Find the alternative number to replace the question mark 2,6,12,20,30,42,?

Answer: 56

Explanation:

• Pattern as product of consecutive integers: each term equals n(n+1).

  1×2 = 2, 2×3 = 6, 3×4 = 12, 4×5 = 20, 5×6 = 30, 6×7 = 42, so the next is 7×8 = 56.

• Pattern by differences: compute differences between consecutive terms.

  Differences: 6−2 = 4, 12−6 = 6, 20−12 = 8, 30−20 = 10, 42−30 = 12. These differences increase by 2 each time, so the next difference is 14.

  Therefore next term = 42 + 14 = 56.

Both viewpoints give the same result, confirming that the correct replacement for the question mark is 56.