Question
The sum of the first n terms of an AP is 3n^2+5n. If the m^ th term of the AP is 68, then what is the value of m ?
NDA
Mathematics
Sequences and Series
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. 9
- B. 10
- C. 11
- D. 12
Answer
C. 11
Step-by-step solution
Given S_n = 3n^2 + 5n The n^ th term of the AP is given by T_n = S_n - S_ n-1 T_n = (3n^2 + 5n) - [3(n-1)^2 + 5(n-1)] T_n = 3n^2 + 5n - (3n^2 - 6n + 3 + 5n - 5) T_n = 6n + 2 Given T_m = 68 6m + 2 = 68 6m = 66 m = 11 Answer: 11
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