Question

Find the next number in the series: 2, 6, 12, 20, 30, ?

• A. 36
• B. 40
• C. 42
• D. 56

Hint:

To solve number series problems, calculate the differences between consecutive terms to identify a pattern. If the differences form a sequence (e.g., increasing by a constant amount), extend that pattern to find the next term. Double-check by verifying if the series fits a mathematical formula, such as arithmetic or quadratic, if time permits.

Answer 1

The Correct Option is C

To resolve this issue, the number series pattern must be determined to ascertain the subsequent number.

1. Conceptual Framework:

- Number Series: A numerical progression governed by a specific rule.
- Pattern Identification: Examination of the incremental differences or generative formulas of the sequence.

2. Presented Series:

2, 6, 12, 20, 30, ?

3. Pattern Analysis:

Observe the sequence's components:

• 2 = 1 × 2
• 6 = 2 × 3
• 12 = 3 × 4
• 20 = 4 × 5
• 30 = 5 × 6

Thus, the nth term is represented as \( n \times (n+1) \)

4. Next Term Computation:

For \( n = 6 \): \[ 6 \times 7 = 42 \]

Concluding Result:

The subsequent numeral in the series is 42.