Question:
If the $10^{\text {th }}$ term of an A.P. is $\frac{1}{20}$ and its $20^{\text {th }}$ term is $\frac{1}{10}$, then the sum of its first 200 terms is:
Correct Option: , 4
Solution:
$T_{10}=\frac{1}{20}=a+9 d$...(i)
$T_{20}=\frac{1}{10}=a+19 d$...(ii)
Solving equations (i) and (ii), we get
$a=\frac{1}{200}, d=\frac{1}{200}$
$\Rightarrow \quad S_{200}=\frac{200}{2}\left[\frac{2}{200}+\frac{199}{200}\right]=\frac{201}{2}=100 \frac{1}{2}$