Question

If the ratio of the sum of the first $n$ terms of two APs is $(7n+1):(4n+27)$ then find the ratio of their 9th terms.

• A. $\frac{24}{19}$
• B. $\frac{2}{19}$
• C. $\frac{4}{19}$
• D. $-\frac{24}{19}$

Answer 1

Answer: (A)

$\frac{24}{19}$

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

(1) __$\frac{a_1+\frac{(n-1)}{2}{d}_1}{a_2+\frac{(n-1)}{2}{d}_2}=\frac{7n+1}{4n+27}$

We need to find ratio of their $q^{th}$ term

i.e $\frac{a_1+8d_1}{a_2+8d_2}$ __(2)

on comparing (1) & (2)

$\frac{n-1}{2}=8\Rightarrow n-1=16$

$n=17$

$\frac{a_1+8d_1}{a_2+8d_2}=\frac{7.17+1}{4.17+27}=\frac{119+1}{68+27}=\frac{120}{95}=\frac{24}{19}$