3, 7, 23, 95,?

The terms of the given series are 3 x l², 3 x 2², 3 x 3², 3 x 4², 3 x 5², 3 x 6²,.....

So, missing term = 3 x 7² = 3 x 49 = 147.

The terms of the given series are (2³ - 1), (3³ - 1), (4³ - 1), (5³ - 1), (6³ - 1), (7³ - 1),.....

So, missing term = (8³ - 1) = (512 - 1) = 511.

Each term in the series, except the first two terms, is the sum of the preceding two

terms.

So, missing term = 16 + 25 = 41.

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

So, missing term = 25 + 4 = 29.

The given sequence is a combination of two series :

I. 0, 3, 8, 15, 24, ? and II. 2, 5, 10, 17, 26

The pattern in each one of I and II is + 3, + 5, + 7, + 9, .....

So, missing term = 24 + 11 = 35.

Each term at an even place in the series is the product of its two adjacent terms.

Thus, if the missing term be x, then we have : 7 x x = 56 or x = 56 ÷ 7 = 8.

The given series consists of squares of consecutive prime numbers

i.e. 2², 3², 5²,.....,

11², 13², 17², 19².

So, missing term = 7² = 49.

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

So, missing term = 59 x 2 + 4 = 122.

The pattern is x 3.

So, missing term = 108 x 3 = 324.

Clearly, 5 + 3 = 8, 8 + 3 = 11, 11 + 3 = 14, .....

So, the series is an A.P. in which a - 5 and d = 3.

Let 320 be the nth term of the series.

Then, 320 = 5 + (n - 1) x 3 or (n - 1) = 105 or n = 106.