Sequence and Series questions
1035 published questions with worked solutions.
- If the sum 3 1^2 + 5 1^2 + 2^2 + 7 1^2 + 2^2 + 3^2 + up to 20 terms is equal to k 21 , then k is equal to
- In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the...
- The sum of the first 20 terms common between the series 3 + 7 + 11 + 15 + and 1 + 6 + 11 + 16 + is
- The least positive integer n such that 1 - 23 - 2 3^2 - - 2 3^ n-1 < 1 100 , is:
- Let f(n) = [ 13 + 3n 100 ]n, where [n] denotes the greatest integer less than or equal to n. Then _ n=1 ^ 56 f(n) is equal to
- The number of terms in an A.P. is even, the sum of the odd terms in it is 24 and that the even terms is 30. If the last term...
- If a_1, a_2, a_3, are in AP then a_p, a_q, a_r are in AP if p, q, r are in
- If p, q, r, s N and they are four consecutive terms of an AP then the pth, qth, rth, sth terms of a GP are in
- If in a progression a_1, a_2, a_3, , etc., (a_r - a_ r+1 ) bears a constant ratio with a_r a_ r+1 then the terms of the...
- If a_2 a_3 a_1 a_4 = a_2 + a_3 a_1 + a_4 = 3 ( a_2 - a_3 a_1 - a_4 ) then a_1, a_2, a_3, a_4 are in
- Let x, y, z be three positive prime numbers. The progression in which x , y , z can be three terms (not necessarily consecutive)...
- Let f(x) = 2x + 1. Then the number of real values of x for which the three unequal numbers f(x), f(2x), f(4x) are in GP is
- If a_r > 0, r N and a_1, a_2, a_3, , a_ 2n are in AP then a_1 + a_ 2n a_1 + a_2 + a_2 + a_ 2n-1 a_2 + a_3 + a_3 + a_ 2n-2 a_3 +...
- If a_1, a_2, a_3, , a_ 2n+1 are in AP then a_ 2n+1 - a_1 a_ 2n+1 + a_1 + a_ 2n - a_2 a_ 2n + a_2 + + a_ n+2 - a_n a_ n+2 + a_n is...
- Let a_1, a_2, a_3, be in AP and a_p, a_q, a_r be in GP. Then a_q : a_p is equal to
- If a, b, c are in GP then a + b, 2b, b + c are in
- If a, b, c, d are nonzero real numbers such that (a^2 + b^2 + c^2)(b^2 + c^2 + d^2) (ab + bc + cd)^2 then a, b, c, d are in
- If a, b, c are in AP then a bc , 1 c , 2 b are in
- If in an AP, t_1 = _ 10 a, t_ n+1 = _ 10 b and t_ 2n+1 = _ 10 c then a, b, c are in
- If n!, 3 n! and (n+1)! are in GP then n!, 5 n! and (n+1)! are in
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