SEQUENCES AND SERIES — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSEQUENCES AND SERIES3 Marks
Question
If the sum of $n$ terms of an A.P. is $3 n^2+5 n$ and its $m^{\text {th }}$ term is 164 , find the value of $m$.
✓
Answer
Given: $S_n=3 n^2+5 n$ and $a_m=164$
Put $\mathrm{n}=1$ and $\mathrm{n}=2$ in $\mathrm{S}_n$ we get,
$\mathrm{S}_1=3+5=8$
$\Rightarrow a=8 \ldots$
and $S_2=3(4)+5(2)=12+10=22$
We have $a_n=S_n-S_{n-1}$
$\therefore a_2=S_2-S_1$
$\Rightarrow a_2=22-8=14$
Now $d=a_2-a_1=14-8=6$
$\therefore a_m=164$
$\Rightarrow a+(m-1) d=164$
$\Rightarrow 8+(m-1) 6=164$
$\Rightarrow 8+6 m-6=164$
$\Rightarrow 6 m=162$
$\Rightarrow m=\frac{162}{6}=27$
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