25, 36, 49, 81, 121, 169, 225

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 terms are alternatively multiplied by 1.5 and divided by 3. However, 18.5 does not satisfy it.

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.

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.

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

So, the correct next number is 1440.

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