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8. Sequences and Series
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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
A
$50 \frac{1}{4}$
B
$100 \frac{1}{2}$
C
$50$
D
$100$
(JEE MAIN-2020)
Solution
$\mathrm{T}_{10}=\frac{1}{20}=\mathrm{a}+9 \mathrm{d}\quad \ldots .(\text {i})$
$\mathrm{T}_{20}=\frac{1}{10}=\mathrm{a}+19 \mathrm{d} \quad \ldots .(\text {ii})$
$a=\frac{1}{200}=d$
Hence, $S_{200}=\frac{200}{2}\left[\frac{2}{200}+\frac{199}{200}\right]=\frac{201}{2}$
Standard 11
Mathematics
