Select the option that will replace the question mark (?) in the following…

Key idea: use differences between consecutive terms to find the pattern.

Compute the differences between consecutive terms:

+1, +1, +2, 0, +3, −1, ?

• Look at the positive increments: +1, +1, +2, +3, +4, ... These are increasing increments that appear at certain positions in the differences.

• Between those positive increments the differences are non-positive and form the sequence 0, −1, −2, ... alternating with the increasing positives.

Following this pattern, after the −1 the next difference should be +4.

So the missing term is 17 + 4 = 21.

Answer: 21