Question

If the ratio of sum of m terms and n terms of an A.P. is $m^2$:$n^2$, then the ratio of its $m^{th}$ and $n^{th}$ terms will be

• A. 2m -1 : 2n - 1
• B. m : n
• C. 2m + 1 : 2n + 1
• D. none

Answer 1

The correct option is A

2m -1 : 2n - 1

$\frac{S_m}{S_n}$ = $\frac{m^2}{n^2}$ = $\frac{S_m}{m^2}$ - $\frac{S_n}{n^2}$ = k(say)

$\frac{T_m}{T_n}$ = $\frac{S_m-S_{m-1}}{S_n-Sn-1}$ = $\frac{k[m^2-(m-1{)}^2]}{k[n^2-(n-1{)}^2]}$ = $\frac{2m-1}{2n-1}$