Mathematics - Sequence & Series Question with Solution | TestHub

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