question 50.
\n12th<\/sup> term of the series 5, 14, 23, ……………. is
\nA) 900
\nB) 104
\nC) 239
\nD) 100
\nAnswer:
\nB) 104<\/p>\n

\"AP<\/p>\n

Question 51.
\n18th<\/sup> term of 13, 8, 3, -2, ……………….. is
\nA) -32
\nB) -72
\nC) 32
\nD) -57
\nAnswer:
\nB) -72<\/p>\n

Question 52.
\nCommon difference of x + \\(\\frac{4 x}{3}+\\frac{5 x}{3}\\) + 2x + ……………… is
\nA) \\(\\frac{x}{3}\\)
\nB) \\(\\frac{1}{3}\\)
\nC) x
\nD) \\(\\frac{2 x}{3}\\)
\nAnswer:
\nA) \\(\\frac{x}{3}\\)<\/p>\n

Question 53.
\nThe common difference of the A.P 13, 8, 3, -2, …………… is
\nA) 10
\nB) 4
\nC) 5
\nD) -5
\nAnswer:
\nD) -5<\/p>\n

Question 54.
\nIf a = -1, d = -3 in an A.P, then 12th<\/sup> term is
\nA) 17
\nB) -23
\nC) -34
\nD) -17
\nAnswer:
\nC) -34<\/p>\n

Question 55.
\nIf the first term of an A.P is -2 and common difference is -5, then 12th<\/sup> term is
\nA) -32
\nB) 32
\nC) -57
\nD) 34
\nAnswer:
\nC) -57<\/p>\n

Question 56.
\nIf nth<\/sup> term of an A.P is \\(\\frac{5 n-4}{7}\\) then common difference is
\nA) \\(\\frac{-4}{7}\\)
\nB) \\(\\frac{5}{7}\\)
\nC) \\(\\frac{1}{7}\\)
\nD) \\(\\frac{3}{7}\\)
\nAnswer:
\nB) \\(\\frac{5}{7}\\)<\/p>\n

Question 57.
\nIn an A.P if 8th<\/sup> term is 23 and 102nd<\/sup> term is 305, then common difference is
\nA) 5
\nB) 2
\nC) 1
\nD) 3
\nAnswer:
\nD) 3<\/p>\n

\"AP<\/p>\n

Question 58.
\nIn an A.P. if first term is 4,9th<\/sup> term is 20, then 15th<\/sup> term is
\nA) 32
\nB) 36
\nC) 16
\nD) 18
\nAnswer:
\nA) 32<\/p>\n

Question 59.
\nIn an A.P if third term is 7 and seventh term is 15, then first term is
\nA) 2
\nB) 0
\nC) 5
\nD) 3
\nAnswer:
\nD) 3<\/p>\n

Question 60.
\nIn an A.P, if 16th<\/sup> term is 47 and 31st<\/sup> term is 92, then 27th<\/sup> term is
\nA) 86
\nB) 120
\nC) 80
\nD) 116
\nAnswer:
\nC) 80<\/p>\n

Question 61.
\nIn an A.P, if 7 times of 7th term is equal to 11 times of 11th term, then 18th term is
\nA) 7
\nB) 0
\nC) 11
\nD) 18
\nAnswer:
\nB) 0<\/p>\n

Question 62.
\nIf 3rd term of an A.P is 11 and 15th term is 59, then 24th term is
\nA) 89
\nB) 95
\nC) 109
\nD) 79
\nAnswer:
\nB) 95<\/p>\n

Question 63.
\nIf 10th term of an A.P is 0 and 42nd term is -32, then nth term is ………………
\nA) 10 – n
\nB) 8 – n
\nC) 11 – n
\nD) 9 – n
\nAnswer:
\nA) 10 – n<\/p>\n

Question 64.
\nSum of 20 terms of 3 + 5 + 7 + 9 + ………………. is
\nA) 440
\nB) 220
\nC) 410
\nD) 460
\nAnswer:
\nA) 440<\/p>\n

\"AP<\/p>\n

Question 65.
\nHow many terms are to be added to make the sum 52 in the series (-8) + (-6) + (-4) + ……………… ?
\nA) 31
\nB) 13
\nC) 3
\nD) 12
\nAnswer:
\nB) 13<\/p>\n

Question 66.
\nIn an A.P. if common difference is 2, sum of n terms is 49,7th term is 13, then n = ………………
\nA) 7
\nB) 0
\nC) 13
\nD) 5
\nAnswer:
\nA) 7<\/p>\n

Question 67.
\nIf the nth<\/sup> term of an A.P, is 2n + 5, its first term is
\nA) 0
\nB) 7
\nC) 2
\nD) 4
\nAnswer:
\nB) 7<\/p>\n

Question 68.
\nHow many numbers are divisible by 9 in between 1 and 1000 ?
\nA) 100
\nB) 101
\nC) 110
\nD) 111
\nAnswer:
\nB) 101<\/p>\n

Question 69.
\nThe number of odd numbers between 1,100 that are divisible by 5 is
\nA) 15
\nB) 5
\nC) 10
\nD) 11
\nAnswer:
\nC) 10<\/p>\n

Question 70.
\nIf the sum of three numbers which are in A.P is 27 and the product of first and last is 77, then the numbers are
\nA) 7, 10,11
\nB) 7, 9, 11
\nC) 6, 9, 12
\nD) 8, 9, 10
\nAnswer:
\nB) 7, 9, 11<\/p>\n

Question 71.
\nIf the sum of three numbers which are in A.P is 15 and the sum of the squares of the extremes is 58, then those numbers are
\nA) 3, 6, 9
\nB) 3, 5, 7
\nC) 2, 5, 8
\nD) 2, 6, 7
\nAnswer:
\nB) 3, 5, 7<\/p>\n

\"AP<\/p>\n

Question 72.
\nIf the sum of four numbers in A.P is 24 and the sum of their squares 164, then those numbers are
\nA) 3, 5, 7, 9
\nB) 3, 4, 5, 6
\nQ 1, 4, 7,11
\nD) 2, 4, 6,12
\nAnswer:
\nA) 3, 5, 7, 9<\/p>\n

Question 73.
\nIf the sum of the series 24, 20, 16, …………… is 60, then the number of terms is
\nA) 13
\nB) 25
\nC) 3
\nD) 25
\nAnswer:
\nC) 3<\/p>\n

Question 74.
\n72 + 70 + 68 + ……………. + 40=
\nA) 952
\nB) 1852
\nC) 1052
\nD) 1252
\nAnswer:
\nA) 952<\/p>\n

Question 75.
\nIf d = 2 and 8th term of an A.P is 15, then the sum of 15 terms is ………………
\nA) \\(\\frac{225}{2}\\)
\nB) 0
\nC) 15
\nD) 225
\nAnswer:
\nD) 225<\/p>\n

Question 76.
\nIf the sum of n terms of an A.P is 4n2<\/sup> + 5n, then common difference is
\nA) 8
\nB) 0
\nC) 4
\nD) 6
\nAnswer:
\nA) 8<\/p>\n

Question 77.
\nIf 5th<\/sup> term of a G.P is 32 and common ratio 2, then the sum of 14 terms is
\nA) 32, 766
\nB) 16, 388
\nC) 64, 432
\nD) 30,746
\nAnswer:
\nA) 32, 766<\/p>\n

\"AP<\/p>\n

Question 78.
\nThe sum of even numbers between 100, 200 is
\nA) 7650
\nB) 6750
\nC) 5670
\nD) 7350
\nAnswer:
\nD) 7350<\/p>\n

Question 79.
\nArithmetic mean of \\(\\frac{1}{2}\\) and \\(\\frac{1}{3}\\) is
\nA) \\(\\frac{12}{5}\\)
\nB) \\(\\frac{6}{5}\\)
\nC) \\(\\frac{5}{12}\\)
\nD) \\(\\frac{5}{6}\\)
\nAnswer:
\nC) \\(\\frac{5}{12}\\)<\/p>\n

Question 80.
\nOne of the four A.M’s between 3, 23 is ………………..
\nA) 15
\nB) 6
\nC) 21
\nD) 8
\nAnswer:
\nA) 15<\/p>\n

Question 81.
\nThe product of two numbers is 91 and their arithmetic mean is 10 then the two numbers are
\nA) 14,6
\nB) 13, 7
\nC) 10, 10
\nD) 12, 8
\nAnswer:
\nB) 13, 7<\/p>\n

Question 82.
\nSum of 10 arithmetic means between 3, 10 is
\nA) 65
\nB) 130
\nC) 0
\nD) 60
\nAnswer:
\nA) 65<\/p>\n

Question 83.
\nSum of 4 arithmetic means between 3 and 23 is
\nA) 69
\nB) 48
\nC) 52
\nD) 50
\nAnswer:
\nC) 52<\/p>\n

Question 84.
\nSum of first 100 odd numbers is
\nA) 10,000
\nB) 100
\nC) 1000
\nD) 1,00,000
\nAnswer:
\nA) 10,000<\/p>\n

\"AP<\/p>\n

Question 85.
\n12<\/sup> + 22<\/sup> + 32<\/sup> + +1002<\/sup> = ……………….
\nA) (5050)2<\/sup>
\nB) 42925
\nC) 5050
\nD) 5500
\nAnswer:
\nD) 5500<\/p>\n

Question 86.
\nSum to ‘n’ terms of 1, 8, 27, 64, ……………
\nA) \\(\\frac{n^{2}(n+1)}{4}\\)
\nB) \\(\\frac{n^{2}(n+1)^{2}}{4}\\)
\nC) \\(\\frac{n(n+1)}{2}\\)
\nD) \\(\\frac{n(n+1)(2 n+1)}{6}\\)
\nAnswer:
\nB) \\(\\frac{n^{2}(n+1)^{2}}{4}\\)<\/p>\n

Question 87.
\nSum to ‘n’ terms of 3.5 + 4.7 + 5.9 + …………………
\nA) \\(\\frac{n(n+1)(n-3)}{12}\\)
\nB) \\(\\frac{n\\left(4 n^{2}+27 n+59\\right)}{6}\\)
\nC) \\(\\frac{n\\left(25 n^{2}+65 n+2\\right)}{12}\\)
\nD) \\(\\frac{n\\left(25 n^{2}+65 n+2\\right)}{6}\\)
\nAnswer:
\nB) \\(\\frac{n\\left(4 n^{2}+27 n+59\\right)}{6}\\)<\/p>\n

Question 88.
\n(1) + (1 + 3) + (1 + 3 + 5) + to ‘n’ terms = ……………….
\nA) \\(\\frac{n(n-1)(2 n-1)}{24}\\)
\nB) \\(\\frac{n(n+1)(2 n-1)}{12}\\)
\nC) \\(\\frac{n(n+1)(2 n+1)}{6}\\)
\nD) \\(\\frac{n(n+1)(2 n+1)}{24}\\)
\nAnswer:
\nC) \\(\\frac{n(n+1)(2 n+1)}{6}\\)<\/p>\n

Question 89.
\nWhich of the following geometric pro-gressions has the common ratio as 2?
\nA) \\(\\sqrt{2}, \\sqrt{6}, \\sqrt{18}\\) , ……………….
\nB) \\(\\sqrt{3}, \\sqrt{6}, \\sqrt{12}\\) , ……………….
\nC) \\(\\sqrt{5}, \\sqrt{15}, \\sqrt{45}\\) , ……………….
\nD) \\(\\sqrt{7}, \\sqrt{21}, \\sqrt{63}\\) , ……………….
\nAnswer:
\nB) \\(\\sqrt{3}, \\sqrt{6}, \\sqrt{12}\\) , ……………….<\/p>\n

Question 90.
\n\\(\\frac{1^{2}}{3}+\\frac{1^{2}+2^{2}}{5}+\\frac{1^{2}+2^{2}+3^{2}}{7}\\) + ………… n terms =
\nA) \\(\\frac{n(n+1)(n+2)}{12}\\)
\nB) \\(\\frac{n(n+1)(n+2)}{24}\\)
\nC) \\(\\frac{n(n+1)(n+2)}{6}\\)
\nD) \\(\\frac{n(n+1)(n+2)}{18}\\)
\nAnswer:
\nD) \\(\\frac{n(n+1)(n+2)}{18}\\)<\/p>\n

\"AP<\/p>\n

Question 91.
\nSum of first n terms of 1.4 + 4.7 + 7.10 + 10.13 + ……………… is
\nA) \u03a3n2<\/sup> – 4\u03a3n + n
\nB) 9\u03a3n2<\/sup> – 3\u03a3n – 2n
\nC) \u03a3n2<\/sup> – 3\u03a3n + 4
\nD) 9\u03a3n2<\/sup> – 3\u03a3n – 2
\nAnswer:
\nB) 9\u03a3n2<\/sup> – 3\u03a3n – 2n<\/p>\n

Question 92.
\nThe nth<\/sup> term of the series 1.3 + 3.5 + 5.7 + …………….. is
\nA) 1 – 4n
\nB) n2<\/sup> + 4
\nC) 4n2<\/sup> – 1
\nD) 4n2<\/sup> + 1
\nAnswer:
\nC) 4n2<\/sup> – 1<\/p>\n

Question 93.
\nnth<\/sup> \\(\\frac{5}{1.2}+\\frac{7}{2.3} \\cdot \\frac{1}{3}+\\frac{9}{3.4} \\cdot \\frac{1}{3^{2}}\\) + \\(\\frac{11}{4.5} \\cdot \\frac{1}{3^{3}}\\) term of the series
\nA) \\(\\frac{2 n+4}{n(n+1)} \\cdot \\frac{1}{3^{n}}\\)
\nB) \\(\\frac{2 n+3}{n(n+1)} \\cdot \\frac{1}{3^{n+1}}\\)
\nC) \\(\\frac{2 n+3}{n(n+1)} \\cdot \\frac{1}{3^{n}}\\)
\nD) \\(\\frac{2 n+3}{n(n+1)} \\cdot \\frac{1}{3^{n-1}}\\)
\nAnswer:
\nD) \\(\\frac{2 n+3}{n(n+1)} \\cdot \\frac{1}{3^{n-1}}\\)<\/p>\n

Question 94.
\nSum to n terms of 1.2.3 + 2.3.4 + 3.4.5 + ……………… is .
\nA) \\(\\frac{n(n+1)(n+2)(n+3)}{6}\\)
\nB) \\(\\frac{n(n+1)(n+2)}{2}\\)
\nC) \\(\\frac{n(n+1)(n+2)(n+3)}{4}\\)
\nD) \\(\\frac{n(n+1)(n+2)(n+3)}{8}\\)
\nAnswer:
\nC) \\(\\frac{n(n+1)(n+2)(n+3)}{4}\\)<\/p>\n

Question 95.
\n\\(\\frac{1+2+3+\\ldots \\ldots+n}{1+3+5+\\ldots \\ldots+(2 n-1)}\\) =
\nA) \\(\\frac{(\\mathrm{n}+1)}{2 \\mathrm{n}}\\)
\nB) \\(\\frac{2}{\\mathrm{n}}\\)
\nC) \\(\\frac{\\mathrm{n}}{2}\\)
\nD) \\(\\frac{(\\mathrm{n}-1)}{2}\\)
\nAnswer:
\nA) \\(\\frac{(\\mathrm{n}+1)}{2 \\mathrm{n}}\\)<\/p>\n

Question 96.
\nIf the common difference of an A.P is 1 and 6th term is \\(\\frac{\\left(4 \\cos ^{2} \\alpha+1\\right)}{\\cos ^{2} \\alpha}\\), then first term is
\nA) cot2<\/sup>\u03b1
\nB) cosec2<\/sup>\u03b1
\nC) tan2<\/sup>\u03b1
\nD) sec2<\/sup>\u03b1
\nAnswer:
\nC) tan2<\/sup>\u03b1<\/p>\n

Question 97.
\nSum of n terms of + ……………. is
\nA) \\(\\frac{(2 n+1)}{n}\\)
\nB) \\(\\frac{n}{(2 n+1)}\\)
\nC) \\(\\frac{n+1}{n}\\)
\nD) \\(\\frac{\\mathrm{n}}{(\\mathrm{n}+1)}\\)
\nAnswer:
\nD) \\(\\frac{\\mathrm{n}}{(\\mathrm{n}+1)}\\)<\/p>\n

\"AP<\/p>\n

Question 98.
\nSum of n terms of 1 + 4 + 13 + 40 + ……………… is
\nA) \\(\\frac{\\left(3^{n+1}+2 n-3\\right)}{4}\\)
\nB) \\(\\frac{\\left(3^{n+1}-2 n-3\\right)}{4}\\)
\nC) \\(\\frac{\\left(3^{n+1}-2 n+3\\right)}{4}\\)
\nD) \\(\\frac{\\left(3^{n+1}+2 n+3\\right)}{4}\\)
\nAnswer:
\nB) \\(\\frac{\\left(3^{n+1}-2 n-3\\right)}{4}\\)<\/p>\n

Question 99.
\nSum of n terms of 2.3 + 3.4 + 4.5 + ………………. is
\nA) \\(\\frac{n\\left(n^{2}+6 n+11\\right)}{3}\\)
\nB) \\(\\frac{n\\left(n^{2}-6 n-11\\right)}{3}\\)
\nC) \\(\\frac{n\\left(n^{2}-6 n+11\\right)}{3}\\)
\nD) \\(\\frac{n\\left(n^{2}+6 n-11\\right)}{3}\\)
\nAnswer:
\nA) \\(\\frac{n\\left(n^{2}+6 n+11\\right)}{3}\\)<\/p>\n

Question 100.
\nIf 2nd term of a G.P is 24 and 5th term is 81, then first term is
\nA) 16
\nB) 20
\nC) \\(\\frac{3}{2}\\)
\nD) 3
\nAnswer:
\nA) 16<\/p>\n

Question 101.
\nThe common ratio of 2 + \\(\\frac{2}{3}+\\frac{2}{9}+\\frac{2}{27}\\)+ …………….. is
\nA) \\(\\frac{1}{2}\\)
\nB) 2
\nC) 3
\nD) \\(\\frac{1}{3}\\)
\nAnswer:
\nD) \\(\\frac{1}{3}\\)<\/p>\n

Question 102.
\nIf the sum of three numbers in G.P is 21 and their product is 216, then the numbers are
\nA) 5, 7,9
\nB) 3, 6, 12
\nC) 2, 4, 8
\nD) 4, 8, 6
\nAnswer:
\nB) 3, 6, 12<\/p>\n

Question 103.
\nIf the product of five numbers in G.P is 1024, then the middle number is
\nA) 2
\nB) 8
\nC) 4
\nD) 16
\nAnswer:
\nC) 4<\/p>\n

Question 104.
\nSum of 20 terms of 3 + 6 + 12 + ……………. is
\nA) 3(219<\/sup> – 1)
\nB) 3(220<\/sup> – 1)
\nC) 3(219<\/sup> -1)\/2
\nD) \\(\\)
\nAnswer:
\nB) 3(220<\/sup> – 1)<\/p>\n

\"AP<\/p>\n

Question 105.
\n1 + \\(\\frac{1}{2}+\\frac{1}{4}+\\frac{1}{8}\\) + ……………. n terms =
\nA) 3
\nB) 2
\nC) \\(\\frac{1}{2}\\)
\nD) 1
\nAnswer:
\nB) 2<\/p>\n

Question 106.
\n1 + 2 + 22<\/sup> + 23<\/sup> + …………. n terms =
\nA) 2n<\/sup> – 1
\nB) 1
\nC) 2n – 1<\/sup> – 1
\nD) 2
\nAnswer:
\nA) 2n<\/sup> – 1<\/p>\n

Question 107.
\nIf 5th<\/sup> term of a G.P is 32 and common ratio 2, then the sum of 14 terms is
\nA) 64,432
\nB) 16,383
\nC) 32,766
\nD) 8,194
\nAnswer:
\nC) 32,766<\/p>\n

Question 108.
\nThe value of 0.234 is
\nA) \\(\\frac{232}{990}\\)
\nB) \\(\\frac{234}{1000}\\)
\nC) \\(\\frac{232}{1000}\\)
\nD) \\(\\frac{234}{990}\\)
\nAnswer:
\nA) \\(\\frac{232}{990}\\)<\/p>\n

Question 109.
\nThe common ratio of the series 3 – 6 + 12 – 24 + 48 ……………. is
\nA) \\(\\frac{1}{2}\\)
\nB) -2
\nC) -3
\nD) 3
\nAnswer:
\nB) -2<\/p>\n

Question 110.
\nIf x, 2x + 2, 3x + 3 are in G.P. then 4th<\/sup> term is
\nA) -27
\nB) 13.5
\nC) 27
\nD) -13.5
\nAnswer:
\nD) -13.5<\/p>\n

\"AP<\/p>\n

Question 111.
\nThe 12th term of a G.P. whose first term is \\(\\frac{1}{8}\\) and second term is \\(\\frac{1}{2}\\) is
\nA) 411<\/sup>
\nB) 2 \u00d7 411<\/sup>
\nC) 2 \u00d7 49<\/sup>
\nD) 2 \u00d7 410<\/sup>
\nAnswer:
\nC) 2 \u00d7 49<\/sup><\/p>\n

Question 112.
\nThe sum to n – terms of the series (1 – x) + (2 + x2<\/sup>) + (3 – x3<\/sup>) + ……………
\nA) \\(\\frac{n(n+1)}{2}+\\frac{x\\left(1-x^{n}\\right)}{1-x}\\)
\nB) \\(\\frac{2}{n(n+1)}-\\frac{1-x}{x\\left(1-x^{n}\\right)}\\)
\nC) \\(\\frac{n(n-1)}{2}-\\frac{x\\left(1-x^{n}\\right)}{1-x}\\)
\nD) \\(\\frac{n(n+1)}{2}-\\frac{x\\left(1-x^{n}\\right)}{1-x}\\)
\nAnswer:
\nD) \\(\\frac{n(n+1)}{2}-\\frac{x\\left(1-x^{n}\\right)}{1-x}\\)<\/p>\n

Question 113.
\nThe seventh term in the sequence 1, \\(\\frac{-1}{2}, \\frac{1}{4}\\), ………………..
\nA) \\(\\frac{1}{64}\\)
\nB) \\(\\frac{-1}{8}\\)
\nC) \\(\\frac{1}{16}\\)
\nD) \\(\\frac{-1}{32}\\)
\nAnswer:
\nA) \\(\\frac{1}{64}\\)<\/p>\n

Question 114.
\nIf x, 2x + 2, 3x + 3, are in G.P. then the fourth term is ……………….
\nA) -13.5
\nB) -27
\nC) 27
\nD) 13.5
\nAnswer:
\nA) -13.5<\/p>\n

Question 115.
\nThe common ratio of G.P.
\n1 – \\(\\frac{1}{3}+\\frac{1}{9}-\\frac{1}{27}\\) + ……………. is
\nA) -3
\nB) \\(\\frac{-1}{3}\\)
\nC) 3
\nD) \\(\\frac{1}{3}\\)
\nAnswer:
\nB) \\(\\frac{-1}{3}\\)<\/p>\n

Question 116.
\n1 + (0.04) + (0.04)2<\/sup> + ………………. \u221e =
\nA) \\(\\frac{24}{25}\\)
\nB) 1
\nC) 0.04
\nD) \\(\\frac{25}{24}\\)
\nAnswer:
\nD) \\(\\frac{25}{24}\\)<\/p>\n

Question 117.
\nIf |x| < 1,y = x – x2<\/sup> + x2<\/sup> – x? + ……………… \u221e,then the value of x in terms of y is
\nA) \\(\\frac{1-y}{y}\\)
\nB) \\(\\frac{y}{1-y}\\)
\nC) \\(\\frac{y}{y+1}\\)
\nD) \\(\\frac{\\mathrm{y}}{\\mathrm{y}-1}\\)
\nAnswer:
\nB) \\(\\frac{y}{1-y}\\)<\/p>\n

\"AP<\/p>\n

Question 118.
\nCoefficient of x2<\/sup> in (x + 1) (x + 2) (x + 3) (x + 4) (x + 5) is ………………..
\nA) 20
\nB) 6
\nC) 15
\nD) 12
\nAnswer:
\nD) 12<\/p>\n

Question 119.
\n\\(\\frac{1}{2}+\\frac{1}{4}+\\frac{1}{8}+\\frac{1}{16}\\) + ……………… = x,
\n\\(\\frac{1}{3}+\\frac{1}{9}+\\frac{1}{21}+\\frac{1}{81}\\) + y, then
\nA) x2<\/sup> = y
\nB) 2x + 4y = 4
\nC) x = y
\nD) x + y = 0
\nAnswer:
\nB) 2x + 4y = 4<\/p>\n

Question 120.
\nThe sum to infinity of \\(\\frac{1}{7}+\\frac{2}{7^{2}}+\\frac{1}{7^{3}}+\\frac{2}{7^{4}}\\) + ……………. is
\nA) \\(\\frac{5}{48}\\)
\nB) \\(\\frac{7}{24}\\)
\nC) \\(\\frac{3}{16}\\)
\nD) \\(\\frac{1}{5}\\)
\nAnswer:
\nC) \\(\\frac{3}{16}\\)<\/p>\n

Question 121.
\nThe least value of n so that 1 + 3+ 32<\/sup> + 33<\/sup> + ………….. n terms is greater than 2000 is …………….
\nA) 8
\nB) 7
\nC) 9
\nD) 6
\nAnswer:
\nA) 8<\/p>\n

Question 122.
\nThe greatest value of n so that 1 + 5 + 52<\/sup> + 53<\/sup> + …………. n terms is less than 4321 is ………………..
\nA) 7
\nB) 6
\nC) 9
\nD) 8
\nAnswer:
\nB) 6<\/p>\n

Question 123.
\n7 + 77 + 777 + ………………….. n terms =
\nA) \\(\\frac{7\\left(10^{\\mathrm{n}}-1\\right)}{81}-\\frac{7 \\mathrm{n}}{9}\\)
\nB) 7(10n<\/sup> – 1) – \\(\\frac{7 \\mathrm{n}}{9}\\)
\nC) \\(\\frac{70\\left(10^{\\mathrm{n}}-1\\right)}{81}-\\frac{7 \\mathrm{n}}{9}\\)
\nD) 70 (10n<\/sup> – 1) – \\(\\frac{7 \\mathrm{n}}{9}\\)
\nAnswer:
\nC) \\(\\frac{70\\left(10^{\\mathrm{n}}-1\\right)}{81}-\\frac{7 \\mathrm{n}}{9}\\)<\/p>\n

Question 124.
\nThe sum to n terms of the series 0.5 + 0.55 + 0.555 + …………………… is
\nA) \\(\\frac{5 n}{9}-\\frac{5}{81}\\left(1-\\frac{1}{10^{n}}\\right)\\)
\nB) \\(\\frac{5 n}{9}+\\frac{5}{81}\\left(1+\\frac{1}{10^{n}}\\right)\\)
\nC) \\(\\frac{5 n}{9}-\\frac{5}{81}\\left(\\frac{1}{10^{n}}-1\\right)\\)
\nD) \\(\\frac{5 n}{9}+\\frac{5}{81}\\left(1-\\frac{1}{10^{n}}\\right)\\)
\nAnswer:
\nA) \\(\\frac{5 n}{9}-\\frac{5}{81}\\left(1-\\frac{1}{10^{n}}\\right)\\)<\/p>\n

Question 125.
\nIf the sum of the three numbers in a G.P is 26 and the sum of products taken two at a time is 156, then the numbers are
\nA) 1, 4, 16
\nB) 2, 6, 18
\nC) 1, 5, 25
\nD) 1, 8, 64
\nAnswer:
\nB) 2, 6, 18<\/p>\n

\"AP<\/p>\n

Question 126.
\nIf the sum of three numbers in G.P is \\(\\frac{7}{64}\\) and the product of the extremes is \\(\\frac{21}{1024}\\) then the numbers are
\nA) \\(\\frac{1}{81}, \\frac{1}{16}, \\frac{1}{32}\\)
\nB) 16, 32, 64
\nC) \\(\\frac{1}{64}, \\frac{1}{32}, \\frac{1}{16}\\)
\nD) \\(\\frac{1}{16}, \\frac{1}{64}, \\frac{1}{32}\\)
\nAnswer:
\nC) \\(\\frac{1}{64}, \\frac{1}{32}, \\frac{1}{16}\\)<\/p>\n

Question 127.
\nIf pth<\/sup>,qth<\/sup>,rth<\/sup> terms of a G.Pare a, b, c then \u03a3(q – r) log a =
\nA) 0
\nB) 1
\nC) abc
\nD) pqr
\nAnswer:
\nA) 0<\/p>\n

Question 128.
\nIf there are 3 geometric means between 4 and 64 then the common ratio is
\nA) 12
\nB) 15
\nC) 4
\nD) 16
\nAnswer:
\nC) 4<\/p>\n

Question 129.
\nGeometric mean of 6 and 24 is
\nA) 13
\nB) 30
\nC) 12
\nD) 15
\nAnswer:
\nC) 12<\/p>\n

Question 130.
\nOne of the 5 geometric means 1 between \\(\\frac {1}{3}\\) and 243 is
\nA) 81
\nB) 80
\nC) 79
\nD) 82
\nAnswer:
\nA) 81<\/p>\n

Question 131.
\nIf the A.M and G.M of two numbers are 13 and 12 respectively then the two numbers are
\nA) 10, 18
\nB) 12, 18
\nC) 8, 18
\nD) 8, 12
\nAnswer:
\nC) 8, 18<\/p>\n

Question 132.
\nIf the arithmetic mean of two numbers is 10 and geometric mean is 6, then the numbers are
\nA) 1, 19
\nB) 2, 18
\nC) 3, 17
\nD) 3, 18
\nAnswer:
\nB) 2, 18<\/p>\n

Question 133.
\nWhich of the following series is an arithmetic progression ?
\nA) 2, 4, 6, 8,
\nB) 1, 2, 4, 8,
\nC) 4, 9, 16, 25,
\nD) 3, 9, 12, 18,
\nAnswer:
\nD) 3, 9, 12, 18,<\/p>\n

\"AP<\/p>\n

Question 134.
\nWhich term of the A.P. 5, 2, -1, ……………….. is -22 ?
\nA) 11
\nB) 8
\nC) 9
\nD) 10
\nAnswer:
\nD) 10<\/p>\n

Question 135.
\nWhich term of 7 + 11 +15 + ………………. is 67?
\nA) 20
\nB) 6
\nC) 16
\nD) 10
\nAnswer:
\nB) 6<\/p>\n

Question 136.
\nWhich series is equal to \\(\\frac{n(n+1)}{2}\\) ?
\nA) 13<\/sup> + 23<\/sup> + 33<\/sup> + + n3<\/sup>
\nB) 1.2 + 2.3 + 3.4 + + n(n + 1)
\nC) 1 + 2 + 3+ ……+ n
\nD) 12<\/sup> + 22<\/sup> + 32<\/sup> + ……………… + n2<\/sup>
\nAnswer:
\nC) 1 + 2 + 3+ ……+ n<\/p>\n

Question 137.
\nWhich term of 0.0004 + 0.02 + 0.1 + ……………… is 12 ?
\nA) 7
\nB) 5
\nC) 8
\nD) 6
\nAnswer:
\nD) 6<\/p>\n

Question 138.
\nWhich term of 2 – \\(\\frac{1}{\\sqrt{2}}+\\frac{1}{4}\\) – \\(\\frac{1}{32}\\) ……………… is ?
\nA) 8
\nB) 7
\nC) 5
\nD) 6
\nAnswer:
\nC) 5<\/p>\n

Question 139.
\nnth<\/sup> term of 4 + 9 + 14 + …………….. is
\nA) 5n +1
\nB) 4n – 1
\nC) 5n – 1
\nD) 4n + 1
\nAnswer:
\nC) 5n – 1<\/p>\n

Question 140.
\nIf x, y, z are in A.P, then 2y =
\nA) \\(\\sqrt{\\mathrm{XZ}}\\)
\nB) xz
\nC) x + z
\nD) x – z
\nAnswer:
\nC) x + z<\/p>\n

\"AP<\/p>\n

Question 141.
\nThe ratio of the sums of m arithmatic means and n arithmetic means between two numbers is
\nA) n : m
\nB) 2m – 1 : 2n – 1
\nC) m : n
\nD) 2m + 1, 2n + 1
\nAnswer:
\nC) m : n<\/p>\n

Question 142.
\nIf the ratio of sum of n terms in two A.P is 2n : n + 1, then the ratio of 8th terms is …………….
\nA) 8 : 13
\nB) 15 : 8
\nC) 5 : 17
\nD) 8 : 17
\nAnswer:
\nB) 15 : 8<\/p>\n

Question 143.
\nArithmetic mean of a and b is
\nA) \\(\\sqrt{a b}\\)
\nB) \\(\\frac{2}{a+b}\\)
\nC) \\(\\frac{a+b}{2}\\)
\nD) a + b
\nAnswer:
\nC) \\(\\frac{a+b}{2}\\)<\/p>\n

Question 144.
\nIf S1<\/sub>, S2<\/sub>, S3<\/sub> are the sums of first n natural numbers, their squares and their cubes respectively, then S3<\/sub>(1 + 8S1<\/sub>) =
\nA) 9S2<\/sub>2<\/sup>
\nB) S2<\/sub>2<\/sup>
\nC) 9S2<\/sub>
\nD) 9S2<\/sup>
\nAnswer:
\nA) 9S2<\/sub>2<\/sup><\/p>\n

Question 145.
\nIf a, b, c are in G.P., then
\nA) c = ab
\nB) a = bc
\nC) b2<\/sup> = ac
\nD) b = ac
\nAnswer:
\nC) b2<\/sup> = ac<\/p>\n

Question 146.
\nThe series (n – 1), (n – 2), (n – 3), ……………… is a type of
\nA) A.P
\nB) G.P
\nC) May be both
\nD) None
\nAnswer:
\nA) A.P<\/p>\n

Question 147.
\nIf nth<\/sup> term of a series is 3n<\/sup>, then the sum of n terms =
\nA) 3(3n – 1<\/sup> – 1)
\nB) \\(\\frac{3\\left(3^{n-1}-1\\right)}{2}\\)
\nC) 3(3n<\/sup> – 1)
\nD) \\(\\frac{3\\left(3^{n}-1\\right)}{2}\\)
\nAnswer:
\nD) \\(\\frac{3\\left(3^{n}-1\\right)}{2}\\)<\/p>\n

\"AP<\/p>\n

Question 148.
\nIf nth<\/sup> term of series is 2n<\/sup> + n, then sum of n terms =
\nA) \\(\\frac{2\\left(2^{\\mathrm{n}}-1\\right)+\\mathrm{n}(\\mathrm{n}+1)}{2}\\)
\nB) n(2n<\/sup> – 1) + n(n + 1)
\nC) \\(\\frac{2\\left(2^{n}-1\\right)}{2}+\\frac{n(n+1)}{2}\\)
\nD) n(2n<\/sup> + 1) + n(n – 1)
\nAnswer:
\nA) \\(\\frac{2\\left(2^{\\mathrm{n}}-1\\right)+\\mathrm{n}(\\mathrm{n}+1)}{2}\\)<\/p>\n

Question 149.
\nnth<\/sup> term of -3 + 6 – 12 + 24 – 48 + …………… is
\nA) 2.3n – 1<\/sup>
\nB) 3.2n + 1<\/sup>
\nC) (-1)n – 1<\/sup>. 3.2n – 1<\/sup>
\nD) (-1)n<\/sup>. 3.2n – 1<\/sup>
\nAnswer:
\nC) (-1)n – 1<\/sup>. 3.2n – 1<\/sup><\/p>\n

Question 150.
\nIf a, b, c are in geometric progression then \\(\\frac{a}{b}\\) =
\nA) [late]\\frac{c}{b}[\/latex]
\nB) \\(\\frac{b}{c}\\)
\nC) \\(\\frac{\\mathrm{b}}{\\mathrm{a}}\\)
\nD) \\(\\frac{\\mathrm{a}}{\\mathrm{c}}\\)
\nAnswer:
\nB) \\(\\frac{b}{c}\\)<\/p>\n

Question 151.
\n\\(\\frac{x}{2}+\\frac{x}{4}+\\frac{x}{8}\\) + ……………….. \u221e =
\nA) 2x
\nB) \\(\\frac{x}{2}\\)
\nC) x
\nD) \\(\\frac{2 x}{2}\\)
\nAnswer:
\nC) x<\/p>\n

Question 152.
\nIf g1<\/sub>, g2<\/sub>, g3<\/sub> are three geometric means between two positive numbers a, b then g1<\/sub>g3<\/sub> =
\nA) g2<\/sub>
\nB) g2<\/sub>2<\/sup>
\nC) 2g2<\/sub>
\nD) 2g2<\/sub>2<\/sup>
\nAnswer:
\nB) g2<\/sub>2<\/sup><\/p>\n

Question 153.
\nIf g1<\/sub>, g2<\/sub>, g3<\/sub> are geometric means between m, n then
\nA) mn = g3<\/sub>2<\/sup>
\nB) mn = g1<\/sub>. g2<\/sub>
\nC) mn = g2<\/sub>2<\/sup>
\nD) mn = g1<\/sub>2<\/sup>
\nAnswer:
\nC) mn = g2<\/sub>2<\/sup><\/p>\n

Question 154.
\nAn employee got Rs. 200 per month in his 11th year service and got \u20b9495 per month in his 24th year service. If his monthly salary is in A.P., then what is his initial salary ? What is his incriment ?
\nA) \u20b9150, \u20b9 20
\nB) \u20b9 200, \u20b9 10
\nC) \u20b9 300,\u20b9 10
\nD) \u20b9 150,\u20b9 15
\nAnswer:
\nD) \u20b9 150,\u20b9 15<\/p>\n

\"AP<\/p>\n

Question 155.
\nIf n arithmetic means are inserted between a and b, then the common difference is ……………….
\nA) \\(\\frac{a+b}{n+1}\\)
\nB) \\(\\frac{n+1}{b+a}\\)
\nC) \\(\\frac{n+1}{b-a}\\)
\nD) \\(\\frac{b-a}{n+1}\\)
\nAnswer:
\nD) \\(\\frac{b-a}{n+1}\\)<\/p>\n

Question 156.
\nSum of the terms 1, 2, 3, 4, ………….. n is
\nA) \\(\\frac{\\mathrm{n}(\\mathrm{n}+1)^{2}}{2}\\)
\nB) \\(\\frac{n^{2}(n+1)}{2}\\)
\nC) \\(\\frac{n(n+1)}{2}\\)
\nD) \\(\\frac{\\mathrm{n}(\\mathrm{n}-1)}{2}\\)
\nAnswer:
\nC) \\(\\frac{n(n+1)}{2}\\)<\/p>\n

Question 157.
\nSum to n terms of 12<\/sup> + 32<\/sup> + 52<\/sup> + …………….. is
\nA) \\(\\frac{n\\left(n^{2}-4\\right)}{6}\\)
\nB) \\(\\frac{\\mathrm{n}(4 n-1)}{6}\\)
\nC) \\(\\frac{n\\left(n^{2}-4\\right)}{3}\\)
\nD) \\(\\frac{n\\left(4 n^{2}-1\\right)}{3}\\)
\nAnswer:
\nD) \\(\\frac{n\\left(4 n^{2}-1\\right)}{3}\\)<\/p>\n

Question 158.
\n12<\/sup> + 1 + 22<\/sup> + 2 + 32<\/sup> + 3 + 42<\/sup> + 4 + …………………… + n2<\/sup> + n =
\nA) \\(\\frac{n(n+1)(n+2)}{3}\\)
\nB) \\(\\frac{n(n+1)}{2}\\)
\nC) \\(\\frac{n(n+1)(n+2)(n+3)}{4}\\)
\nD) \\(\\left[\\frac{n(n+1)}{2}\\right]^{2}\\)
\nAnswer:
\nA) \\(\\frac{n(n+1)(n+2)}{3}\\)<\/p>\n

Question 159.
\n1, 4, 9, 16, ………………. sum to ‘n’ terms =
\nA) \\(\\frac{n^{2}(n+1)^{2}}{4}\\)
\nB) \\(\\frac{n(n+1)(2 n+1)}{6}\\)
\nC) \\(\\frac{(\\mathrm{n}+1)(2 \\mathrm{n}+1)}{3}\\)
\nD) \\(\\frac{\\mathrm{n}(\\mathrm{n}+1)}{2}\\)
\nAnswer:
\nB) \\(\\frac{n(n+1)(2 n+1)}{6}\\)<\/p>\n

Question 160.
\nSum to ‘n’ terms of 23<\/sup> + 43<\/sup> + 63<\/sup> + ……………. is
\nA) 4n2<\/sup> (n + 1)2<\/sup>
\nB) 4n2<\/sup>(n – 1)2<\/sup>
\nC) 2n2<\/sup>(n + 1)2<\/sup>
\nD) n2<\/sup> (n + 1)2<\/sup>
\nAnswer:
\nC) 2n2<\/sup>(n + 1)2<\/sup><\/p>\n

\"AP<\/p>\n

Question 161.
\nSum to n terms of 1.2 + 2.3 + 3.4 + …………….. is
\nA) \\(\\frac{n(n-1)(n+2)}{3}\\)
\nB) \\(\\frac{n(n+1)(n+2)}{3}\\)
\nC) \\(\\frac{n(n+1)(n+2)}{2}\\)
\nD) \\(\\frac{n(n-1)(n+2)}{6}\\)
\nAnswer:
\nB) \\(\\frac{n(n+1)(n+2)}{3}\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

Practice the AP 10th Class Maths Bits with Answers Chapter 6 Progressions on a regular basis so that you can attempt exams with utmost confidence. AP State Syllabus 10th Class Maths Bits 6th Lesson Progressions with Answers Question 1. Which term of the G.P. …………………… is A) 5th B) 6th C) 7th D) 8th Answer: …<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[12],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/17110"}],"collection":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/comments?post=17110"}],"version-history":[{"count":0,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/17110\/revisions"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=17110"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=17110"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=17110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}