8, 7, 11, 12, 14, 17, 17, 22, (....)

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

So, the correct next number is 1440.

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.

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.

Numbers are (2³ - 1), (3³ - 1), (4³ - 1), (5³ - 1), (6³ - 1), (7³ - 1) etc.

So, the next number is (8³ - 1) = (512 - 1) = 511.