Question:

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

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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.
Updated On: Jun 22, 2025
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The Correct Option is C

Solution and Explanation

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.

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