JEE PYQ: Sequence And Series Question 41
Question 41 - 2020 (08 Jan Shift 2)
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:
(1) 50
(2) $50\frac{1}{4}$
(3) 100
(4) $100\frac{1}{2}$
Show Answer
Answer: (4)
Solution
$T_{10} = \frac{1}{20} = a + 9d$ …(i)
$T_{20} = \frac{1}{10} = a + 19d$ …(ii)
Solving equations (i) and (ii), we get
$a = \frac{1}{200}, d = \frac{1}{200}$
$\Rightarrow S_{200} = \frac{200}{2}\left[\frac{2}{200} + \frac{199}{200}\right] = \frac{201}{2} = 100\frac{1}{2}$
BETA
