Question

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

• A. 28
• B. 30
• C. 32
• D. 36

Hint:

Look for patterns:
Products of consecutive numbers $n(n+1)$ or increasing differences are common in series questions.

Answer 1

The Correct Option is B

Concept: The given sequence follows a pattern based on the product of consecutive natural numbers: \[ a_n = n(n+1) \]

Step 1: Verify the pattern.
\[ 1 \times 2 = 2,\quad 2 \times 3 = 6,\quad 3 \times 4 = 12,\quad 4 \times 5 = 20 \]

Step 2: Apply pattern for next term.
\[ 5 \times 6 = 30 \]

Step 3: Alternative observation (difference method).
\[ 6 - 2 = 4,\quad 12 - 6 = 6,\quad 20 - 12 = 8 \] Differences increase by 2, so next difference = 10: \[ 20 + 10 = 30 \]

Step 4: Conclusion.
Thus, the next number in the series is 30.