Mathematics - Sequence & Series Question with Solution | TestHub

Given: $\frac{a_{10}}{a_5}=\frac{15}{7}$

$\Rightarrow \frac{{\displaystyle a+9d}}{{\displaystyle a+4d}}=\frac{{\displaystyle 15}}{{\displaystyle 7}}$

$\Rightarrow 7a+63d=15a+60d$

$\Rightarrow 3d=8a$

Also, $S_{10}=390$

$\Rightarrow \frac{10}{2}\left[2a+9d\right]=390$

$\Rightarrow 2a+24a=78$

$\Rightarrow a=3$

$\Rightarrow d=8$

$\Rightarrow S_{15}-S_5=\frac{15}{2}\left(6+14\times 8\right)-\frac{5}{2}\left(6+4\times 8\right)$

$\Rightarrow S_{15}-S_5=\frac{15}{2}\times 118-\frac{5}{2}\times 38$

$\Rightarrow S_{15}-S_5=885-95$

$\Rightarrow S_{15}-S_5=790$