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Assignment 1 Sequence Series Mathongo

SEQUENCE SERIES

Q1 Consider an infinite geometric series with first term a and common ratio r. If its sum is 4
and the second term is ¾ then find a and r
(a) a = 4/7, r = 3/7 (b) a = 2, r = 3/8
(c) a = 3/2, r = 1/2 (d) a = 3, r = 1/4

Q2 If the sum of the first 2n terms of the AP 2,5, 8, ... is equal to the sum of the first n terms
of the AP 57, 59, 61 ... then find the value of n
(a) 10 (b) 12
(c) 11 (d) 13

Q3 The digit of a positive integer having three digits are in A.P. and their sum is 15. If the
number obtained by reversing the digits is 594 less than the original number, then the number
is
(a) 352 (b) 652
(c) 852 (d) none

( ) ( )
Q4 If 1, log 9 31− x + 2, log 3 4.3x - 1 are in AP then x equals

(a) log 3 4 (b) 1 - log 3 4

(c) 1- log 3 4 (d) log 4 3

Q5 Suppose a, b, c are in AP and a 2, b 2, c 2 are in GP. If a value of a
(a) 1/2 2 (b) 1/2 3
1 1 1 1
(c) - (d) -
2 3 2 2

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SEQUENCE SERIES

a1 + a2 + ... a p p2
Q6 Let a1… an be terms of AP. If = where p and q are distinct then find
a1 + a2 + ... aq q2

a6
a21
(a) 41 // 11 (b) 7/2
(c) 2/7 (d) 11/41

Q7 A person is to count 4500 currency notes. Let a (n) denote the number of notes he counts
in the nth minute. If a1 = a2 =… = a10 = 150 and a10, a11 are in AP with common difference -2,

then the time taken by him to count all the notes is.
(a) 34 minutes (b) 125 minutes
(c) 135 minutes (d) 24 minutes

1 2
Q8 The maximum value of the sum of the series 20 + 19 + 18 + .... is
3 3
(a) 300 (b) 310
(c) 320 (d) none

1099 1099
Q9 Let tn be the nth term of an A.P. If ∑ a 2r = 10100 and
r = 1
∑a
r = 1
2r −1 = 1099, then the common

difference of A.P. is
(a) 1 (b) 10
(c) 9 (d) 1099

Q10 In a geometric progression consisting of positive terms, each term equal to the sum of the
next two terms. Then the common ratio of this progression equals:

(a)
1
2
(
1− 5) (b)
1
2
5

(c) 5 (d)
1
2
( 5 −1 )

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SEQUENCE SERIES

Q11 The first two terms of a geometric progression add up to 12. The sum of the third and
the fourth terms is 48. If the terms of the geometric progression are alternately positive and
negative, then the first term is:
(a) -4 (b) -12
(c) 12 (d) 4

Q12 If a, b, c be three successive terms of a G.P. with common ratio r and a> 0 satisfying the
relation c> 4b - 3a, then
(a) 1 (c) r> 3 or r <1 (d) none

Q13 A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the
sum of the terms occupying odd places, the common ratio will be
(a) 2 (b) 3
(c) 4 (d) 5

Q14 There are (4n + 1) terms in a certain sequence of which the first (2n + 1) terms from an
A.P. of common difference 2 and the last (2n + 1) terms are in G.P. of common ratio 1/2. If
the middle terms of both A.P. and G.P. be the same, then mid-term of this sequence is

n ⋅ 2n +1 n ⋅ 2n +1
(a) (b)
2n - 1 22n - 1
(c) n ⋅ 2n (d) none

Q15 Three numbers form an increasing G.P. if the middle number is doubled, then the new
numbers are in A.P. The common ratio of G.P. is
(a) 2 - 3 (b) 2 + 3

(c) 3−2 (d) none of these

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SEQUENCE SERIES

Q16 The minimum value of n such that 1 + 3 + 32 + ..... + 3n> 1000 is


(a) 7 (b) 8
(c) 9 (d) none of these

a n +1 1 20
Q17 For a sequence a n, a1 = 2 and
at
=. Then,
3
∑a
r = 1
r
is

20  1 
(a) [4 + 19 × 3] (b) 3 1 - 
2  320 

(c) 2 (1 - 320) (d) none of these

Q18 If a, b, c, d, e, f are A.M.’s between 2 and 12, then a + b + c + d + e + f is equal to


(a) 14 (b) 42
(c) 84 (d) none of these

Q19 The sum of the squares of three distinct real numbers which are in G.P. is S2. If their
sum is α S, then
(a) 1 <α 2 <3 (b)
1
<α2 <3
3
(c) 1 <α <3 1
(d) <α <1
3
Q20 If a, b, c are three unequal numbers such that a, b, c are in A.P. and b - a, c - b, a are in
G.P., then a: b: c is
(a) 1: 2: 3 (b) 1: 3: 5
(c) 2: 3: 4 (d) 1: 2: 4

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