Question

If the ratio of the sum to n terms of two A.P.'s is $(5n+3):(3n+4)$. Then the ratio of their ${17}^{th}$ terms is

• A. 172:99
• B. 168:103
• C. 175:99
• D. 171:103

Answer 1

The correct option is B

168:103

$\frac{\frac{n}{2}(2a+(n-1\left)d\right)}{\frac{n}{2}(2a^{\prime }+(n-1\left)d^{\prime }\right)}=\frac{5n+3}{3n+4}$

$\Rightarrow \frac{(2a+(2n-1\left)d\right)}{(2a^{\prime }+(2n-1\left)d^{\prime }\right)}=\frac{5(2n-1)+3}{5(2n-1)+4}$(replace n by 2n-1)

$\Rightarrow \frac{(a+(n-1\left)d\right)}{(a^{\prime }+(n-1\left)d^{\prime }\right)}=\frac{10n-2}{6n+1}$

$\Rightarrow \frac{(a+(17-1\left)d\right)}{(a^{\prime }+(17-1\left)d^{\prime }\right)}=\frac{168}{103}$