What is the next number in the series? 2, 4, 7, 10, 15, 18, …

Concept: A number series can secretly interleave two independent progressions — the terms at odd positions and the terms at even positions. When the single-step gaps between consecutive terms look irregular, split the series by position; each half often turns out to be a clean second-order progression, where the gaps of that half themselves increase by a constant amount.

Application

1. Write the series with position labels: 2 (1st), 4 (2nd), 7 (3rd), 10 (4th), 15 (5th), 18 (6th).

2. Split by position. Odd positions (1st, 3rd, 5th, 7th): 2, 7, 15, ?. Even positions (2nd, 4th, 6th): 4, 10, 18.

3. Find the gaps within the odd-position subsequence: 7 − 2 = 5, and 15 − 7 = 8.

4. These gaps themselves increase by a constant 3 (5, then 8 = 5 + 3), so the next gap is 8 + 3 = 11.

5. Add that gap to the last known odd-position term: 15 + 11 = 26 — the missing 7th term.

Cross-check: The even-position subsequence (4, 10, 18) has gaps 6 and 8, which also increase by a constant (2 each time) — confirming the series genuinely splits into two well-behaved interleaved progressions rather than needing one contrived single-sequence pattern. Fitting both halves to their own quadratic in the position index reproduces every given term exactly, including 4, 10, 18 and 2, 7, 15.

So the next number in the series is 26.