Question

Find the missing number in the series 2, 6, 14, 30, ?, 126

• A. 63
• B. 73
• C. 62
• D. 95

Hint:

When analyzing number series, check the difference between terms first.
Look for arithmetic patterns such as constant difference, doubling difference, or multiplication.

Answer 1

The Correct Option is C

Given the series: 2, 6, 14, 30, ?, 126, we are asked to find the missing number.
Step 1: Observe the pattern
Look at the differences between consecutive terms:
6 - 2 = 4
14 - 6 = 8
30 - 14 = 16
The differences are 4, 8, and 16, which double each time. This suggests the difference follows a pattern of powers of 2 (i.e., $2^2$, $2^3$, $2^4$).
Step 2: Find the next difference
Following this pattern, the next difference should be $2^5 = 32$.
Step 3: Calculate the missing term
Add this difference to the last known term:
30 + 32 = 62
Step 4: Verify with the next term
Next difference should be $2^6 = 64$. Check if:
62 + 64 = 126 \quad \checkmark
Thus, the missing number in the series is 62.