Sequence and Series questions
1035 published questions with worked solutions.
- Let a_1, a_2, a_3, …. be an A.P. If a_7 = 3, the product a_1a_4 is minimum and the sum of its first n terms is zero, then n! –...
- The sum 1^2-2.3^2+3.5^2-4.7^2+5.9^2- +15.29^2 is________.
- If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296, respectively, then the sum of common ratio...
- Let a_1, a_2, …, a_n be in A.P. If a_5=2a_7 and a_ 11 = 18, then 12 ( 1 a_ 10 + a_ 11 + 1 a_ 11 + a_ 12 + + 1 a_ 17 + a_ 18 ) is...
- Let g(x) = log f(x) where f(x) is a twice differentiable positive function on (0, ∞) such that f(x + 1) = x f(x). Then, for N =...
- Suppose four distinct positive numbers a_1, a_2, a_3, a_4 are in G.P. Let b_1 = a_1, b_2 = b_1 + a_2, b_3 = b_2 + a_3 and b_4 =...
- If the sum of first n terms of an A.P. is cn^2, then the sum of squares of these n terms is
- Let ℝ denote the set of all real numbers. Let f : ℝ → ℝ be a function such that f(x) > 0 for all x ∈ ℝ, and f(x + y) = f(x)f(y)...
- If 1, _9 (3^ 1-x + 2 ), _3 (4.3^x - 1 ) are in A.P. then x equals
- The value of 2^ 1/4 , 4^ 1/8 , 8^ 1/6 + is
- Fifth term of a GP is 2, then the product of its 9 terms is
- Sum of infinite number of terms of GP is 20 and sum of their square is 100. The common ratio of GP is
- If f : R R satisfies f(x + y) = f(x) + f(y), for all x, y R and f(1) = 7, then _ r=1 ^ n f(r) is
- Let T_r be the rth term of an A.P. whose first term is a and common difference is d. If for some positive integers m, n, m n, T_m...
- The sum of the first n terms of the series 1^2 + 2 2^2 + 3^2 + 2 4^2 + 5^2 + 2 6^2 + is n(n+1)^2 2 when n is even. When n is odd...
- If x = _ n=0 ^ a^n, y = _ n=0 ^ b^n, z = _ n=0 ^ c^n where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, then x, y, z are in
- Let a_1, a_2, a_3, be terms of an A.P. If a_1 + a_2 + + a_p a_1 + a_2 + + a_q = p^2 q^2 , p q, then a_6 a_ 21 equals
- In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of...
- 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...
- The sum to the infinity of the series 1 + 23 + 6 3^2 + 10 3^3 + 14 3^4 + is
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