Sequence and Series questions
1035 published questions with worked solutions.
- If the 6th, 11th and 16th terms of a GP are a, b, c respectively then
- If a_0=1, a_1=1 and a_n=a_ n-1 a_ n-2 +1, n>2, then
- If a,b,c are in AP and x,y,z are finite numbers such that x= _ n=0 ^ a^n, y= _ n=0 ^ b^n and z= _ n=0 ^ c^n then x,y,z are in
- a_1, a_2, a_3, , a_n are in AP. STATEMENT-1: 1 a_1a_n + 1 a_2a_ n-1 + 1 a_3a_ n-2 + + 1 a_na_1 = 2 a_1 + a_n ( 1 a_1 + 1 a_2 + 1...
- a, b, c are three unequal positive numbers. STATEMENT-1: The product of their sum and the sum of their reciprocals exceeds 9....
- If _ p=1 ^ n _ m=1 ^ p ( _ k=1 ^ m k ) = a_0n^4 + a_1n^3 + a_2n^2 + a_3n + a_4 then
- Suppose four distinct positive numbers a_1, a_2, a_3, a_4 are in GP. Let b_1 = a_1, b_2 = b_1 + a_2, b_3 = b_2 + a_3 and b_4 =...
- The sum of first 9 terms of the series 1^3 1 + 1^3 + 2^3 1+3 + 1^3 + 2^3 + 3^3 1+3+5 + is
- The value of _ r=16 ^ 30 (r+2)(r-3) is equal to:
- Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P....
- The sum of the 3^ rd and the 4^ th terms of a G.P. is 60 and the product of its first three terms is 1000. If the first term of...
- Let a_1, a_2, a_3, a_n, be in A.P. If a_3+a_7+a_ 11 +a_ 15 = 72, then the sum of its first 17 terms is equal to :
- The sum _ r=1 ^ 10 (r^2+1 ) (r!), is equal to:
- If the arithmetic mean of two numbers a and b, a > b > 0, is five times their geometric mean, then a+b a-b is equal to:
- If the sum of the first n terms of the series 3 + 75 + 243 + 507 + is 435 3, then n equals:
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