Question

If the ratio of the ${11}^{th}$ term of an A.P to its ${18}^{th}$ term is $2:3$, find the ratio of the sum of the first five terms to the sum of its first $10$ terms.

• A. $5:16$
• B. $6:17$
• C. $5:6$
• D. $6:19$

Answer 1

Answer: (B)

$6:17$

$\frac{T_{11}}{T_{18}}=\frac{a+10d}{a+17d}=\frac{2}{3}$

$\Rightarrow a=4d$

$\frac{S_5}{S_{10}}=\frac{\frac{5}{2}(2a+(5-1\left)d\right)}{\frac{10}{2}(2a+(10-1\left)d\right)}=\frac{12d}{2\times 17d}=\frac{6}{17}$