Mathematics - Sequence & Series Question with Solution | TestHub

$$\begin{array}{rl}& \frac{\frac{p}{2}\left[2a_1+(p-1)d\right]}{\frac{q}{2}\left[2a_1+(q-1)d\right]}=\frac{p^2}{q^2}\Rightarrow \frac{2a_1+(p-1)d}{2a_1+(q-1)d}=\frac{p}{q}\\ & \frac{a_1+\left(\frac{p-1}{2}\right)d}{a_1+\left(\frac{q-1}{2}\right)d}=\frac{p}{q}\end{array}$$ For $\frac{a_6}{a_{21}},p=11,q=41\to \frac{a_6}{a_{21}}=\frac{11}{41}$