NDA 2026 · PYQ · Arithmetic Progression · easy
The sum of the first n terms of an AP is 3n² + 5n. If the mᵗʰ term of the AP is 68, then what is the value of m?
Answer
The correct answer is C: 11. The mᵗʰ term = Sₘ − Sₘ₋₁ = (3m² + 5m) − (3(m−1)² + 5(m−1)) = 3m² + 5m − 3m² + 6m − 3 − 5m + 5 = 6m + 2. Setting 6m + 2 = 68 gives 6m = 66, so m = 11.
- A.9
- B.10
- C.11✓ Correct
- D.12
The mᵗʰ term = Sₘ − Sₘ₋₁ = (3m² + 5m) − (3(m−1)² + 5(m−1)) = 3m² + 5m − 3m² + 6m − 3 − 5m + 5 = 6m + 2. Setting 6m + 2 = 68 gives 6m = 66, so m = 11.
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