20, 20, 19, 16, 17, 13, 14, 11, ?

Concept

This is an alternating (interleaved) number series: the terms actually form two separate subsequences rather than one single sequence — one built from the odd-position terms (1st, 3rd, 5th, ...) and one from the even-position terms (2nd, 4th, 6th, ...). Each subsequence follows its own difference pattern and must be analysed on its own to find the missing term.

Application

1. Split the series 20, 20, 19, 16, 17, 13, 14, 11, ? by position: the odd positions (1st, 3rd, 5th, 7th, 9th) give the subsequence 20, 19, 17, 14, ?, and the even positions (2nd, 4th, 6th, 8th) give 20, 16, 13, 11.

2. Find the difference pattern within the odd-position subsequence: 19 − 20 = −1, 17 − 19 = −2, 14 − 17 = −3. The gap between consecutive terms grows by 1 each step.

3. Extend that growing-gap rule one more step: after a gap of −3, the next gap is −4, so the missing term = 14 − 4 = 10.

Cross-check

The even-position subsequence 20, 16, 13, 11 has differences −4, −3, −2 — the exact mirror (reverse order) of the odd-position subsequence's differences (−1, −2, −3, and now −4). This symmetric design confirms the split is correct; continuing the even subsequence one more step with the mirrored gap of −1 gives 11 − 1 = 10 as well, the same value, reinforcing that 10 is consistent with the series' governing pattern.

So the missing term is 10.