Question

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

• A. \(38\)
• B. \(40\)
• C. \(42\)
• D. \(44\)

Hint:

In many number series questions, the pattern lies in the differences between consecutive terms. Always check first differences and second differences to identify the rule.

Answer 1

The Correct Option is C

Concept: In number series problems, observe the pattern in the difference between consecutive terms. If the differences follow a recognizable pattern, extend it to determine the next term.

Step 1: Find the differences between consecutive terms. \[ 6 - 2 = 4 \] \[ 12 - 6 = 6 \] \[ 20 - 12 = 8 \] \[ 30 - 20 = 10 \] Thus, the differences are: \[ +4, +6, +8, +10 \]

Step 2: Identify the pattern. The difference increases by \(2\) each time. Therefore, the next difference is \[ 10 + 2 = 12 \]

Step 3: Find the next term. \[ 30 + 12 = 42 \] Hence, the missing number is \[ \boxed{42} \]