sequence-and-series

SEQUENCE AND SERIES 1.

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1 2 18 ......... is 3 3 (a) 310 (b) 300 (c) 320 (d) None of these The sum of the numbers between 100 and 1000 which is divisible by 9 will be (a) 55350 (b) 57228 (c) 97015 (d) 62140 2 2 The ratio of sum of m and n terms of an A.P. is m : n , then the ratio of m th and n th term will be m 1 n 1 2m 1 2n 1 (a) (b) (c) (d) n 1 m 1 2n 1 2m 1 r n a The value of log r 1 is b r 1 The maximum sum of the series 20 19

n an n an 1 n an 1 n an (b) log n 1 (c) log n 1 (d) log n 1 log n 2 b 2 2 2 b b b The solution of the equation (x 1) (x 4) (x 7) ......... (x 28) 155 is (a) 1 (b) 2 (c) 3 (d) 4 The sum of all two digit numbers which, when divided by 4, yield unity as a remainder is (a) 1190 (b) 1197 (c) 1210 (d) None of these If S n denotes the sum of n terms of an arithmetic progression, then the value of (S 2n S n ) is equal to 1 1 (a) 2Sn (b) S3n (c) S3n (d) S n 3 2 The solution of log 3 x log 3 x log 3 x ......... log 3 x 36 is

(a) 5.

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(a) x 3 (b) x 4 If S k denotes the sum of first common difference are a and d (a) 2a d 0 (b) a d n A series whose nth term is x

6

16

3 3 (c) x 9 (d) x k terms of an arithmetic progression whose first term and respectively, then Skn / Sn be independent of n if (c) a 2d 0 (d) None of these 0 y, the sum of r terms will be

r (r 1) r (r 1) r (r 1) r (r 1) ry ry (b) (c) (d) rx 2x 2x 2x 2y The sum of the integers from 1 to 100 which are not divisible by 3 or 5 is (a) 2489 (b) 4735 (c) 2317 (d) 2632 The sum of the first and third term of an arithmetic progression is 12 and the product of first and second term is 24, then first term is (a) 1 (b) 8 (c) 4 (d) 6 If the sum of the first 2n terms of 2, 5, 8... is equal to the sum of the first n terms of 57, 59, 61... , then n is equal to (a) 10 (b) 12 (c) 11 (d) 13 (a)

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The sum of numbers from 250 to 1000 which are divisible by 3 is (a) 135657 (b) 136557 (c) 161575 (d) 156375 7 th term of an A.P. is 40, then the sum of first 13 terms is (a) 53 (b) 520 (c) 1040 (d) 2080 1 1 1 If a 1 , a 2 ,...., a n 1 are in A.P., then is ..... a 1a 2 a 2 a 3 ana n 1 n 1 1 n 1 n (a) (b) (c) (d) a 1a n 1 a 1a n 1 a 1a n 1 a 1a n 1 If the sum of the first n terms of a series be 5n 2 2n , then its second term is (a) 7 (b) 17 (c) 24 (d) 42 a 1 , a 2 , a 3 ,......... ....a 2 n Let the sequence form an A.P. a

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2 1

a

2 2

a

3 3

......... a

2 2n 1

Then

2 2n

a n 2n n (a) (a 12 a 22 n ) (b) (a 22 n a 12 ) (c) (a 12 a 22 n ) 2n 1 n 1 n 1 2 3 n 5 n If sum of n terms of an A.P. is and Tm 164 then m (a) 26 (b) 27 (c) 28 1 If Sn nP n (n 1)Q , where S n denotes the sum of the first n 2 common difference is (a) P Q (b) 2P 3Q (c) 2Q

(d) None of these (d) None of these terms of an A.P., then the

(d) Q S Let S n denotes the sum of n terms of an A.P. If S2 n 3Sn , then ratio 3n Sn (a) 4 (b) 6 (c) 8 (d) 10 The first term of an A.P. of consecutive integers is p 2 1 The sum of (2 p 1) terms of this series can be expressed as (a) ( p 1) 2 (b) (p 1) 3 (c) (2p 1)(p 1) 2 (d) p 3 (p 1) 3 The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, the number of terms is (a) 10 (b) 11 (c) 12 (d) None of these The number of terms of the A.P. 3,7,11,15...to be taken so that the sum is 406 is (a) 5 (b) 10 (c) 12 (d) 14 There are 15 terms in an arithmetic progression. Its first term is 5 and their sum is 390. The middle term is (a) 23 (b) 26 (c) 29 (d) 32

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ANSWERS 1 6 11 16 21

a c d d b

2 7 12 17 22

a c c b d

3 8 13 18 23

c d c a b

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4 9 14 19 24

c a d b d

5 10 15 20 25

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a a b d b