1, 1, 4, 8, 9, 27, 16, ?

Answer: Option B

Explanation:

The series consists of squares and cubes of consecutive natural numbers i.e. 1^{2}, 1^{3}, 2^{2}, 2^{3}, 3^{2}, 3^{3}, 4^{2}, .....

So, missing term = 4^{3} = 64.

1, 2, 3, 6, 9, 18, ?, 54

The pattern is x 2, x 3/2, x 2, x 3/2, x 2,.....

So, missing term = 18 x 3/2 = 27.

6, 13, 25, 51, 101, ?

Answer: Option C

The pattern is x 2 + 1, x 2 - 1, x 2 + 1, x 2 - 1,.....

So, missing term = 101 x 2 + 1 = 203.

5,6,9, 15, ?, 40

The pattern is + 1, + 3, + 6,....., i.e. + 1, + (1, + 2), + (1 + 2 + 3),.....

So, missing term = 15 + (1 + 2 + 3 + 4) = 25.

1, 3, 4, 8, 15, 27, ?

The sum of any three consecutive terms of the series gives the next term.

So, missing number = 8 + 15 + 27 = 50.