Find the alternative number to replace the question mark: 2, 6, 12, 20, 30,…

Key pattern: each term is a pronic number n×(n+1).

• 1 × 2 = 2

• 2 × 3 = 6

• 3 × 4 = 12

• 4 × 5 = 20

• 5 × 6 = 30

• 6 × 7 = 42

• 7 × 8 = 56 (next term)

Alternate explanation:

• Consecutive differences: 6−2 = 4, 12−6 = 6, 20−12 = 8, 30−20 = 10, 42−30 = 12.

• Differences increase by 2 each time, so the next difference is 14 and 42 + 14 = 56.

Answer: 56