If the sum of n terms of an A.P. is 3$\mathbf{n}^{2}$ + 5n then which of its terms is 164 ?
A. 26th B. 27th C. 28th D. None of these Answer: Option BShow Answer
Solution(By Apex Team)
Sum of n terms of an A.P. = $3 n^{2}+5 n$
Let a be the first term and d be the common difference
$\begin{array}{l}\mathrm{S}_{\mathrm{n}}=3\mathrm{n}^2+5\mathrm{n}\\
\mathrm{S}_1=3(1)^2+5\times1=3+5=8\\
\mathrm{~S}_2=3(2)^2+5\times2=12+10=22\\
\therefore\text{ First term }(\mathrm{a})=8\\
\mathrm{a}_2=\mathrm{S}_2-\mathrm{S}_1=22-8=14\\
\mathrm{~d}=\mathrm{a}_2-\mathrm{a}_1=14-8=6\\
\text{ Now }\mathrm{a}_{\mathrm{n}}=\mathrm{a}+(\mathrm{n}-1)\mathrm{d}\\
\Rightarrow164=8+(\mathrm{n}-1)\times6\\
\Rightarrow6\mathrm{n}-6=164-8\\
\Rightarrow6\mathrm{n}=156+6\\
\Rightarrow6\mathrm{n}=162\end{array}$
⇒ n = $\Large\frac{162}{6}$
⇒ n = 27
∴ 168 is 27th term
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