Verbal Reasoning - Series Completion

The given sequence is a combination of two series :

I. 3, 7, 13, 21, 31, ? and II. 4, 7, 13, 22, 34

The pattern in I is + 4, + 6, + 8, + 10,.....

The pattern in II is + 3, + 6, + 9, + 12,.....

So, missing term = 31 + 12 = 43.

The pattern is - 4, - 9, - 16,.....i.e. - 2², - 3², - 4²,.....

So, missing pattern = 169 - 5² = 169 - 25 = 144.

Clearly, the given series consists of prime numbers starting from 2. So, the missing

term is the prime number after 11, which is 13.

The pattern is + 6, + 9, + 12, + 15, .....

So, missing term = 21 + 12 = 33.

Clearly, 5 x 2 = 10, 10 x 2 = 20, 20 x 2 = 40,.....

So, the series is a G.P. in which a = 5 and r = 2.

Let 1280 be the rath term of the series.

Then, 5x2^n-1 = 1280 2^n-1 = 256 = 2⁸ n - 1 = 8 n = 9.