the middle sequence will read :

9, 36,81, 144,225,324,441,576. what your looking at is multiples of 3 that are squared (3×3 =9 6×6=36 …18×18=324 etc.) the other one is too much for me. But I hope what I did give you helps !!!!

142

324

don’t you mean 1000 on the last one?

there isn’t really a strict method to figuring this kind of thing out… basically run through all of the mathematical tools that are at the level you expect the questioner to be interested in…

the first one is about how much you add to get the next item:

15, 21, 27, 33… these are going up by 6, so add 39 now

the second one is all squares, they’re going up by 3

last one is 125.. they’re all cubes

2. 324, 441, 576 (square increases by 3 each time)

3. (first number should be 1000) 125, 64, 27 (cuberoot reduces by 1 each time)

I just solve it by playing around with the numbers in my head. Large difference that increase and reduce quicker are usually atributable to geometric models (squares/roots/etc) and slower increases and reductions are usually due to linear models (plus/minus)

There you go!