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

Step 1: Understanding the Question:
We need to identify the logical pattern governing the sequence of numbers to determine the value that follows \( 30 \).
Step 2: Key Formula or Approach:
The most common approach for such series is calculating the first-order differences between consecutive terms to see if a steady progression exists.
Step 3: Detailed Explanation:
Let's find the difference between consecutive terms:
\[ 6 - 2 = 4 \]
\[ 12 - 6 = 6 \]
\[ 20 - 12 = 8 \]
\[ 30 - 20 = 10 \]
The differences observed are \( 4, 6, 8, 10 \).
This sub-sequence follows an arithmetic progression with a common difference of \( 2 \).
Therefore, the next difference must be \( 10 + 2 = 12 \).
To find the missing term, add this difference to the last known term:
\[ 30 + 12 = 42 \]
Step 4: Final Answer:
The missing number in the series is \( 42 \).