Question

The ratio of $7th$ to the $3rd$ term of an $A.P$ is $12:5$. Find the ratio of $13th$ to the $4th$ term.

Answer 1

$\frac{T_7}{T_3}=\frac{a+6d}{a+2d}=\frac{12}{5}$

$5a+30d=12a+24d$

$6d=7a$ so $a=\frac{6d}{7}$

$\frac{T_{13}}{T_4}=\frac{a+12d}{a+3d}=\frac{6d+84d}{6d+21d}$

$=\frac{90d}{27d}=\frac{10}{3}$.