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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Sequences and Series

NDA 2019 · Mathematics · Sequences and Series

Let S_n be the sum of the first n terms of an AP. If S_ 2 n =3 n+14...

Let SnS_n be the sum of the first nn terms of an AP. If S2n=3n+14n2S_{2 n}=3 n+14 n^2, then what is the common difference?

Options

  1. A5
  2. B6
  3. C7
  4. D9

Correct answer

C. 7

Step-by-step solution

S2n=3n+14n2∴Sn=3n2+14(n2)2∴Sn=3n+7n22∴S1=3+72=5=T1S2=6+282=17=T1+T2∴(T1+T2)−(T1)=17−5=12⇒T2=12∴d=T2−T1=12−5=7\begin{aligned} & S_{2 n}=3 n+14 n^2 \\ & \therefore S_n=3 \frac{n}{2}+14\left(\frac{n}{2}\right)^2 \\ & \therefore \quad S_n=\frac{3 n+7 n^2}{2} \\ & \therefore S_1=\frac{3+7}{2}=5=T_1 \\ & S_2=\frac{6+28}{2}=17=T_1+T_2 \\ & \therefore\left(T_1+T_2\right)-\left(T_1\right)=17-5=12 \\ & \Rightarrow T_2=12 \\ & \therefore \quad d=T_2-T_1=12-5=7\end{aligned}
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