What should come in place of the ‘?’ in the given series? 5 14 41 122 ?

Question

What should come in place of the ‘?’ in the given series? 5 14 41 122 ?

1. A. 365 (Correct answer)
2. B. 361
3. C. 381
4. D. 368

Correct Answer

Option A — 365

Detailed Solution & Explanation

The correct answer is 365.

Key Points

• The gaps grow too fast for a simple addition, so test a multiplicative rule with a constant:
  • $5 \times 3 - 1 = 14$ ✓
  • $14 \times 3 - 1 = 41$ ✓
  • $41 \times 3 - 1 = 122$ ✓
• The rule is $\times 3 - 1$, so the missing term is $122 \times 3 - 1 = \textbf{365}$.
• Confirm against the term after it: $365 \times 3 - 1 = 1094$ ✓, which matches the last given value.

Additional Information

• The number after the gap is the strongest check available. Having 1094 given lets you verify the rule from both sides, and a rule that reproduces it exactly is almost certainly right.
• The standard sequence for diagnosing a number series is: constant difference → constant ratio → difference of differences → $\times a \pm b$ → squares and cubes. Here the ratios (2.8, 2.93, 2.98) approach 3, which points straight to $\times 3$ with a small correction.
• Distractors 361, 368 and 381 sit close to 365, so the rule must be applied rather than the answer estimated from the growth pattern.
• Note that $365 = 122 \times 3 - 1$ and also that each term is one less than a multiple of 3 — a structural feature that follows from the rule and can serve as a quick sanity check.