What should come in place of the ‘?’ in the given series? 13 19 31 55 103 ?

Question

What should come in place of the ‘?’ in the given series? 13 19 31 55 103 ?

1. A. 199 (Correct answer)
2. B. 203
3. C. 190
4. D. 195

Correct Answer

Option A — 199

Detailed Solution & Explanation

The correct answer is 199.

Key Points

• Take the differences between consecutive terms:
  • $19 - 13 = 6$, $31 - 19 = 12$, $55 - 31 = 24$, $103 - 55 = 48$
• The differences double each time: 6, 12, 24, 48, so the next is 96.
• The missing term is $103 + 96 = \textbf{199}$.

Additional Information

• The same series can be read as $\times 2 - 7$: $13 \times 2 - 7 = 19$, $19 \times 2 - 7 = 31$, $55 \times 2 - 7 = 103$, and $103 \times 2 - 7 = \textbf{199}$ — two different descriptions of one pattern, each confirming the other.
• Always compute the first differences before anything else. When they form a recognisable pattern of their own — here a geometric doubling — the series is solved without guessing at a formula.
• Where the first differences are irregular, take second differences; a constant second difference indicates a quadratic pattern.
• Distractors 190, 195 and 203 cluster tightly around 199, so the arithmetic must be completed rather than the trend extrapolated by eye.