Insert the missing number.

7, 26, 63, 124, 215, 342, (....)

Let the given numbers be A, B, C, D, E, F, G.

Then, A, A x 1 + 1, B x 2 + 2, C x 3 + 3, D x 4 + 4, E x 5 + 5, F x 6 + 6 are the required numbers.

Clearly, 228 is wrong.

There are two series (8, 11, 14, 17, 20) and (7, 12, 17, 22) increasing by 3 and 5 respectively.

Go on multiplying the given numbers by 2, 3, 4, 5, 6.

So, the correct next number is 1440.

The numbers are 7 x 8, 8 x 9, 9 x 10, 10 x 11, 11 x 12, 12 x 13.

So, 150 is wrong.

Subtract 1, 3, 5, 7, 9, 11 from successive numbers.

So, 34 is wrong.

1, 1 + 1² = 2, 2 + 2² = 6, 6 + 3² = 15, 15 + 4² = 31, 31 + 5² = 56, 56 + 6² = 92

Last number of given series must be 92 not 91.

Each of the numbers except 81 is a prime number.

(1*1)+1 , (2*2)+1 , (3*3)+1 , (4*4)+1 , (5*5)+1 , (6*6)+1 , (7*7)+1 , (8*8)+1

But, 64 is out of pattern.