2, 4, 12, 48, 240, (....)

Numbers are 1², 2², 3², 4², 5², 6², 7².

So, the next number is 8² = 64.

There are two series (10, 13, 16, 19) and (5, 10, 20, 40), one increasing by 3 and the other multiplied by 2.

Each number is twice the preceding one with 1 added or subtracted alternatively.

So, the next number is (2 x 261 + 1) = 523.

The numbers are squares of odd natural numbers, starting from 5 up to 15.

So, 36 is wrong.

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.

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

Numbers are all primes. The next prime is 43.

Numbers are alternatively multiplied by 3 and divided by 2.

So, the next number = 54 ? 2 = 27.

The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8.

So, the next number is 8 x 9 = 72.

Each number is the proceeding number multiplied by -2.

So, the required number is -128.