Question

In an AP, $a_3=15$ $S_{10}=125$

Find $(d\times a_{10}{)}^2$

Answer 1

$a_3=15,$ $a+2d=15.$

$S_{10}=125$

$S_{10}=$ $\frac{10}{2}[2a+9d]=1252a+9d=25a+\frac{9}{2}d=\frac{25}{2}$

$a+\frac{9d}{2}=\frac{25}{2}a+2d=15$

$\frac{5d}{2}=-\frac{5}{2}d=-1,a=17.$

$a_{10}=a+9d=17-9=8$

${(d\times a_{10})}^2={(-1\times 8)}^2=64$