1. Tardigrade
  2. Question
  3. Mathematics
  4. If the 10th term of an A.P. is (1/20) and its 20th term is (1/10), then the sum of its first 200 terms is :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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 :

JEE MainJEE Main 2020Sequences and Series

Solution:

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