# Series Completion

Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

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.

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.

6, 13, 25, 51, 101, ?

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

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

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.

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

The series consists of squares and cubes of consecutive natural numbers i.e. 12, 13, 22, 23, 32, 33, 42, .....

So, missing term = 43 = 64.

125,80,45,20,?

The pattern is - 45, - 35, - 25, .....

So, missing term = 20 - 15 = 5.

In the series 2, 6, 18, 54, …… what will be the 8th term ?

Clearly, 2 x 3 = 6, 6 x 3 = 18, 18 x 3 = 54,.....

So, the series is a G.P. in which a = 2, r = 3.

Therefore 8th term = ar8-1 = ar7 = 2 x 37 = (2 x 2187) = 4374.

3, 10, 101,?

Each term in the series is obtained by adding 1 to the square of the preceding term.

So, missing term = (101)2 + 1 = 10202.

589654237, 89654237, 8965423, 965423, ?