1, 10, 27, 64, 66 — what is the next number in the sequence?

Concept: A “find the next number” series is sometimes built from two separate sequences interleaved at alternating positions — odd positions (1st, 3rd, 5th, …) form one sub-sequence and even positions (2nd, 4th, 6th, …) form another. Each sub-sequence grows by adding a fixed base value multiplied by an increasing step count (×2, then ×3, then ×4, …).

Application:

1. Split the series 1, 10, 27, 64, 66 into two sub-sequences by position: odd positions give 1, 27, 66, …; even positions give 10, 64, …

2. Odd-position sub-sequence: 1 + 13×2 = 27, then 27 + 13×3 = 66 — each step multiplies the base value 13 by an increasing count.

3. Even-position sub-sequence: 10 + 27×2 = 64 — the base value here is 27, following the same increasing-multiplier rule.

4. The next number in the overall series (the 6th term) is the 3rd term of the even-position sub-sequence, so continue with the next step count (×3): 64 + 27×3 = 145.

Cross-check: The odd-position sub-sequence independently follows the identical rule — its next term (7th overall) would be 66 + 13×4 = 118 — confirming both interleaved sub-sequences use the same increasing-multiplier structure and that 145 is the correctly derived next term for the even-position sub-sequence.