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 solve the problem, we need to identify the pattern in the number series and find the next number.

1. Understanding the Concepts:

- Number Series: A sequence of numbers following a certain rule.
- Pattern Recognition: Analyze the differences or formulas generating the series.

2. Given Series:

2, 6, 12, 20, 30, ?

3. Analyzing the Pattern:

Look at the pattern in the terms:

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

So, the nth term = \( n \times (n+1) \)

4. Calculate the Next Term:

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

Final Answer:

The next number in the series is 42.