Question

The ratio of the sum of first $n$ terms of two APs is $(7n+1):(4n+27)$. Find the ratio of their $mth$ terms.

Answer 1

$\frac{\frac{n}{2}\left[2a_1+\left(n-1\right)d_1\right]}{\frac{n}{2}\left[2a_2+\left(n-1\right)d_2\right]}=\frac{7n+1}{4n+27}$

$\frac{2a_1+\left(n-1\right)d_1}{2a_2+\left(n-1\right)d_2}=\frac{7n+1}{4n+27}$

if $n=17$

$\frac{2a_1+16d_1}{2a_2+16d_2}=\frac{120}{95}=\frac{24}{19}$

$\frac{a_1+8d_1}{a_2+8d_2}=\frac{24}{19}$