Mathematics - Sequence & Series Question with Solution | TestHub

$\begin{array}{rl}& \frac{a_1+a_2+a_3+\dots \dots +a_p}{a_1+a_2+a_3+\dots \dots +a_q}=\frac{p^3}{q^3}\\ \Rightarrow & \frac{a_1+a_2}{a_1}=\frac{8}{1}\Rightarrow a_1+\left(a_1+d\right)=8a_1\\ \Rightarrow & d=6a_1\\ & \text{ Now }\frac{a_6}{a_{21}}=\frac{a_1+5d}{a_1+20d}\\ =& \frac{a_1+5\times 6a_1}{a_1+20\times 6a_1}=\frac{1+30}{1+120}=\frac{31}{121}\end{array}$