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NDA 2026
Exam
NDA
Year
2026
Subject
Mathematics
Chapter
Sequences and Series

NDA 2026 · Mathematics · Sequences and Series

The sum of the first n terms of an AP is 3n^2+5n . If the m^ th...

The sum of the first nn terms of an AP is 3n2+5n3n^2+5n. If the mthm^{\text{th}} term of the AP is 6868, then what is the value of mm ?

Options

  1. A99
  2. B1010
  3. C1111
  4. D1212

Correct answer

C. 1111

Step-by-step solution

Given Sn=3n2+5nS_n = 3n^2 + 5n

The nthn^{\text{th}} term of the AP is given by Tn=Sn−Sn−1T_n = S_n - S_{n-1}

Tn=(3n2+5n)−[3(n−1)2+5(n−1)]T_n = (3n^2 + 5n) - [3(n-1)^2 + 5(n-1)]

Tn=3n2+5n−(3n2−6n+3+5n−5)T_n = 3n^2 + 5n - (3n^2 - 6n + 3 + 5n - 5)

Tn=6n+2T_n = 6n + 2

Given Tm=68T_m = 68

6m+2=686m + 2 = 68

6m=666m = 66

m=11m = 11

Answer: 1111
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