Find the number that fits: 2, 5, 10, 17, ?

Question

Find the number that fits: 2, 5, 10, 17, ?

1. A. 26 (Correct answer)
2. B. 24
3. C. 21
4. D. 20

Correct Answer

Option A — 26

Detailed Solution & Explanation

The correct answer is 26.

Key Points

• Differences are 5 − 2 = 3, 10 − 5 = 5, 17 − 10 = 7 — consecutive odd numbers.
• The next difference is 9, so 17 + 9 = 26.
• Equivalently every term is n² + 1: 1²+1, 2²+1, 3²+1, 4²+1, 5²+1 = 26.
• Spotting the n² + 1 form is faster than differencing once you recognise 2, 5, 10, 17.
• Both readings agree, which is the useful check: the odd-number differences 3, 5, 7, 9 are exactly the gaps between consecutive squares, since (n+1)² − n² = 2n + 1.
• Recognising 2, 5, 10, 17, 26 as one more than a perfect square makes the whole series readable at a glance.

Additional Information

• The series 2, 5, 10, 17, 26 is n² + 1; recognising an offset from the squares is faster than differencing.
• Worth memorising the first squares (1, 4, 9, 16, 25, 36, 49, 64, 81, 100) and cubes (1, 8, 27, 64, 125, 216, 343) — most "hidden pattern" series are one of these plus or minus a small constant.
• Consecutive odd differences always signal a square-based series, since (n+1)² − n² = 2n + 1.

प्रश्न (हिन्दी में)

वह संख्या ज्ञात करें जो उपयुक्त हो: 2, 5, 10, 17, ?

1. A. 26
2. B. 24
3. C. 21
4. D. 20