If the ratio between the sums of $n$ terms of two

A.P. $\text{'}s$ is $3n+8:7n+15$ then the ratio between their 12th terms is

If the ratio of the sums of n terms two arithmetic progressions is given, then the ratio of their $n^{th}$ terms is - obtained by replacing n by $(2n -1)$ in the ratio of the sums of $n$ terms.

Here, we have

Ratio o. the sums of $n$ terms $=\frac{3n+8}{7n+15}$

$\therefore$ Ratio of $n^{th}$ terms $=\frac{3(2n-1)+8}{7(2n-1)+15}=\frac{6n+5}{14n+8}$

$\Rightarrow$ Ratio of ${12}^{th}$ terms $=\frac{6\times 12+5}{14\times 12+8}=\frac{77}{176}=\frac{7}{16}$