In the sequence 2, 6, 12, 20, what is the next term?

In the sequence 2, 6, 12, 20, what is the next term?

• A. 42
• B. 40
• C. 30
• D. 48

Answer: (C)

Recognize a pattern where the gap between terms grows by a constant amount. The differences are 6−2 = 4, 12−6 = 6, 20−12 = 8. Each gap is 2 more than the previous one, so the next gap should be 10. Add that to 20 to get 30. Another way to see it is each term is the product of consecutive integers: 1×2, 2×3, 3×4, 4×5; the next is 5×6 = 30. The other options would require an inconsistent jump in the differences.

Recognize a pattern where the gap between terms grows by a constant amount. The differences are 6−2 = 4, 12−6 = 6, 20−12 = 8. Each gap is 2 more than the previous one, so the next gap should be 10. Add that to 20 to get 30. Another way to see it is each term is the product of consecutive integers: 1×2, 2×3, 3×4, 4×5; the next is 5×6 = 30. The other options would require an inconsistent jump in the differences.