Math Unit Test: Sequences & Series(June 20) - JEE MCQ

Let S_n denote the sum of first n terms of an arithmetic progression. If S₁₀ = 530, S₅ = 140, then S₂₀ - S₆ is equal to:

Let 3, 6, 9, 12, ... upto 78 terms and 5, 9, 13, 17, ... upto 59 terms be two series. Therefore, the sum of the terms common to both the series is equal to ___. (in integer)

The sum of 10 terms of the series  + ... is:

Let a_n be the n^th term of a G.P. of positive terms. If  = 200 and  = 100, then  is equal to:

Let a₁, a₂, ... a_n be a given A.P. whose common difference is an integer and S_n = a₁ + a₂ + ... + a_n. If a₁ = 1, a_n = 300 and 15  n  50, then the ordered pair (S_{n - 4}, a_{n - 4}) is equal to

Let  be a sequence such that a₁ = 1, a₂ = 1 and a_{n + 2} = 2a_{n + 1} + a_n for all n  1. Then the value of 47  is equal to __________. (in integer)

Let S₁ be the sum of first 2n terms of an arithmetic progression. Let S₂ be the sum of first 4n terms of the same arithmetic progression. If (S₂ - S₁) is 1000, then the sum of the first 6n terms of the arithmetic progression is equal to:

If , then the remainder when K is divided by 6 is

If (r³ + 6r² + 2r + 5) = (11!), then value of  is equal to ________. (in integer)

The greatest positive integer k, for which 49^k + 1 is a factor of the sum 49¹²⁵ + 49¹²⁴ + ... + 49² + 49 + 1, is

The value of (0.16)^log2.5 is equal to ________. (in integer)

If the sum of the first ten terms of the series  is , where m and n are co-prime numbers, then m + n is equal to ___________. (in integer)