Find the next term in the series given below: 2, 6, 12, 20, .....

Concept

For the term in position n, multiply n by the next integer, n + 1. These products increase by successive even numbers.

Application

1. At position 1: 1 × 2 = 2.

2. At position 2: 2 × 3 = 6.

3. At position 3: 3 × 4 = 12.

4. At position 4: 4 × 5 = 20.

5. At position 5: 5 × 6 = 30.

Cross-check

The differences are 6 − 2 = 4, 12 − 6 = 6, and 20 − 12 = 8. The next successive even difference is 10, so 20 + 10 = 30. Hence the next term is 30.