Question

Find the missing number in the series: \(2, 6, 12, 20, 30, \_\_\).

• A. \(40 \)
• B. \(42 \)
• C. \(44 \)
• D. \(46 \)

Hint:

When solving number series, always check: - Differences between terms - Second differences - Multiplication or mixed patterns Increasing differences are a common pattern in reasoning sequences.

Answer 1

The Correct Option is B

Concept: In number series problems, observing the pattern of differences between consecutive terms often helps identify the rule governing the sequence.

Step 1: Compute the differences between consecutive terms. \[ 6 - 2 = 4, \quad 12 - 6 = 6, \quad 20 - 12 = 8, \quad 30 - 20 = 10 \]

Step 2: Identify the pattern in the differences. The differences form the sequence: \[ 4, 6, 8, 10 \] This sequence increases by \(2\) each time.

Step 3: Determine the next difference. \[ 10 + 2 = 12 \]

Step 4: Find the next term in the series. \[ 30 + 12 = 42 \] Thus, the missing number in the sequence is: \[ \boxed{42} \]