What number would replace the question mark in the series given below? 3, 8, 17, 32, 57, ?, 177

The missing term is 100.

The differences are 5, 9, 15, 25, ...

The differences of those differences are 4, 6, 10, 18, 34, which themselves double their gaps 2, 4, 8, 16.

So the next differences become 43 and then 77.

57 + 43 = 100 and 100 + 77 = 177, matching the last term.

Thus the blank is 100.