Sequence and Series questions
1035 published questions with worked solutions.
- The common difference of the A.P. b_1,b_2, ,b_m is 2 more than the common difference of A.P. a_1,a_2, ,a_n. If a_ 40 =-159, a_...
- In an increasing geometric series, the sum of the second and the sixth term is 25 2 and the product of the third and fifth term...
- The sum of infinite series 1+ 23+ 7 3^2 + 12 3^3 + 17 3^4 + 22 3^5 + is equal to
- If , , are natural numbers such that 100^ -199 =(100)(100)+(99)(101)+(98)(102)+ +(1)(199), then the slope of the line passing...
- Let S_1 be the sum of first 2n terms of an arithmetic progression. Let S_2 be the sum of first 4n terms of the same arithmetic...
- Let S_n denote the sum of first n -terms of an arithmetic progression. If S_ 10 =530, S_5=140, then S_ 20 -S_6 is equal to
- Let S_n be the sum of the first n terms of an arithmetic progression. If S_ 3n =3S_ 2n , then the value of S_ 4n S_ 2n is
- If [x] be the greatest integer less than or equal to x, then _ n=8 ^ 100 [ (-1)^nn 2 ] is equal to
- If ( 9 ),x, ( 7 18 ) are in arithmetic progression and ( 9 ),y, ( 5 18 ) are also in arithmetic progression, then |x-2y| is equal...
- If the sum of an infinite GP a,ar,ar^2,ar^3, is 15 and the sum of the squares of its each term is 150, then the sum of...
- If 0<x<1, then 32x^2+ 53x^3+ 74x^4+ , is equal to
- Three numbers are in an increasing geometric progression with common ratio r. If the middle number is doubled, then the new...
- The sum of 10 terms of the series 3 1^2 2^2 + 5 2^2 3^2 + 7 3^2 4^2 + is
- Let a_1,a_2,a_3, be an A.P. If a_1+a_2+ +a_ 10 a_1+a_2+ +a_p = 100 p^2 , p 10, then a_ 11 a_ 10 is equal to
- Let S_n=1 (n-1)+2 (n-2)+3 (n-3)+ +(n-1) 1, n 4. The sum _ n=4 ^ ( 2S_n n! - 1 (n-2)! ) is equal to
- Let a_1,a_2, ,a_ 21 be an AP such that _ n=1 ^ 20 1 a_na_ n+1 = 49. If the sum of this AP is 189, then a_6a_ 16 is equal to
- If a_i _ i=1 ^n, where n is an even integer, is an arithmetic progression with common difference 1, and _ i=1 ^na_i=192, _ i=1 ^...
- If 1 2 3^ 10 + 1 2^2 3^9 + + 1 2^ 10 3 = K 2^ 10 3^ 10 , then the remainder when K is divided by 6 is
- The sum 1+2 3+3 3^2+ +10 3^9 is equal to
- If A= _ n=1 ^ 1 (3+(-1)^n)^n and B= _ n=1 ^ (-1)^n (3+(-1)^n)^n , then AB is equal to
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