6, 13,28,59,?

The given series consists of squares of consecutive prime numbers

i.e. 2², 3², 5²,.....,

11², 13², 17², 19².

So, missing term = 7² = 49.

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

So, missing term = 95 x 5 + 4 = 479.

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.

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.

The given sequence is a combination of three series :

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

II. 2nd, 5th, 8th, 11th terms i.e. 9, 10, 11, 12

III. 3rd, 6th, 9th terms i.e. 8, 9, 10 The pattern in I is - 1.

So, missing term = 6 - 1 = 5.

Each number in the series is one more than twice the preceding number.

So, missing term = (15 x 2) + 1 = 31.

Each number in the series is 2 less than thrice the preceding number.

So, missing number = (10 x 3) - 2 = 28.