Find the missing term?1, 6, 15, ?, 45, 66, 91

The correct answer is Option (1) → 28

The differences between the terms rise by 4 each time, so the missing term is found from the gaps.

• Known gaps: \(6-1=5\), \(15-6=9\), \(66-45=21\), \(91-66=25\), each 4 more than the one before

• So the two gaps around the blank are 13 and 17, which together make \(45-15=30\)

• Missing term \(=15+13=28\)

Tip: These are the hexagonal numbers \(n(2n-1)\): \(1\times1,\ 2\times3,\ 3\times5,\ 4\times7=28,\ 5\times9,\ \ldots\)