JEE Mains · Maths · STD 11 - 8. sequence and series
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 \(100\)
Answer & Solution
Correct Answer
(B) \(100 \frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{T}_{10}=\frac{1}{20}=\mathrm{a}+9 \mathrm{d}\quad \ldots .(\text {i})\) \(\mathrm{T}_{20}=\frac{1}{10}=\mathrm{a}+19 \mathrm{d} \quad \ldots .(\text {ii})\) \(a=\frac{1}{200}=d\) Hence, \(S_{200}=\frac{200}{2}\left[\frac{2}{200}+\frac{199}{200}\right]=\frac{201}{2}\)
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