Let $\mathrm{a}_{\mathrm{n}}$ be the $\mathrm{n}^{\text {th }}$ term of an A. P.
If $S_n=a_1+a_2+a_3+\ldots+a_n=700, a_6=7$ and $S_7=7$, then $\mathrm{a}_{\mathrm{n}}$ is equal to :

Question

Let $\mathrm{a}_{\mathrm{n}}$ be the $\mathrm{n}^{	ext {th }}$ term of an A. P. If $S_n=a_1+a_2+a_3+\ldots+a_n=700, a_6=7$ and $S_7=7$, then $\mathrm{a}_{\mathrm{n}}$ is equal to :

Aicharya · Accepted Answer

$\mathrm{S}_{\mathrm{n}}=700=\frac{\mathrm{n}}{2}[2 \mathrm{a}+(\mathrm{n}-1) \mathrm{d}]$...(i)
$a_6=7 \Rightarrow a+5 d=7$...(ii)
$\mathrm{S}_7=7 \Rightarrow \frac{7}{2}(2 \mathrm{a}+6 \mathrm{~d})=7$
$a+3 d=1$...(iii)
Solve (ii) and (iii)
$\begin{aligned}
& \frac{\mathrm{n}}{2}(-16+3 n-3)=700 \Rightarrow 3 n^2-19 n-1400=0 \\ & (3 n+56)(\mathrm{n}-25)=0 \\ & \therefore \mathrm{a}_{25}=\mathrm{a}+24 \mathrm{~d}=-8+24 \times 3 \\ & =-8+72
\end{aligned}$
=64 ~

Let $\mathrm{a}_{\mathrm{n}}$ be the $\mathrm{n}^{\text {th }}$ term of an A. P. If…

Solution