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. $$\frac{1}{3}, \frac{1}{9}, \frac{1}{27},$$ …………………… is $$\frac{1}{2187}$$
A) 5th
B) 6th
C) 7th
D) 8th
C) 7th

Question 2.
The 21st term of an A.P., whose first two terms are -3 and 4 is …………………
A) 143
B) -143
C) 137
D) 17
C) 137 Question 3.
The common difference of an A.P. for which a18 – a14 = 32 is ……………..
A) 8
B) -8
C) -4
D) 4
A) 8

Question 4.
In an A.P., if a = 1, an = 20 and Sn = 399, then n = ………………
A) 19
B) 42
C) 28
D) 38
D) 38

Question 5.
Which term of G.P. 3, 3√3,9, …………….. equals to 243?
A) 6
B) 7
C) 8
D) 9
B) 7

Question 6.
If x, x + 2, x + 6 are three consecutive terms in G.P, find the value of ‘x’.
A) 3
C) 2
B) 4
D) 1
D) 1

Question 7.
If an = $$\frac{n(n+3)}{n+2}$$ , then find a17 = ………………….
A) $$\frac{340}{20}$$
B) $$\frac{341}{19}$$
C) $$\frac{340}{19}$$
D) $$\frac{341}{20}$$
C) $$\frac{340}{19}$$

Question 8.
A famous book written by ancient mathematician Aryabhatta is …………………
A) Arya Tharkam
B) Aryabhatteeyam
C) Siddhantha Siromani
D) Karana Kuthuhalam
B) Aryabhatteeyam

Question 9.
The sum of first 100 natural numbers is ………………….
A) 4050
B) 4500
C) 5500
D) 5050
D) 5050 Question 10.
If a, b, c are in G.P., then b = ……………….
A) ac
B) $$\sqrt{\mathrm{ac}}$$
C) $$\frac{a+c}{2}$$
D) a2c2
B) $$\sqrt{\mathrm{ac}}$$

Question 11.
Which term of the A.P -18, -16, -14, …………………. is first positive term ?
A) t9
B) t10
C) t11
D) t12
C) t11

Question 12.
If 16, x, 36 are in G.P. then x =
A) 24
B) 26
C) 28
D) 30
A) 24

Question 13.
The next term of the A.P(a + 3d),(a + d). (a – d), ………………….. is
A) a + 2d
B) a – 2d
C) a – 4d
D) a – 3d
D) a – 3d

Question 14.
In an A.P the nth term an is ………………….
A) an = a + (n – 1)d
B) d + (n – 1)a
C) a + d
D) $$\frac{(n-1)}{d}$$ + a
A) an = a + (n – 1)d

Question 15.
In a G.P. the 3rd term is 24 and 6th term is 192 then 10th term is …………………….
A) 2062
B) 3072
C) 4072
D) 1072
B) 3072

Question 16.
In a G.P. aP + Q = m,a P – Q = n then
aP= …………………..
A) mn
B) $$\sqrt{m n}$$
C) $$\frac{\mathrm{mn}}{2}$$
D) $$\frac{\mathrm{m}}{2}$$
B) $$\sqrt{m n}$$ Question 17.
If an = $$\frac{n(n+1)(2 n+1)}{6}$$ then a6 = ……………….
A) ±1
B) n(n + 1)
C) 55
D) 91
D) 91

Question 18.
If the sum of first ‘n’ terms of an A.P. 2, 5, 8, ………………… is equal to the sum of first n
terms of the A.P. 57, 59, 61, …………………… then ‘n’ is equal to …………………..
A) 110
C) 112
B) 111
D) 113
B) 111

Question 19.
If p, q, r are in A.P. and x, y, z in G.P., then Xq – r × Yr – p × Zp – q is equal to …………………..
A) p + q + r
B) x × y × z
C) 1
D) px + qy + rz
C) 1

Question 20.
In an A.P., pth term is q and qth term is p, then its common difference is ………………….
A) 1
B) -1
C) 2
D) -2
B) -1

Question 21.
The next term of √2, √8, √18, √32, …………………. is …………………..
A) $$\sqrt{34}$$
B) $$\sqrt{38}$$
C) $$\sqrt{42}$$
D) $$\sqrt{50}$$
D) $$\sqrt{50}$$

Question 22.
The common difference of an AP in which a25 – a12 = -52 is ………………….
A) 4
B) -4
C) -3
D) 3
B) -4

Question 23.
What will be the value of x if 8x + 4 , 6x – 2 and 2x + 7 are in arithmetic progression?
A) $$\frac{-15}{2}$$
B) $$\frac{15}{2}$$
C) 15
D) -15
B) $$\frac{15}{2}$$ Question 24.
The nth 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
A) 12
B) 13
C) 14
D) 15
A) 12

Question 25.
If the first and fifth term’s sum is 10, then the third term of an arithmetic progression is………………
A) 3
B) 1
C) 5
D) 2
C) 5

Question 26.
If the 10th term of the sequence $$\sqrt{3}, \sqrt{12}, \sqrt{27}$$ ……………..is $$\sqrt{3 n^{2}}$$ then the value of $$\frac{\mathbf{n}}{2}$$ is ………………..
A) 3
B) √3
C) 5
D) √5
C) 5

Question 27.
If the product of five numbers in GP is 1024, then the middle number is
A) 8
B) 4
C) 2
D) None
B) 4

Question 28.
If the second term of a GP is 2 and the sum of infinite terms is 8, then the first term is
A) 8
B) 6
C) 4
D) 3
B) 6

Question 29.
If a, b and c are in AP and also in GP, then
A) a = b ≠ c
B) a ≠ b = c
C) a ≠ b ≠ c
D) a = b = c
A) a = b ≠ c

Question 30.
The least value of n for which 1 + 2 + 22 + ……………….. (n terms) is greater than 1000 is
A) 7
B) 8
C) 9
D) 10
D) 10 Question 31.
The number of numbers between 100 and 1000 which are divisible by 7 is
A) 7
B) 128
C) 132
D) None
B) 128

Question 32.
Which is the three digit number divisible by 7 ?
A) 100
B) 133
C) 137
D) 143
B) 133

Question 33.
The 6th term in the GP 2, 8, 32, ……………….. is
A) 512
B) 128
C) 2048
D) 256
C) 2048

Question 34.
1 + 1 + 1 + ………….. n terms =
A) $$\frac{\mathrm{n}}{2}$$
B) $$\frac{\mathrm{n}-1}{2}$$
C) n
D) $$\frac{n+1}{2}$$
C) n

Question 35.
1 + 3 + 6 + 10 + …………………. n terms =
A) $$\frac{n(n+1)(n+2)}{4}$$
B) $$\frac{n(n+1)(n+2)}{8}$$
C) $$\frac{n(n+1)(n+2)}{6}$$
D) None
C) $$\frac{n(n+1)(n+2)}{6}$$

Question 36.
How many two-digit numbers are divisible by 6 ?
A) 12
B) 15
C) 10
D) 17
B) 15

Question 37.
If the 2nd term of an AP is 4 and the 6th term is 16, then its 11th term is
A) 29
B) 33
C) 34
D) 31
A) 29 Question 38.
Which term of the AP 24, 21, 18,……………. is the first negative ?
A) 10th
B) 8th
C) 7th
D) 6th
C) 7th

Question 39.
If a = 2 and d = 2, then S15 =
A) 220
B) 230
C) 240
D) 245
C) 240

Question 40.
The nth term of a Geometric Progression is an = arn – 1, where ‘ r ‘ represents
A) Common difference
B) Common ratio
C) First term
B) Common ratio

Question 41.
If the nth term of an A.P. is an = 3 + 2n, then the common difference d is ……………………
A) 2
B) 3
C) 4
D) 5
A) 2

Question 42.
The common difference of the AP, x – y, x, x + y,………… is ……………….
A) x
B) y
C) – x
D) -y
B) y

Question 43.
Common difference of an Arithmetic Progression, whose 3rd term is 5 and 7th term is 9, is
A) 1
B) 2
C) 3
D) 4
A) 1

Question 44.
If (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 ?
A) (i) only
B) (ii) only
C) (i) and (ii) both
D) None of them
B) (ii) only Question 45.
If nth term of a series is $$\frac{3 n-4}{7}$$, then 6th term =
A) $$\frac{15}{7}$$
B) 1
C) 2
D) $$\frac{18}{7}$$
C) 2

Question 46.
If nth term of a series is  then 7th term =
A) $$\frac{73}{90}$$
B) $$\frac{5}{9}$$
C) $$\frac{49}{9}$$
D) $$\frac{7}{9}$$
B) $$\frac{5}{9}$$

Question 47.
Which of the following is an A.P ?
A) 1 + 8 +27 + ……………….
B) 1 + 4 + 9 + ……………….
C) 1 – 2 + 3 – 4 + …………….
D) 1 + 2 + 3 + ……………
D) 1 + 2 + 3 + ……………

Question 48.
10th term of 4 + 6 + 8 + ………….. is
A) 26
B) 18
C) 22
D) 20
C) 22

Question 49.
27th term of 5, 14, 23, ……………… is
A) 900
B) 101
C) 100
D) 239
D) 239

Question 50.
12th term of the series 5, 14, 23, ……………. is
A) 900
B) 104
C) 239
D) 100
B) 104 Question 51.
18th term of 13, 8, 3, -2, ……………….. is
A) -32
B) -72
C) 32
D) -57
B) -72

Question 52.
Common difference of x + $$\frac{4 x}{3}+\frac{5 x}{3}$$ + 2x + ……………… is
A) $$\frac{x}{3}$$
B) $$\frac{1}{3}$$
C) x
D) $$\frac{2 x}{3}$$
A) $$\frac{x}{3}$$

Question 53.
The common difference of the A.P 13, 8, 3, -2, …………… is
A) 10
B) 4
C) 5
D) -5
D) -5

Question 54.
If a = -1, d = -3 in an A.P, then 12th term is
A) 17
B) -23
C) -34
D) -17
C) -34

Question 55.
If the first term of an A.P is -2 and common difference is -5, then 12th term is
A) -32
B) 32
C) -57
D) 34
C) -57

Question 56.
If nth term of an A.P is $$\frac{5 n-4}{7}$$ then common difference is
A) $$\frac{-4}{7}$$
B) $$\frac{5}{7}$$
C) $$\frac{1}{7}$$
D) $$\frac{3}{7}$$
B) $$\frac{5}{7}$$

Question 57.
In an A.P if 8th term is 23 and 102nd term is 305, then common difference is
A) 5
B) 2
C) 1
D) 3
D) 3 Question 58.
In an A.P. if first term is 4,9th term is 20, then 15th term is
A) 32
B) 36
C) 16
D) 18
A) 32

Question 59.
In an A.P if third term is 7 and seventh term is 15, then first term is
A) 2
B) 0
C) 5
D) 3
D) 3

Question 60.
In an A.P, if 16th term is 47 and 31st term is 92, then 27th term is
A) 86
B) 120
C) 80
D) 116
C) 80

Question 61.
In an A.P, if 7 times of 7th term is equal to 11 times of 11th term, then 18th term is
A) 7
B) 0
C) 11
D) 18
B) 0

Question 62.
If 3rd term of an A.P is 11 and 15th term is 59, then 24th term is
A) 89
B) 95
C) 109
D) 79
B) 95

Question 63.
If 10th term of an A.P is 0 and 42nd term is -32, then nth term is ………………
A) 10 – n
B) 8 – n
C) 11 – n
D) 9 – n
A) 10 – n

Question 64.
Sum of 20 terms of 3 + 5 + 7 + 9 + ………………. is
A) 440
B) 220
C) 410
D) 460
A) 440 Question 65.
How many terms are to be added to make the sum 52 in the series (-8) + (-6) + (-4) + ……………… ?
A) 31
B) 13
C) 3
D) 12
B) 13

Question 66.
In an A.P. if common difference is 2, sum of n terms is 49,7th term is 13, then n = ………………
A) 7
B) 0
C) 13
D) 5
A) 7

Question 67.
If the nth term of an A.P, is 2n + 5, its first term is
A) 0
B) 7
C) 2
D) 4
B) 7

Question 68.
How many numbers are divisible by 9 in between 1 and 1000 ?
A) 100
B) 101
C) 110
D) 111
B) 101

Question 69.
The number of odd numbers between 1,100 that are divisible by 5 is
A) 15
B) 5
C) 10
D) 11
C) 10

Question 70.
If 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
A) 7, 10,11
B) 7, 9, 11
C) 6, 9, 12
D) 8, 9, 10
B) 7, 9, 11

Question 71.
If 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
A) 3, 6, 9
B) 3, 5, 7
C) 2, 5, 8
D) 2, 6, 7
B) 3, 5, 7 Question 72.
If the sum of four numbers in A.P is 24 and the sum of their squares 164, then those numbers are
A) 3, 5, 7, 9
B) 3, 4, 5, 6
Q 1, 4, 7,11
D) 2, 4, 6,12
A) 3, 5, 7, 9

Question 73.
If the sum of the series 24, 20, 16, …………… is 60, then the number of terms is
A) 13
B) 25
C) 3
D) 25
C) 3

Question 74.
72 + 70 + 68 + ……………. + 40=
A) 952
B) 1852
C) 1052
D) 1252
A) 952

Question 75.
If d = 2 and 8th term of an A.P is 15, then the sum of 15 terms is ………………
A) $$\frac{225}{2}$$
B) 0
C) 15
D) 225
D) 225

Question 76.
If the sum of n terms of an A.P is 4n2 + 5n, then common difference is
A) 8
B) 0
C) 4
D) 6
A) 8

Question 77.
If 5th term of a G.P is 32 and common ratio 2, then the sum of 14 terms is
A) 32, 766
B) 16, 388
C) 64, 432
D) 30,746
A) 32, 766 Question 78.
The sum of even numbers between 100, 200 is
A) 7650
B) 6750
C) 5670
D) 7350
D) 7350

Question 79.
Arithmetic mean of $$\frac{1}{2}$$ and $$\frac{1}{3}$$ is
A) $$\frac{12}{5}$$
B) $$\frac{6}{5}$$
C) $$\frac{5}{12}$$
D) $$\frac{5}{6}$$
C) $$\frac{5}{12}$$

Question 80.
One of the four A.M’s between 3, 23 is ………………..
A) 15
B) 6
C) 21
D) 8
A) 15

Question 81.
The product of two numbers is 91 and their arithmetic mean is 10 then the two numbers are
A) 14,6
B) 13, 7
C) 10, 10
D) 12, 8
B) 13, 7

Question 82.
Sum of 10 arithmetic means between 3, 10 is
A) 65
B) 130
C) 0
D) 60
A) 65

Question 83.
Sum of 4 arithmetic means between 3 and 23 is
A) 69
B) 48
C) 52
D) 50
C) 52

Question 84.
Sum of first 100 odd numbers is
A) 10,000
B) 100
C) 1000
D) 1,00,000
A) 10,000 Question 85.
12 + 22 + 32 + +1002 = ……………….
A) (5050)2
B) 42925
C) 5050
D) 5500
D) 5500

Question 86.
Sum to ‘n’ terms of 1, 8, 27, 64, ……………
A) $$\frac{n^{2}(n+1)}{4}$$
B) $$\frac{n^{2}(n+1)^{2}}{4}$$
C) $$\frac{n(n+1)}{2}$$
D) $$\frac{n(n+1)(2 n+1)}{6}$$
B) $$\frac{n^{2}(n+1)^{2}}{4}$$

Question 87.
Sum to ‘n’ terms of 3.5 + 4.7 + 5.9 + …………………
A) $$\frac{n(n+1)(n-3)}{12}$$
B) $$\frac{n\left(4 n^{2}+27 n+59\right)}{6}$$
C) $$\frac{n\left(25 n^{2}+65 n+2\right)}{12}$$
D) $$\frac{n\left(25 n^{2}+65 n+2\right)}{6}$$
B) $$\frac{n\left(4 n^{2}+27 n+59\right)}{6}$$

Question 88.
(1) + (1 + 3) + (1 + 3 + 5) + to ‘n’ terms = ……………….
A) $$\frac{n(n-1)(2 n-1)}{24}$$
B) $$\frac{n(n+1)(2 n-1)}{12}$$
C) $$\frac{n(n+1)(2 n+1)}{6}$$
D) $$\frac{n(n+1)(2 n+1)}{24}$$
C) $$\frac{n(n+1)(2 n+1)}{6}$$

Question 89.
Which of the following geometric pro-gressions has the common ratio as 2?
A) $$\sqrt{2}, \sqrt{6}, \sqrt{18}$$ , ……………….
B) $$\sqrt{3}, \sqrt{6}, \sqrt{12}$$ , ……………….
C) $$\sqrt{5}, \sqrt{15}, \sqrt{45}$$ , ……………….
D) $$\sqrt{7}, \sqrt{21}, \sqrt{63}$$ , ……………….
B) $$\sqrt{3}, \sqrt{6}, \sqrt{12}$$ , ……………….

Question 90.
$$\frac{1^{2}}{3}+\frac{1^{2}+2^{2}}{5}+\frac{1^{2}+2^{2}+3^{2}}{7}$$ + ………… n terms =
A) $$\frac{n(n+1)(n+2)}{12}$$
B) $$\frac{n(n+1)(n+2)}{24}$$
C) $$\frac{n(n+1)(n+2)}{6}$$
D) $$\frac{n(n+1)(n+2)}{18}$$
D) $$\frac{n(n+1)(n+2)}{18}$$ Question 91.
Sum of first n terms of 1.4 + 4.7 + 7.10 + 10.13 + ……………… is
A) Σn2 – 4Σn + n
B) 9Σn2 – 3Σn – 2n
C) Σn2 – 3Σn + 4
D) 9Σn2 – 3Σn – 2
B) 9Σn2 – 3Σn – 2n

Question 92.
The nth term of the series 1.3 + 3.5 + 5.7 + …………….. is
A) 1 – 4n
B) n2 + 4
C) 4n2 – 1
D) 4n2 + 1
C) 4n2 – 1

Question 93.
nth $$\frac{5}{1.2}+\frac{7}{2.3} \cdot \frac{1}{3}+\frac{9}{3.4} \cdot \frac{1}{3^{2}}$$ + $$\frac{11}{4.5} \cdot \frac{1}{3^{3}}$$ term of the series
A) $$\frac{2 n+4}{n(n+1)} \cdot \frac{1}{3^{n}}$$
B) $$\frac{2 n+3}{n(n+1)} \cdot \frac{1}{3^{n+1}}$$
C) $$\frac{2 n+3}{n(n+1)} \cdot \frac{1}{3^{n}}$$
D) $$\frac{2 n+3}{n(n+1)} \cdot \frac{1}{3^{n-1}}$$
D) $$\frac{2 n+3}{n(n+1)} \cdot \frac{1}{3^{n-1}}$$

Question 94.
Sum to n terms of 1.2.3 + 2.3.4 + 3.4.5 + ……………… is .
A) $$\frac{n(n+1)(n+2)(n+3)}{6}$$
B) $$\frac{n(n+1)(n+2)}{2}$$
C) $$\frac{n(n+1)(n+2)(n+3)}{4}$$
D) $$\frac{n(n+1)(n+2)(n+3)}{8}$$
C) $$\frac{n(n+1)(n+2)(n+3)}{4}$$

Question 95.
$$\frac{1+2+3+\ldots \ldots+n}{1+3+5+\ldots \ldots+(2 n-1)}$$ =
A) $$\frac{(\mathrm{n}+1)}{2 \mathrm{n}}$$
B) $$\frac{2}{\mathrm{n}}$$
C) $$\frac{\mathrm{n}}{2}$$
D) $$\frac{(\mathrm{n}-1)}{2}$$
A) $$\frac{(\mathrm{n}+1)}{2 \mathrm{n}}$$

Question 96.
If 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
A) cot2α
B) cosec2α
C) tan2α
D) sec2α
C) tan2α

Question 97.
Sum of n terms of + ……………. is
A) $$\frac{(2 n+1)}{n}$$
B) $$\frac{n}{(2 n+1)}$$
C) $$\frac{n+1}{n}$$
D) $$\frac{\mathrm{n}}{(\mathrm{n}+1)}$$
D) $$\frac{\mathrm{n}}{(\mathrm{n}+1)}$$ Question 98.
Sum of n terms of 1 + 4 + 13 + 40 + ……………… is
A) $$\frac{\left(3^{n+1}+2 n-3\right)}{4}$$
B) $$\frac{\left(3^{n+1}-2 n-3\right)}{4}$$
C) $$\frac{\left(3^{n+1}-2 n+3\right)}{4}$$
D) $$\frac{\left(3^{n+1}+2 n+3\right)}{4}$$
B) $$\frac{\left(3^{n+1}-2 n-3\right)}{4}$$

Question 99.
Sum of n terms of 2.3 + 3.4 + 4.5 + ………………. is
A) $$\frac{n\left(n^{2}+6 n+11\right)}{3}$$
B) $$\frac{n\left(n^{2}-6 n-11\right)}{3}$$
C) $$\frac{n\left(n^{2}-6 n+11\right)}{3}$$
D) $$\frac{n\left(n^{2}+6 n-11\right)}{3}$$
A) $$\frac{n\left(n^{2}+6 n+11\right)}{3}$$

Question 100.
If 2nd term of a G.P is 24 and 5th term is 81, then first term is
A) 16
B) 20
C) $$\frac{3}{2}$$
D) 3
A) 16

Question 101.
The common ratio of 2 + $$\frac{2}{3}+\frac{2}{9}+\frac{2}{27}$$+ …………….. is
A) $$\frac{1}{2}$$
B) 2
C) 3
D) $$\frac{1}{3}$$
D) $$\frac{1}{3}$$

Question 102.
If the sum of three numbers in G.P is 21 and their product is 216, then the numbers are
A) 5, 7,9
B) 3, 6, 12
C) 2, 4, 8
D) 4, 8, 6
B) 3, 6, 12

Question 103.
If the product of five numbers in G.P is 1024, then the middle number is
A) 2
B) 8
C) 4
D) 16
C) 4

Question 104.
Sum of 20 terms of 3 + 6 + 12 + ……………. is
A) 3(219 – 1)
B) 3(220 – 1)
C) 3(219 -1)/2
D) 
B) 3(220 – 1) Question 105.
1 + $$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}$$ + ……………. n terms =
A) 3
B) 2
C) $$\frac{1}{2}$$
D) 1
B) 2

Question 106.
1 + 2 + 22 + 23 + …………. n terms =
A) 2n – 1
B) 1
C) 2n – 1 – 1
D) 2
A) 2n – 1

Question 107.
If 5th term of a G.P is 32 and common ratio 2, then the sum of 14 terms is
A) 64,432
B) 16,383
C) 32,766
D) 8,194
C) 32,766

Question 108.
The value of 0.234 is
A) $$\frac{232}{990}$$
B) $$\frac{234}{1000}$$
C) $$\frac{232}{1000}$$
D) $$\frac{234}{990}$$
A) $$\frac{232}{990}$$

Question 109.
The common ratio of the series 3 – 6 + 12 – 24 + 48 ……………. is
A) $$\frac{1}{2}$$
B) -2
C) -3
D) 3
B) -2

Question 110.
If x, 2x + 2, 3x + 3 are in G.P. then 4th term is
A) -27
B) 13.5
C) 27
D) -13.5
D) -13.5 Question 111.
The 12th term of a G.P. whose first term is $$\frac{1}{8}$$ and second term is $$\frac{1}{2}$$ is
A) 411
B) 2 × 411
C) 2 × 49
D) 2 × 410
C) 2 × 49

Question 112.
The sum to n – terms of the series (1 – x) + (2 + x2) + (3 – x3) + ……………
A) $$\frac{n(n+1)}{2}+\frac{x\left(1-x^{n}\right)}{1-x}$$
B) $$\frac{2}{n(n+1)}-\frac{1-x}{x\left(1-x^{n}\right)}$$
C) $$\frac{n(n-1)}{2}-\frac{x\left(1-x^{n}\right)}{1-x}$$
D) $$\frac{n(n+1)}{2}-\frac{x\left(1-x^{n}\right)}{1-x}$$
D) $$\frac{n(n+1)}{2}-\frac{x\left(1-x^{n}\right)}{1-x}$$

Question 113.
The seventh term in the sequence 1, $$\frac{-1}{2}, \frac{1}{4}$$, ………………..
A) $$\frac{1}{64}$$
B) $$\frac{-1}{8}$$
C) $$\frac{1}{16}$$
D) $$\frac{-1}{32}$$
A) $$\frac{1}{64}$$

Question 114.
If x, 2x + 2, 3x + 3, are in G.P. then the fourth term is ……………….
A) -13.5
B) -27
C) 27
D) 13.5
A) -13.5

Question 115.
The common ratio of G.P.
1 – $$\frac{1}{3}+\frac{1}{9}-\frac{1}{27}$$ + ……………. is
A) -3
B) $$\frac{-1}{3}$$
C) 3
D) $$\frac{1}{3}$$
B) $$\frac{-1}{3}$$

Question 116.
1 + (0.04) + (0.04)2 + ………………. ∞ =
A) $$\frac{24}{25}$$
B) 1
C) 0.04
D) $$\frac{25}{24}$$
D) $$\frac{25}{24}$$

Question 117.
If |x| < 1,y = x – x2 + x2 – x? + ……………… ∞,then the value of x in terms of y is
A) $$\frac{1-y}{y}$$
B) $$\frac{y}{1-y}$$
C) $$\frac{y}{y+1}$$
D) $$\frac{\mathrm{y}}{\mathrm{y}-1}$$
B) $$\frac{y}{1-y}$$ Question 118.
Coefficient of x2 in (x + 1) (x + 2) (x + 3) (x + 4) (x + 5) is ………………..
A) 20
B) 6
C) 15
D) 12
D) 12

Question 119.
$$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}$$ + ……………… = x,
$$\frac{1}{3}+\frac{1}{9}+\frac{1}{21}+\frac{1}{81}$$ + y, then
A) x2 = y
B) 2x + 4y = 4
C) x = y
D) x + y = 0
B) 2x + 4y = 4

Question 120.
The sum to infinity of $$\frac{1}{7}+\frac{2}{7^{2}}+\frac{1}{7^{3}}+\frac{2}{7^{4}}$$ + ……………. is
A) $$\frac{5}{48}$$
B) $$\frac{7}{24}$$
C) $$\frac{3}{16}$$
D) $$\frac{1}{5}$$
C) $$\frac{3}{16}$$

Question 121.
The least value of n so that 1 + 3+ 32 + 33 + ………….. n terms is greater than 2000 is …………….
A) 8
B) 7
C) 9
D) 6
A) 8

Question 122.
The greatest value of n so that 1 + 5 + 52 + 53 + …………. n terms is less than 4321 is ………………..
A) 7
B) 6
C) 9
D) 8
B) 6

Question 123.
7 + 77 + 777 + ………………….. n terms =
A) $$\frac{7\left(10^{\mathrm{n}}-1\right)}{81}-\frac{7 \mathrm{n}}{9}$$
B) 7(10n – 1) – $$\frac{7 \mathrm{n}}{9}$$
C) $$\frac{70\left(10^{\mathrm{n}}-1\right)}{81}-\frac{7 \mathrm{n}}{9}$$
D) 70 (10n – 1) – $$\frac{7 \mathrm{n}}{9}$$
C) $$\frac{70\left(10^{\mathrm{n}}-1\right)}{81}-\frac{7 \mathrm{n}}{9}$$

Question 124.
The sum to n terms of the series 0.5 + 0.55 + 0.555 + …………………… is
A) $$\frac{5 n}{9}-\frac{5}{81}\left(1-\frac{1}{10^{n}}\right)$$
B) $$\frac{5 n}{9}+\frac{5}{81}\left(1+\frac{1}{10^{n}}\right)$$
C) $$\frac{5 n}{9}-\frac{5}{81}\left(\frac{1}{10^{n}}-1\right)$$
D) $$\frac{5 n}{9}+\frac{5}{81}\left(1-\frac{1}{10^{n}}\right)$$
A) $$\frac{5 n}{9}-\frac{5}{81}\left(1-\frac{1}{10^{n}}\right)$$

Question 125.
If 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
A) 1, 4, 16
B) 2, 6, 18
C) 1, 5, 25
D) 1, 8, 64
B) 2, 6, 18 Question 126.
If 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
A) $$\frac{1}{81}, \frac{1}{16}, \frac{1}{32}$$
B) 16, 32, 64
C) $$\frac{1}{64}, \frac{1}{32}, \frac{1}{16}$$
D) $$\frac{1}{16}, \frac{1}{64}, \frac{1}{32}$$
C) $$\frac{1}{64}, \frac{1}{32}, \frac{1}{16}$$

Question 127.
If pth,qth,rth terms of a G.Pare a, b, c then Σ(q – r) log a =
A) 0
B) 1
C) abc
D) pqr
A) 0

Question 128.
If there are 3 geometric means between 4 and 64 then the common ratio is
A) 12
B) 15
C) 4
D) 16
C) 4

Question 129.
Geometric mean of 6 and 24 is
A) 13
B) 30
C) 12
D) 15
C) 12

Question 130.
One of the 5 geometric means 1 between $$\frac {1}{3}$$ and 243 is
A) 81
B) 80
C) 79
D) 82
A) 81

Question 131.
If the A.M and G.M of two numbers are 13 and 12 respectively then the two numbers are
A) 10, 18
B) 12, 18
C) 8, 18
D) 8, 12
C) 8, 18

Question 132.
If the arithmetic mean of two numbers is 10 and geometric mean is 6, then the numbers are
A) 1, 19
B) 2, 18
C) 3, 17
D) 3, 18
B) 2, 18

Question 133.
Which of the following series is an arithmetic progression ?
A) 2, 4, 6, 8,
B) 1, 2, 4, 8,
C) 4, 9, 16, 25,
D) 3, 9, 12, 18,
D) 3, 9, 12, 18, Question 134.
Which term of the A.P. 5, 2, -1, ……………….. is -22 ?
A) 11
B) 8
C) 9
D) 10
D) 10

Question 135.
Which term of 7 + 11 +15 + ………………. is 67?
A) 20
B) 6
C) 16
D) 10
B) 6

Question 136.
Which series is equal to $$\frac{n(n+1)}{2}$$ ?
A) 13 + 23 + 33 + + n3
B) 1.2 + 2.3 + 3.4 + + n(n + 1)
C) 1 + 2 + 3+ ……+ n
D) 12 + 22 + 32 + ……………… + n2
C) 1 + 2 + 3+ ……+ n

Question 137.
Which term of 0.0004 + 0.02 + 0.1 + ……………… is 12 ?
A) 7
B) 5
C) 8
D) 6
D) 6

Question 138.
Which term of 2 – $$\frac{1}{\sqrt{2}}+\frac{1}{4}$$ – $$\frac{1}{32}$$ ……………… is ?
A) 8
B) 7
C) 5
D) 6
C) 5

Question 139.
nth term of 4 + 9 + 14 + …………….. is
A) 5n +1
B) 4n – 1
C) 5n – 1
D) 4n + 1
C) 5n – 1

Question 140.
If x, y, z are in A.P, then 2y =
A) $$\sqrt{\mathrm{XZ}}$$
B) xz
C) x + z
D) x – z
C) x + z Question 141.
The ratio of the sums of m arithmatic means and n arithmetic means between two numbers is
A) n : m
B) 2m – 1 : 2n – 1
C) m : n
D) 2m + 1, 2n + 1
C) m : n

Question 142.
If the ratio of sum of n terms in two A.P is 2n : n + 1, then the ratio of 8th terms is …………….
A) 8 : 13
B) 15 : 8
C) 5 : 17
D) 8 : 17
B) 15 : 8

Question 143.
Arithmetic mean of a and b is
A) $$\sqrt{a b}$$
B) $$\frac{2}{a+b}$$
C) $$\frac{a+b}{2}$$
D) a + b
C) $$\frac{a+b}{2}$$

Question 144.
If S1, S2, S3 are the sums of first n natural numbers, their squares and their cubes respectively, then S3(1 + 8S1) =
A) 9S22
B) S22
C) 9S2
D) 9S2
A) 9S22

Question 145.
If a, b, c are in G.P., then
A) c = ab
B) a = bc
C) b2 = ac
D) b = ac
C) b2 = ac

Question 146.
The series (n – 1), (n – 2), (n – 3), ……………… is a type of
A) A.P
B) G.P
C) May be both
D) None
A) A.P

Question 147.
If nth term of a series is 3n, then the sum of n terms =
A) 3(3n – 1 – 1)
B) $$\frac{3\left(3^{n-1}-1\right)}{2}$$
C) 3(3n – 1)
D) $$\frac{3\left(3^{n}-1\right)}{2}$$
D) $$\frac{3\left(3^{n}-1\right)}{2}$$ Question 148.
If nth term of series is 2n + n, then sum of n terms =
A) $$\frac{2\left(2^{\mathrm{n}}-1\right)+\mathrm{n}(\mathrm{n}+1)}{2}$$
B) n(2n – 1) + n(n + 1)
C) $$\frac{2\left(2^{n}-1\right)}{2}+\frac{n(n+1)}{2}$$
D) n(2n + 1) + n(n – 1)
A) $$\frac{2\left(2^{\mathrm{n}}-1\right)+\mathrm{n}(\mathrm{n}+1)}{2}$$

Question 149.
nth term of -3 + 6 – 12 + 24 – 48 + …………… is
A) 2.3n – 1
B) 3.2n + 1
C) (-1)n – 1. 3.2n – 1
D) (-1)n. 3.2n – 1
C) (-1)n – 1. 3.2n – 1

Question 150.
If a, b, c are in geometric progression then $$\frac{a}{b}$$ =
A) [late]\frac{c}{b}[/latex]
B) $$\frac{b}{c}$$
C) $$\frac{\mathrm{b}}{\mathrm{a}}$$
D) $$\frac{\mathrm{a}}{\mathrm{c}}$$
B) $$\frac{b}{c}$$

Question 151.
$$\frac{x}{2}+\frac{x}{4}+\frac{x}{8}$$ + ……………….. ∞ =
A) 2x
B) $$\frac{x}{2}$$
C) x
D) $$\frac{2 x}{2}$$
C) x

Question 152.
If g1, g2, g3 are three geometric means between two positive numbers a, b then g1g3 =
A) g2
B) g22
C) 2g2
D) 2g22
B) g22

Question 153.
If g1, g2, g3 are geometric means between m, n then
A) mn = g32
B) mn = g1. g2
C) mn = g22
D) mn = g12
C) mn = g22

Question 154.
An employee got Rs. 200 per month in his 11th year service and got ₹495 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 ?
A) ₹150, ₹ 20
B) ₹ 200, ₹ 10
C) ₹ 300,₹ 10
D) ₹ 150,₹ 15
D) ₹ 150,₹ 15 Question 155.
If n arithmetic means are inserted between a and b, then the common difference is ……………….
A) $$\frac{a+b}{n+1}$$
B) $$\frac{n+1}{b+a}$$
C) $$\frac{n+1}{b-a}$$
D) $$\frac{b-a}{n+1}$$
D) $$\frac{b-a}{n+1}$$

Question 156.
Sum of the terms 1, 2, 3, 4, ………….. n is
A) $$\frac{\mathrm{n}(\mathrm{n}+1)^{2}}{2}$$
B) $$\frac{n^{2}(n+1)}{2}$$
C) $$\frac{n(n+1)}{2}$$
D) $$\frac{\mathrm{n}(\mathrm{n}-1)}{2}$$
C) $$\frac{n(n+1)}{2}$$

Question 157.
Sum to n terms of 12 + 32 + 52 + …………….. is
A) $$\frac{n\left(n^{2}-4\right)}{6}$$
B) $$\frac{\mathrm{n}(4 n-1)}{6}$$
C) $$\frac{n\left(n^{2}-4\right)}{3}$$
D) $$\frac{n\left(4 n^{2}-1\right)}{3}$$
D) $$\frac{n\left(4 n^{2}-1\right)}{3}$$

Question 158.
12 + 1 + 22 + 2 + 32 + 3 + 42 + 4 + …………………… + n2 + n =
A) $$\frac{n(n+1)(n+2)}{3}$$
B) $$\frac{n(n+1)}{2}$$
C) $$\frac{n(n+1)(n+2)(n+3)}{4}$$
D) $$\left[\frac{n(n+1)}{2}\right]^{2}$$
A) $$\frac{n(n+1)(n+2)}{3}$$

Question 159.
1, 4, 9, 16, ………………. sum to ‘n’ terms =
A) $$\frac{n^{2}(n+1)^{2}}{4}$$
B) $$\frac{n(n+1)(2 n+1)}{6}$$
C) $$\frac{(\mathrm{n}+1)(2 \mathrm{n}+1)}{3}$$
D) $$\frac{\mathrm{n}(\mathrm{n}+1)}{2}$$
B) $$\frac{n(n+1)(2 n+1)}{6}$$

Question 160.
Sum to ‘n’ terms of 23 + 43 + 63 + ……………. is
A) 4n2 (n + 1)2
B) 4n2(n – 1)2
C) 2n2(n + 1)2
D) n2 (n + 1)2 A) $$\frac{n(n-1)(n+2)}{3}$$
B) $$\frac{n(n+1)(n+2)}{3}$$
C) $$\frac{n(n+1)(n+2)}{2}$$
D) $$\frac{n(n-1)(n+2)}{6}$$
B) $$\frac{n(n+1)(n+2)}{3}$$