9, 27, 31, 155, 161, 1127,?

The pattern is + 1, x 1, + 2, x 2, + 3, x 3, + 4, x 4, + 5.

So, missing term = 13 x 3 = 39.

The pattern is + 3, + 4, + 5, + 6,.....

So, missing term = 9 + 5 = 14.

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.

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

So, missing term = 21 + 12 = 33.

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 given sequence is a combination of three series :

I. 1st, 4th, 7th, 10th, 13th terms i.e. 2, 4, 6, 8, ?

II. 2nd, 5th, 8th, 11th terms i.e. 1, 4, 7, 10

III. 3rd, 6th, 9th, 12th terms i.e. 2, 5, 8, 11

Clearly, I consists of consecutive even numbers. So, the missing term is 10.

The given series consists of cubes of natural numbers only. 256 is not the cube of

any natural number.

The given sequence is a combination of two series:

I. 13, 24, 35, 46, 57 and II. 32, 43, ?, 65, 76

The pattern in both I and II is + 11. So, missing term = 43 + 11 = 54.

The pattern is + 2, + 4, + 8, + 16,.....

So, missing term = 28 + 8 = 36.

The terms of the given series are (2² - 1), (4² - 1),....., (8² - 1), (10² - 1), (12² - 1).

So, missing term = (6² - 1) - (36 - 1) = 35.