Question

What number will come in the blank in the following number series?
13, 14, 22, 31, _____, 120, 336}

• A. 35
• B. 45
• C. 65
• D. 95

Hint:

Look for alternating power series ($n^2$ and $n^3$) in increments.

Answer 1

The Correct Option is D

Step 1: Concept
Analyze the differences between consecutive terms to find the pattern.
Step 2: Analysis
- $14 - 13 = 1 = 1^3$
- $22 - 14 = 8 = 2^3$
- $31 - 22 = 9$ (Pattern deviation)
Alternative pattern: $13 + 1^2 = 14$; $14 + 2^3 = 22$; $22 + 3^2 = 31$; $31 + 4^3 = 31 + 64 = 95$.
Step 3: Conclusion
Following the alternating squares and cubes pattern ($+1^2, +2^3, +3^2, +4^3$), the next number is 95. Final Answer:(D)