Question

If ratio of the sum of $n$ terms of $2$ different A.P. is $\frac{3n+2}{4n+23}$, then the ratio of ${10}^{\text{th}}$ term is

• A. $\frac{59}{99}$
• B. $\frac{50}{99}$
• C. $\frac{69}{99}$
• D. $\frac{59}{79}$

Answer 1

The correct option is A $\frac{59}{99}$

Given : $\frac{S_n}{S_n^{\prime }}=\frac{3n+2}{4n+23}$
Putting $n\to 2n-1$, we get
$\Rightarrow \frac{T_n}{T_n^{\prime }}=\frac{3(2n-1)+2}{4(2n-1)+23}\Rightarrow \frac{T_n}{T_n^{\prime }}=\frac{6n-1}{8n+19}\therefore \frac{T_{10}}{T_{10}^{\prime }}=\frac{59}{99}$