Question

Select the number from the given options that can replace the question mark (?) in the following series.
4, 12, ?, 60, 124, 252

• A. 28
• B. 36
• C. 24
• D. 32

Hint:

For number series, checking the difference between terms is often the quickest way to spot a pattern. If differences grow rapidly, check for multiplication or powers.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
We need to find the missing number in the series that follows the established mathematical pattern.
Step 2: Detailed Explanation:
Let's analyze the pattern between consecutive terms.

\(4 \times 2 + 4 = 8 + 4 = 12\)
Let's test this pattern for the next step: \(12 \times 2 + 4 = 24 + 4 = 28\)
Verify with the next term: \(28 \times 2 + 4 = 56 + 4 = 60\) (Matches given term)
Verify next: \(60 \times 2 + 4 = 120 + 4 = 124\) (Matches)
Verify next: \(124 \times 2 + 4 = 248 + 4 = 252\) (Matches)
The pattern is \( \text{Next Term} = \text{Previous Term} \times 2 + 4 \). Alternatively, looking at differences:

\(12 - 4 = 8\)
\(60 - 28 = 32\)
\(124 - 60 = 64\)
\(252 - 124 = 128\)
The differences are \(8, 16, 32, 64, 128\), which are powers of 2 (multiplied by 8). If missing term is 28, then difference \(28 - 12 = 16\). This fits the sequence \(8, 16, 32...\). Step 3: Final Answer:
The missing number is 28.