36, 54, 18, 27, 9, 18.5, 4.5

The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5.

So, 40 is wrong.

The terms are successively divided by 12, 10, 8, 6, ...etc.

So, 24 is wrong, it should be 8 (48/6 = 8).

Prime numbers 2, 3, 5, 7, 11, 13 are to be added successively.

So, 165 is wrong.

Terms at odd places are 5, 6, 7, 8 etc. and each term at even place is 16.

So, 9 is wrong.

Subtract 20, 25, 30, 35, 40, 45 from successive numbers.

So, 0 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.

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

So, 36 is wrong.

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

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

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

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

So, the next number is 8² = 64.