Sequence and Series questions
1035 published questions with worked solutions.
- Let <a_n> be a sequence such that a_1+a_2+ +a_n= n^2+3n (n+1)(n+2) . If 28 _ k=1 ^ 10 1 a_k =P_1P_2P_3 P_m, where P_1, P_2, ….....
- Let the positive numbers a_1, a_2, a_3, a_4, and a_5 be in a G.P. Let their mean and variance be 31 10 and m n respectively,...
- Let the digits a, b, c be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three...
- Let a_1, a_2, a_3,….. be a G.P. of increasing positive numbers. Let the sum of its 6^ th and 8^ th terms be 2 and the product of...
- Let s_1,s_2,s_3,……,s_ 10 respectively be the sum of 12 terms of 10 A.Ps whose first terms are 1, 2, 3, ……, 10 and the common...
- The sum to 20 terms of the series 2.2^2-3^2+2.4^2-5^2+2.6^2- . is equal to _________
- Let A_1 and A_2 be two arithmetic means and G_1, G_2 and G_3 be three geometric means of two distinct positive numbers. Then...
- Let the six numbers a_1, a_2, a_3, a_4, a_5, a_6 be in A.P. and a_1+a_3 = 10. If the mean of these six numbers is 19 2 and their...
- For three positive integers p, q, r, x^ pq^2 =y^ qr =z^ p^2r and r = pq+1 such that 3, 3 _yx, 3 _zy, 7 _xz are in A.P with common...
- The 4th term of GP is 500 and its common ratio is 1 m , m N. Let S_n denote the sum of the first n terms of this GP. If S_6>S_5+1...
- Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that N–2, 3N , N + 2 are in...
- For the two positive number a, b, if a, b and 1 18 are in a geometric progression, while 1 a , 10 and 1 b are in arithmetic...
- Let A_1, A_2, A_3 be the three A.P. with the same common difference d and having their first terms as A, A + 1, A + 2,...
- Consider a function f : N R, satisfying f(1) + 2f(2) + 3f(3) + …. + xf(x) = x(x +1)f(x) ; x 2 with f(1) = 1. Then 1 f(2022) + 1...
- Let a_k and b_k , k N, be two G.Ps with common ratios r_1 and r_2 respectively such that a_1 = b_1 = 4 and r_1<r_2. Let...
- Let a_1=b_1=1 and a_n=a_ n-1 +(n-1), b_n=b_ n-1 +a_ n-1 , n 2. If S = _ n=1 ^ 10 b_n 2^n and T = _ n=1 ^8 n 2^ n-1 , then...
- Let a_1, a_2, a_3, … be a G.P of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth...
- Suppose f is a function satisfying f(x+y) + f(x) + f(y) for all x, y N and f(1) = 1 5 . If _ n=1 ^mf(n)(n+1)(n+2)= 1 12 , then m...
- Let a, b, c > 1, a^3,b^3 and c^3 be in A.P., and _ab, _ca and _bc be in G.P. If the sum of first 20 terms of an A.P., whose first...
- The 8^ th common term of the series S_1 = 3 + 7 + 11 + 15 + 19 + …, S_2 = 1 + 6 + 11 + 16 + 21 + …, is________.
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