Sequences and Series

ASSIGNMENT

1. The 3rd term of G.P. is 4. The product of its first 5 term is

(a) 43 (b) 44 (c) 45 (d) 46 ANS (c)
2. Let A be the arithmetic mean between two numbers and S be the sum of n
arithmetic means between the same numbers, then
(a) S = nA (b) A = nS (c) A = S (d) S = 2A ANS (a)
3. If n geometric means be inserted between a and b, then the nth geometric
mean will be
𝑛 𝑛−1 𝑛 1
𝑏 𝑛−1 𝑏 𝑛 𝑏 𝑛+1 𝑏 𝑛
(a) 𝑎 ( ) (b) 𝑎 ( ) (c) 𝑎 ( ) (d) 𝑎( ) ANS (c)
𝑎 𝑎 𝑎 𝑎
1 1
4. If a, b and c are in G.P. , then + is
𝑎2 − 𝑏2 𝑏2
1 1 1 1
(a) (b) (c) (d) ANS (b)
𝑐 2 − 𝑏2 𝑏2 − 𝑐 2 𝑐 2 − 𝑎2 𝑏2 − 𝑎2
5. If the 10th term of a G.P. is 9 and 4th term is 4, then its 7th term is
27 56
(a) 6 (b) 14 (c) (d) ANS (a)
14 15
6. If the arithmetic and geometric means of two numbers are 10 and 8
respectively, then one number exceeds the other number by
(a) 8 (b) 10 (c) 12 (d) 16 Ans(c)
7. If A be one A.M. and p, q be two GMʼs between two numbers, then 2A is
equal to
𝑝3 + 𝑞 3 𝑝3 − 𝑞 3 𝑝2 + 𝑞 2 𝑝𝑞
(a) (b) (c) (d) ANS (a)
𝑝𝑞 𝑝𝑞 2 2
8. Geometric mean of 4 and 9 is
(a) 36 (b) 6 (c) 5 (d) 13 ANS (b)
9. If in a G.P. , a3 + a5 = 90 and r = 2 then its first term will be
5 9
(a) 6 (b) (c) (d) 4 ANS (c)
2 2
5
10. The sum of first 8 terms of the G.P. 10, 5, , ……… is
2
1 1
(a) 20 (1 − ) (c) 10 (1 − )
28 28
1 1
(b) 20 (1 + ) (d) (1 − ) ANS (a)
28 28
 ASSERTION - REASON TYPE QUESTIONS
Directions : Each of these questions contains two statements, Assertion
and Reason. Each of these questions also has four alternative choices, only
one of which is the correct answer. You have to select one of the codes (a),
(b), (c) and (d) given below.
(a) Assertion is correct, reason is correct; reason is a correct explanation
for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct
explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.
2 7
11. Assertion: For x = ±1, the numbers − , x, − are in G.P.
7 2
Reason: Three numbers a, b, c are in G.P. if b2 = ac. ANS (a)
12. Assertion: The arithmetic mean (A.M.) between two numbers is 34 and
their geometric mean is 16. The numbers are 4 and 64.
𝑎+𝑏
Reason: For two numbers a and b, A.M. = A = , G.M. = G = √𝑎𝑏
2
ANS (a)
2 2 2 2 2 2
13. If a, b, c, d are in G.P. prove that a – b , b – c , c – d are also in G.P.
14. If the pth and qth terms of a G.P. are q and p respectively, show that its
1
𝑞 𝑝 𝑝−𝑞
(p + q)th term is ( 𝑞 ) .
𝑝
15. The third term of the G.P. is 4. Find the product of its first five terms.
ANS 45
𝑏
16. If b = a + a2 + a3 + …….., prove that a = .
𝑎+𝑏
17. The sum of an infinite G.P. is 8, its second term is 2, find the first term.
ANS 4
1/3 1/9 1/27
18. Find the value of 9 x 9 x 9 x ……… ANS 3
16
19. Evaluate : ∑10
𝑛=2 4
𝑛
ANS (49 − 1)
3
20. Which term of the G.P. 5, 10, 20, 40, …… is 5120? ANS 11