Question

If the $10^{th}$ term of an A.P. is $\frac{1}{20}$ and its $20^{th}$ term is $\frac{1}{10}$, then the sum of its first $200$ terms is :

• A. $50\frac{1}{4}$
• B. $100$
• C. $50$
• D. $100\frac{1}{2}$

Answer 1

Answer: (D)

$T_{10}=\frac{1}{20}=a+9d...\left(i\right)$
$T_{20}=\frac{1}{10}=a+19d...\left(ii\right)$
$a=\frac{1}{200}=d$
Hence, $S_{200}=\frac{200}{2}\left[\frac{2}{200}+\frac{199}{200}\right]=\frac{201}{2}$