Question

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

Answer 1

$\frac{7_7}{7_3}=\frac{a+6d}{a+2d}=\frac{12}{5}$

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

$\Rightarrow 6d=7a$

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

$\Rightarrow \frac{7_{13}}{7_4}=\frac{a+12d}{a+3d}=\frac{a+12\frac{7a}{6}}{a+3\frac{7a}{6}}$

$\frac{7_{13}}{7_4}=\frac{6a+84a}{6a+21a}=\frac{90d}{27d}=\frac{10}{3}$