What is the next number? __________, 12, 26, 24, 39, 36

Solution: Recognize two alternating subsequences.

• Subsequence for positions 1, 3, 5: ?, 26, 39 — these are multiples of 13, so the terms are 13, 26, 39.

• Subsequence for positions 2, 4, 6: 12, 24, 36 — these are multiples of 12.

Therefore the missing first term is 13.