TS 10th Class Maths Bits Chapter 6 Progressions

Solving these TS 10th Class Maths Bits with Answers Chapter 6 Progressions Bits for 10th Class will help students to build their problem-solving skills.

Progressions Bits for 10th Class

Question 1.
How many terms of A.P – 6, \(\frac{-11}{2}\), -5, …………… are needed to obtain a sum – 25 ?
A) 10 or 15
B) 15 or 18
C) 5 or 20
D) 8 or 12
Answer:
C) 5 or 20

Question 2.
The sum of natural numbers from 1 to 100 is
A) 4050
B) 10100
C) 55
D) 5050
Answer:
D) 5050

Question 3.
The sum of first 50 even numbers is
A) 1250
B) 2550
C) 1275
D) 2275
Answer:
B) 2550

Question 4.
The sum of first 20 odd numbers is
A) 400
B) 210
C) 420
D) 05
Answer:
A) 400

Question 5.
If x – 1, x + 3, 3x – 1 are in A.P, then x is equal
A) 5
B) 8
C) 420
D) 405
Answer:
D) 405

Question 6.
The numbers -15, -11, -7, -3, …………… is
A) A.P. with d = 4
B) A.P. with d = – 4
C) A.P. with d = 8
D) G.P.
Answer:
A) A.P. with d = 4

Question 7.
The next term of the A.P. \(\sqrt{48}\), \(\sqrt{75}\), \(\sqrt{147}\), ………………. is
A) \(\sqrt{27}\)
B) \(\sqrt{197}\)
C) \(\sqrt{192}\)
D) \(\sqrt{243}\)
Answer:
C) \(\sqrt{192}\)

Question 8.
Which term of the A.P. 24, 21, 18, ……………… is the first negative ?
A) a₁₀
B) a₉
C) a₆
D) a₁₁
Answer:
A) a₁₀

Question 9.
Which term of the A.P. 125, 120, 115, …. is the first negative ?
A) 25^th
B) 26^th
C) 24^th
D) 27^th
Answer:
D) 27^th

Question 10.
Which term of the A.P. 100, 90, 80, …………….. is zero ?
A) 10^th
B) 9^th
C) 11^th
D) 12^th
Answer:
C) 11^th

Question 11.
(a + 3d), (a + d), (a – d), …… the next term of the A.P. is
A) a + 2d
B) a – 2d
C) a – 4d
D) a – 3d
Answer:
D) a – 3d

Question 12.
The sum of 15 terms of the A.P. 4, 7, 10, …………….. is
A) 385
B) 475
C) 375
D) 325
Answer:
C) 375

Question 13.
If a₇ – a₃ = 32, then the common difference of the A.P. is
A) 8
B) 6
C) 4
D) 6
Answer:
A) 8

Question 14.
a₂₈ – a₂₃ = 15, then the common difference of the A.P. is
A) 3
B) 5
C) 7
D) 15
Answer:
A) 3

Question 15.
If a, b, c are in A.P. then b = ………………
A) a + c
B) \(\frac{a+c}{2}\)
C) a – c
D) \(\frac{a-c}{2}\)
Answer:
B) \(\frac{a+c}{2}\)

Question 16.
The 17^th term of 1.1, 2.2, 3.3, 4.4, ………….. is
A) 18.7
B) 19.8
C) 17.6
D) 17.17
Answer:
A) 18.7

Question 17.
The 25^th term of – 300, – 290, – 280, …. is
A) – 60
B) – 80
C) 60
D) 80
Answer:
A) – 60

Question 18.
How many numbers are divisible by 4 lying between 101 and 250 ?
A) 40
B) 62
C) 38
D) 37
Answer:
D) 37

Question 19.
The common ratio of the G.P. 3, 6, 12, 24, ……………. is
A) 3
B) 2
C) \(\frac{1}{2}\)
D) \(\frac{1}{3}\)
Answer:
B) 2

Question 20.
The common ratio of the G.P. 192, 36, 9, ……………. is
A) 4
B) 2
C) 6
D) \(\frac{1}{4}\)
Answer:
D) \(\frac{1}{4}\)

Question 21.
The 103^rd term of 1, -1, 1, -1, ……….. is
A) 1
B) -1
C) 0
D) -2
Answer:
B) -1

Question 22.
Which term of the G.P. 2,6,18, 54, is 2 × 3¹⁰ ?
A) 10^th
B) 11^th
C) 12^th
D) 9^th
Answer:
B) 11^th

Question 23.
If a₇ + a₄ of a G.P. is 343, then the common ratio is
A) 11
B) 9
C) 3
D) 7
Answer:
D) 7

Question 24.
If a, b, c are in G.P, then b = …….
A) ac
B) \(\frac{a+c}{2}\)
C) a²c²
D) \(\sqrt{\mathrm{ac}}\)
Answer:
D) \(\sqrt{\mathrm{ac}}\)

Question 25.
If 4, x, 9 are in G.P, then x = …………..
A) 7
B) 6
C) 8
D) 5
Answer:
B) 6

Question 26.
If 3, x, 11 are in A.P, then x = …………..
A) \(\sqrt{21}\)
B) 14
C) 4
D) 7
Answer:
D) 7

Question 27.
If x, xy, xy², xy³, …….. forms a G.P, then its 15^th term is
A) xy¹⁵
B) xy¹⁴
C) x¹⁴y
D) x¹⁵y
Answer:
B) xy¹⁴

Question 28.
If a = 3 and a₇ = 33, then a₁₁ is
A) 55
B) 53
C) 73
D) 63
Answer:
B) 53

Question 29.
-20, -18, -16, …… which term of this A.P. is a first positive term ?
A) 10
B) 11
C) 12
D) 9
Answer:
C) 12

Question 30.
1, -1, 1, -1, 1, -1, …………. up to 131 terms, then S₁₃₁ = ………….
A) 1
B) -1
C) 131
D) 130
Answer:
A) 1

Question 31.
The 10^th term of the AP 3, 11, 19, ……….. is
A) 73
B) 16
C) 75
D) 85
Answer:
C) 75

Question 32.
…………. term of AP 21, 18, 15, ………. is – 81.
A) 35
B) 16
C) 30
D) none
Answer:
A) 35

Question 33.
The 8^th term from the end of the AP 7,10, 13, ……….. 1814 is
A) 324
B) 181
C) 163
D) 161
Answer:
C) 163

Question 34.
The n^th term of a, a + d, a + 2d, ………… is
A) a + (n – 1)d
B) a – (n + 1)d
C) a² – (n – 1)d
D) d + (n – 1)a
Answer:
A) a + (n – 1)d

Question 35.
In the AP, first term is 4 and common difference is -1 then AP is …………
A) 9, 3,-6, ….
B) 10, 12, 14,
C) 5,8,16,….
D) 4, 3, 2, ……
Answer:
D) 4, 3, 2, ……

Question 36.
The AP with first term is 8 and common difference 2 1/2 is …………
A) 8, 10 1/2, 13
B) 8, 10, 11 1/2
C) 16, 15 1/2, 10 1/2
D) none
Answer:
A) 8, 10 1/2, 13

Question 37.
In the AP -9, -14, -19, -24 ……. a₃₀ – a₂₀ = ……….
A) 80
B) -60
C) 50
D) -50
Answer:
D) -50

Question 38.
The next term of the AP 51, 59, 67, 75 is …………….
A) 12
B) 16
C) 83
D) 38
Answer:
C) 83

Question 39.
Number of terms of the AP – 5 + (- 8) + (-11) + ………. +(-230) is …………
A) 66
B) 76
C) 86
D) none
Answer:
B) 76

Question 40.
15^th term of the AP x – 7, x – 2, x + 3, ………… is
A) x + 63
B) x – 6
C) x – 63
D) x + 16
Answer:
A) x + 63

Question 41.
The common ratio of the GP 4, 20, 100, 500, …. is …….
A) 8
B) 2
C) 5
D) 9
Answer:
C) 5

Question 42.
The 16^th term of 4, -4, 4, -4, ………… is ………….
A) 16
B) 8
C) 4
D) -4
Answer:
D) -4

Question 43.
A.P 1, -1, -3, -5, ……. d = …………
A) -2
B) 1
C) 2
D) 10
Answer:
A) -2

Question 44.
In the A.P -11, -9, -7, ….. d = ……….
A) 4
B) 3
C) -2
D) 2
Answer:
D) 2

Question 45.
In the A.P 100, 103, 106, … d = ……..
A) 4
B) 8
C) 6
D) none
Answer:
D) none

Question 46.
A G.P with r = – 2 is …………
A) 5, – 10, 20, -40, …..
B) 2, 4, 8, 16
C) 3, -6, 10, 16
D) all
Answer:
A) 5, – 10, 20, -40, …..

Question 47.
A G.P with r = 2 is ………..
A) 7, 14, 28, …..
B) 8, 16, 10 ……
C) 12, 24, 19, …
D) none
Answer:
A) 7, 14, 28, …..

Question 48.
5, 10, 15, ….. 10^th term is ……
A) 20
B) 90
C) 60
D) 50
Answer:
D) 50

Question 49.
8, 16, 32, …. 6^th term is …….
A) 256
B) 156
C) 108
D) none
Answer:
A) 256

Question 50.
-1, 1, -1, … 11^th term is ………
A) 1
B) -1
C) 10
D) 9
Answer:
B) -1

Question 51.
– 8, -6, -4, …… a₇ = ……….
A) 1
B) 12
C) 10
D) 6
Answer:
D) 6

Question 52.
1, 2, 3, ………. sum to 10 terms is ….
A) 55
B) 65
C) 60
D) 90
Answer:
A) 55

Question 53.
If a, b, c are in GP then b² = ………..
A) \(\frac{\mathrm{c}}{\mathrm{a}}\)
B) \(\frac{\mathrm{a}}{\mathrm{c}}\)
C) \(\sqrt{\mathrm{ac}}\)
D) ac
Answer:
D) ac

Question 54.
In a GP a₆ = ………..
A) ar⁵
B) a⁵r
C) a⁵r⁵
D) all
Answer:
A) ar⁵

Question 55.
Which term of G.P 2, 8, 32, … is 512 ?
A) 16
B) 5
C) 9
D) 10
Answer:
B) 5

Question 56.
\(\frac{1}{3}\), \(\frac{1}{9}\), \(\frac{1}{27}\), …… a₇ = …….
A) \(\frac{1}{1827}\)
B) \(\frac{1}{2187}\)
C) \(\frac{1}{8127}\)
D) none
Answer:
B) \(\frac{1}{2187}\)

Question 57.
3, \(\frac{3}{2}\), \(\frac{3}{4}\), ….. r = …………
A) 1
B) 2
C) -1
D) none
Answer:
D) none

Question 58.
If 2, x, 6 are in GP then x = ……..
A) 2\(\sqrt{3}\)
B) 8\(\sqrt{3}\)
C) 2\(\sqrt{2}\)
D) \(\sqrt{3}\)
Answer:
A) 2\(\sqrt{3}\)

Question 59.
4, 16, ☐, 256 then ☐ = …………
A) 161
B) 64
C) 62
D) 68
Answer:
B) 64

Question 60.
1 + 2+ 3 + ……. + n = ……..
A) \(\frac{\mathrm{n}(\mathrm{n}+1)}{2}\)
B) \(\frac{\mathrm{n}(\mathrm{n}-1)}{2}\)
C) \(\frac{\mathrm{n}^2+1}{2}\)
D) none
Answer:
A) \(\frac{\mathrm{n}(\mathrm{n}+1)}{2}\)

Question 61.
1² + 2² + 3² + ……. + n² = ……….
A) \(\frac{\mathrm{n}^2(\mathrm{n}-1)^2}{2}\)
B) \(\frac{\mathrm{n}(2 \mathrm{n}+1)}{4}\)
C) \(\frac{\mathrm{n}(\mathrm{n}+1)(2 \mathrm{n}+1)}{6}\)
D) \(\frac{(\mathrm{n}+1)^2}{2}\)
Answer:
C) \(\frac{\mathrm{n}(\mathrm{n}+1)(2 \mathrm{n}+1)}{6}\)

Question 62.
In an AP 7a₇ = 11a₁₁ then a₁₈ = ……..
A) -1
B) 0
C) 1
D) 7
Answer:
B) 0

Question 63.
AM of 24 and 16 is …….
A) 22
B) 19
C) 16
D) 20
Answer:
D) 20

Question 64.
If a, b, c are in AP then 2b = ………..
A) a + c
B) a – c
C) \(\frac{\mathrm{a+c}}{2}\)
D) \(\frac{\mathrm{a}}{2}\)
Answer:
C) \(\frac{\mathrm{a+c}}{2}\)

Question 65.
The sum of first 40 positive integers divisible by 6 is ……………
A) 9420
B) 4920
C) 9920
D) 1290
Answer:
B) 4920

Question 66.
a_n = 9 – 5n, a₄ = …………
A) 30
B) 10
C) 11
D) -11
Answer:
D) -11

Question 67.
In a GP, a₈ = 192, r = 2 then a₁₂ = ………….
A) 3072
B) 7032
C) 1032
D) 1100
Answer:
A) 3072

Question 68.
2, – 6,18, – 54, …. r = ………..
A) -3
B) 3
C) 1
D) – 2
Answer:
A) -3

Question 69.
\(\frac{5}{2}\), \(\frac{5}{4}\), \(\frac{5}{8}\), ……. a_n = ………….
A) \(\frac{5}{2^{\mathrm{n}-1}}\)
B) \(\frac{5}{2^{\mathrm{n}}}\)
C) \(\frac{5}{2^{\mathrm{n}-2}}\)
D) none
Answer:
B) \(\frac{5}{2^{\mathrm{n}}}\)

Question 70.
\(\frac{1}{\sqrt{2}}\), -2, \(\frac{8}{\sqrt{2}}\), ……….. a₅ = …………
A) 16 \(\sqrt{2}\)
B) 32 \(\sqrt{2}\)
C) 6 \(\sqrt{2}\)
D) 31 \(\sqrt{2}\)
Answer:
B) 32 \(\sqrt{2}\)

Question 71.
3, -3², 3³, …. a₆ = ………
A) -729
B) 729
C) 829
D) 114
Answer:
A) -729

Question 72.
In a G.P, a = 81, r = –\(\frac{1}{3}\), a₃ = …………..
A) -9
B) 9
C) -3
D) none
Answer:
B) 9

Question 73.
In a G.P 25, -5, 1, –\(\frac{1}{5}\), ……. r = ………….
A) \(\frac{-3}{5}\)
B) 2
C) -1
D) \(\frac{-1}{5}\)
Answer:
D) \(\frac{-1}{5}\)

Question 74.
S_n in AP = …………..
A) \(\frac{\mathrm{n}}{2}\) [a + l]
B) \(\frac{\mathrm{n}}{3}\) [a + l]
C) 2n[a + l]
D) none
Answer:
A) \(\frac{\mathrm{n}}{2}\) [a + l]

Question 75.
In AP a₁₂ = 37, d = 3, then a = ………..
A) 8
B) – 4
C) -3
D) 4
Answer:
D) 4

Question 76.
In the above problem S₁₂ = ………….
A) 246
B) 146
C) 123
D) 112
Answer:
A) 246

Question 77.
-1, \(\frac{1}{4}\), \(\frac{3}{2}\), ….. Sum to 10 terms = ……..
A) 26.5
B) 16.25
C) 36.25
D) 46.25
Answer:
D) 46.25

Question 78.
-5 + (-8) + (-11) + ….. + (-230) = …..
A) -8930
B) 8930
C) 8390
D) none
Answer:
A) -8930

Question 79.
The sum of first 1000 positive integers is ………..
A) 500500
B) 50051
C) 8005
D) none
Answer:
A) 500500

Question 80.
16 + 11 + 6 + ……. 23 terms = ……….
A) 119
B) -987
C) 891
D) -897
Answer:
D) -897

Question 81.
Identify the 3-digit number that divisible by
A) 126
B) 128
C) 122
D) none
Answer:
B) 128

Question 82.
In an A.P a₁ = – 4, a₆ = 6 then a₂ = ………….
A) 3
B) 6
C) 1
D) -2
Answer:
D) -2

Question 83.
In the above problem a₅ = …………….
A) 4
B) -3
C) 6
D) -4
Answer:
A) 4

Question 84.
In the formula a_n = 3.6, a = -18.9, d = 2.5, n = ……………
A) 13
B) 12
C) 10
D) 20
Answer:
C) 10

Question 85.
5, 1, -3, -7, …….. a₁₀ = ………..
A) -23
B) 22
C) 31
D) -31
Answer:
D) -31

Question 86.
\(\frac{1}{4}\), \(\frac{-1}{4}\), \(\frac{-3}{4}\), \(\frac{-5}{4}\), …… d = …………
A) \(\frac{-1}{2}\)
B) \(\frac{1}{2}\)
C) 2
D) -1
Answer:
A) \(\frac{-1}{2}\)

Question 87.
If 4, x, 16 are in G.P then x = …………..
A) 12
B) 16
C) 8
D) None
Answer:
C) 8

Question 88.
1³ + 2³ + 3³ + ……….. + n³ = ………….
A) \(\frac{\mathrm{n}}{2}\)
B) \(\frac{(\mathrm{n}+1)^2}{2}\)
C) \(\frac{\mathrm{n}(\mathrm{n}+1)}{2}\)
D) \(\frac{\mathrm{n}^2(\mathrm{n}+1)^2}{4}\)
Answer:
D) \(\frac{\mathrm{n}^2(\mathrm{n}+1)^2}{4}\)

Question 89.
G.M of a and b is ……
A) \(\sqrt{a b}\)
B) \(\frac{a b}{2}\)
C) \(\frac{a+b}{2}\)
D) none
Answer:
A) \(\sqrt{a b}\)

Question 90.
G.M of a and \(\frac{1}{a}\) is ……
A) -3
B) 1
C) 7
D) 8
Answer:
B) 1

Question 91.
Reciprocals of term of GP is ………..
A) AP
B) GP
C) HP
D) none
Answer:
B) GP

Question 92.
If a, b, c are in GP then \(\frac{\mathrm{b}}{\mathrm{a}}\) = ……………
A) \(\frac{\mathrm{c}}{\mathrm{b}}\)
B) \(\frac{\mathrm{b}}{\mathrm{c}}\)
C) \(\frac{1}{\mathrm{b}}\)
D) none
Answer:
A) \(\frac{\mathrm{c}}{\mathrm{b}}\)

Question 93.
a_n in GP = …………
A) ar
B) ar^n-1
C) a^n-1
D) \(\frac{\mathrm{a}}{2}\)r^n-1
Answer:
B) ar^n-1

Question 94.
1 + 1+ 1 + ………. + n terms = …………
A) \(\frac{\mathrm{n}}{2}\)
B) n
C) n – 1
D) none
Answer:
B) n

Question 95.
If a, b, c are in GP then b is called …….
A) Geometric mean
B) Arithmetic mean
C) Number
D) None
Answer:
A) Geometric mean

Question 96.
Σ n = 10, Σ n³ = ………….
A) 100
B) 1001
C) 200
D) 80
Answer:
A) 100

Question 97.
In a series a_n = \(\frac{\mathrm{n}(\mathrm{n}+1)}{3}\), a₂ = …….
A) 41
B) 3
C) 4
D) 2
Answer:
D) 2

Question 98.
AM of 10 and 20 is ……..
A) 12
B) 15
C) 25
D) 10
Answer:
B) 15

Question 99.
a_n = (n – 1) (n – 2) then a₂ = ………….
A) 1
B) 0
C) 2
D) 3
Answer:
B) 0

Question 100.
If a, b, c are in AP then b – a = …………..
A) c + b
B) a + b
C) c – b
D) none
Answer:
C) c – b

Question 101.
If \(\frac{-2}{7}\), x, \(\frac{-7}{2}\) are 3 consecutive terms of a GP then x = ………….
A) ± 1
B) ± 2
C) ± 3
D) ± 4
Answer:
A) ± 1

Question 102.
GM of 5 and 125 is ……………
A) 13
B) 16
C) 10
D) 25
Answer:
D) 25

Question 103.
S_n in AP = …………..
A) \(\frac{\mathrm{n}}{2}\) [2a + (n – 1)d]
B) \(\frac{\mathrm{n}}{2}\) [a + (n + 1)d]
C) n[2a + (n – 1)d]
D) none
Answer:
A) \(\frac{\mathrm{n}}{2}\) [2a + (n – 1)d]

Question 104.
a_n = \(\frac{n}{n+2}\); a₃ = ……………
A) \(\frac{1}{2}\)
B) \(\frac{5}{3}\)
C) \(\frac{3}{5}\)
D) none
Answer:
C) \(\frac{3}{5}\)

Question 105.
The n^th term of a GP is 2(0.5)^n-1, r = ………..
A) – 2
B) \(\frac{1}{2}\)
C) 2
D) -1
Answer:
B) \(\frac{1}{2}\)

Question 106.
The common ratio of the GP 2, \(\sqrt{8}\), 4,……. is ……….
A) \(\sqrt{3}\)
B) 4
C) 3
D) \(\sqrt{2}\)
Answer:
D) \(\sqrt{2}\)

Question 107.
a, b, c are in AP then 3^a, 3^b, 3^c are in …………
A) GP
B) HP
C) AP
D) none
Answer:
A) GP

Question 108.
2, \(\frac{5}{2}\), 3, ……. S₂₅ = …………..
A) 110
B) 180
C) 100
D) none
Answer:
D) none

Question 109.
AM of M, P, C is ……..
A) \(\frac{\text { MPC }}{3}\)
B) M-P-C
C) \(\frac{\mathrm{M}+\mathrm{P}+\mathrm{C}}{3}\)
D) \(\frac{\mathrm{M}+\mathrm{P}-\mathrm{C}}{3}\)
Answer:
C) \(\frac{\mathrm{M}+\mathrm{P}+\mathrm{C}}{3}\)

Question 110.
a_n = 2ⁿ, a₅ = ……………..
A) 32
B) 23
C) 18
D) 13
Answer:
A) 32

Question 111.
AM of 5 and 95 is …………
A) 105
B) 505
C) 501
D) 50
Answer:
D) 50

Question 112.
GM of x³ and \(\frac{1}{\mathrm{x}^3}\) = ……………
A) -7
B) 1
C) 3
D) none
Answer:
B) 1

Question 113.
n – 1, n – 2, n – 3, ……….. a₁₀ = ………….
A) n – 10
B) n – 9
C) n + 9
D) n – 3
Answer:
A) n – 10

Question 114.
Product of n GMs between a and b is ………..
A) (ab)^n/2
B) (ab)ⁿ
C) \(\frac{\mathrm{a}}{\mathrm{b}}\)
D) \(\frac{\mathrm{a}^n}{\mathrm{b}}\)
Answer:
A) (ab)^n/2

Question 115.
If \(\frac{a^{n+1}+b^{n+1}}{a^n+b^n}\) is the AM of a and b then n = ………..
A) \(\frac{-1}{2}\)
B) 1
C) 0
D) 4
Answer:
C) 0

Question 116.
7, 10, 13, ……, a₅ = …………….
A) 19
B) 100
C) 131
D) 12
Answer:
A) 19

Question 117.
22, 32, 42, ………., a₇ = …………
A) 81
B) 92
C) 69
D) 82
Answer:
D) 82

Question 118.
1, 4, 7, 10, ………., d = ………..
A) 13
B) 3
C) 4
D) none
Answer:
B) 3

Question 119.
In AP a_p = q, a_q = p then a_p+q = ………….
A) q – p
B) p – q
C) 0
D) – 1
Answer:
C) 0

Question 120.
Which term of AP 7 + 4 + 1 + ……… is – 56 ?
A) 22
B) 20
C) 18
D) 19
Answer:
A) 22

Question 121.
1 + 6 + 4 + 9 + 7 + 12 + ………….. to 40 terms.
A) 20
B) 60
C) 90
D) none
Answer:
D) none

Question 122.
AM of x² + y² and x² – y² is ……….
A) \(\frac{x^2}{2}\)
B) x²
C) x
D) 2x
Answer:
B) x²

Question 123.
\(\frac{\mathrm{b}+\mathrm{c}-\mathrm{a}}{\mathrm{a}}, \frac{\mathrm{c}+\mathrm{a}-\mathrm{b}}{\mathrm{b}}, \frac{\mathrm{a}+\mathrm{b}-\mathrm{c}}{\mathrm{c}}\) are in AP then \(\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\) are in ……………
A) HP
B) GP
C) AP
D) None
Answer:
C) AP

Question 124.
If there are n AM’s between a and b then d = ……………

Answer:
(A)

Question 125.
10, 100, 1000, ….., r = ……………
A) 12
B) 9
C) 8
D) 10
Answer:
D) 10

Question 126.
1 + \(\frac{1}{2}\) + \(\frac{1}{2^2}\) + …………., r = ………………
A) 3
B) \(\frac{1}{2}\)
C) 2
D) -1
Answer:
B) \(\frac{1}{2}\)

Question 127.
3, 6, 12, r = …………..
A) 1
B) 10
C) 3
D) none
Answer:
D) none

Question 128.
a, a², a³, …………., r = ………….
A) a
B) a²
C) a³
D) none
Answer:
A) a

Question 129.
a, b, c are in A.P then \(\frac{1}{\mathrm{a}}, \frac{1}{\mathrm{~b}}, \frac{1}{\mathrm{c}}\) are in ……………..
A) GP
B) AP
C) HP
D) none
Answer:
C) HP

Question 130.
GM of x, y, z is …………..
A) xyz³
B) \(\sqrt[3]{x y z}\)
C) \(\frac{x y z}{3}\)
D) \(\frac{x+y+z}{3}\)
Answer:
B) \(\sqrt[3]{x y z}\)

Question 131.
The n^th term of a GP = a_n = ar^{n – 1} here ‘r’ meters ……..
A) common difference
B) common ratio
C) first term
D) radius
Answer:
B) common ratio

Question 132.
The ‘n’ th term of an A.P. is a_n = 3 + 2n then the common difference is …………….. (A.P. Mar. ’15)
A) 2
B) 3
C) 4
D) 5
Answer:
A) 2

Question 133.
The common difference of the AP x – y, x, x + y is …………… (A.P. Mar. ’15)
A) x
B) y
C) -x
D) -y
Answer:
B) y

Question 134.
The common difference in the AP 2a – b, 4a – 3b, 6a – 5b is ………….. (A.P. June ’15)
A) 2a – 2b
B) a – b
C) 2a-b
D) 4a – 3b
Answer:
A) 2a – 2b

Question 135.
In a GP a₁ = 20 and a₄ = 540 then r = …………. (A.P. June ’15)
A) 27
B) 3
C) 520
D) 18
Answer:
B) 3

Question 136.
Formula for sum of ‘n’ terms in an A.P. = ………….. (A.P. June ’15)
A) Σ_n = \(\frac{\mathrm{n}(\mathrm{n}+1)}{2}\)
B) Σ_n² = \(\frac{\mathrm{n}^2(\mathrm{n}+1)(\mathrm{n}+2)}{6}\)
C) S_n = \(\frac{\mathrm{n}}{2}\)[2a + (n – 1)d] or S_n = \(\frac{\mathrm{n}}{2}\)[a + l]
D) a_n = a + (n – 1) d
Answer:
C) S_n = \(\frac{\mathrm{n}}{2}\)[2a + (n – 1)d] or S_n = \(\frac{\mathrm{n}}{2}\)[a + l]

Question 137.
In an A.P. the 3^rd term = 5 and 7^th term = 9 then the common difference = ………….. (T.S. Mar. ’15)
A) 1
B) 2
C) 3
D) 4
Answer:
A) 1

Question 138.
The term ‘r’ refers to …. in the formula of ‘n’ ^th term of a GP a_n = ar^{n – 1}. (T.S. Mar. ’16)
A) n^th term
B) number of terms
C) common ratio
D) first term
Answer:
C) common ratio

Question 139.
Which of the following is a GP with a common ration “r”. (T.S. Mar. ’16)
A) \(\sqrt{2}\), \(\sqrt{6}\), \(\sqrt{18}\)
B) \(\sqrt{3}\), \(\sqrt{6}\), \(\sqrt{12}\)
C) \(\sqrt{5}\), \(\sqrt{15}\), \(\sqrt{45}\)
D) \(\sqrt{7}\), \(\sqrt{21}\), \(\sqrt{63}\)
Answer:
B) \(\sqrt{3}\), \(\sqrt{6}\), \(\sqrt{12}\)

Question 140.
Which term of the G.P.3, 9, 22, …………. is 243?
A) 7
B) 8
C) 6
D) 5
Answer:
D) 5

Question 141.
The series (n – 1), (n – 2), (n – 3), ……….. is a type of
A) AP
B) GP
C) may be both
D) none
Answer:
A) AP

Question 142.
If log a, log b, log c are in A.P. then a, b, c are
A) A.P.
B) G.P.
C) Both A.P. and G.P.
D) neither A.P. nor G.P.
Answer:
B) G.P.