Mathematics - Sequence & Series Question with Solution | TestHub

Let the 1^stterms of A.P. be$\mathrm{\text{'}}\mathrm{a}\mathrm{\text{'}}$and common difference$\mathrm{\text{'}}\mathrm{d}\mathrm{\text{'}}$.
Given$\hspace{0.17em}{\mathrm{a}}_1+{\mathrm{a}}_7+{\mathrm{a}}_{16}=40$
$\Rightarrow \mathrm{a}+\mathrm{a}+6\mathrm{d}+\mathrm{a}+15\mathrm{d}=40$
$\Rightarrow \mathrm{a}+7\mathrm{d}=\frac{40}{3}$….(1)
Sum of first$15$term
${\mathrm{S}}_{15}=\frac{15}{2}[2\mathrm{a}+14\mathrm{d}]$
$=\frac{15}{2}\times 2\times \frac{40}{3}=200$