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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Sequences and Series

NDA 2015 · Mathematics · Sequences and Series

The n th term of an AP. is (3+n)/(4) , then the sum of first 105...

The nnth term of an AP. is 3+n4\frac{3+n}{4}, then the sum of first 105 terms is

Options

  1. A270
  2. B735
  3. C1409
  4. D1470

Correct answer

D. 1470

Step-by-step solution

Tn=3+n4Sn=∑n=0∞Tn=∑(34+n4)=34n+14×n(n+1)2=78n+n28S105=78×105+(105)28=1470\begin{aligned} & \mathrm{T}_{\mathrm{n}}=\frac{3+\mathrm{n}}{4} \\ & \mathrm{ S}_{\mathrm{n}}=\sum_{\mathrm{n}=0}^{\infty} \mathrm{T}_{\mathrm{n}} \\ & =\sum\left(\frac{3}{4}+\frac{\mathrm{n}}{4}\right) \\ & =\frac{3}{4} \mathrm{n}+\frac{1}{4} \times \frac{\mathrm{n}(\mathrm{n}+1)}{2} \\ & =\frac{7}{8} \mathrm{n}+\frac{\mathrm{n}^2}{8} \\ & \mathrm{ S}_{105}=\frac{7}{8} \times 105+\frac{(105)^2}{8}=1470\end{aligned}
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