JEE Mains · Maths · STD 11 - 8. sequence and series
Let the sum of an infinite \(G.P.\), whose first term is \(a\) and the common ratio is \(r\), be \(5\). Let the sum of its first five terms be \(\frac{98}{25}\). Then the sum of the first \(21\) terms of an \(AP\), whose first term is \(10\,ar , n ^{\text {th }}\) term is \(a_{n}\) and the common difference is \(10{a r^{2}}\), is equal to.
- A \(21\,a _{11}\)
- B \(22 a _{11}\)
- C \(15 a _{16}\)
- D \(14 a_{16}\)
Answer & Solution
Correct Answer
(A) \(21\,a _{11}\)
Step-by-step Solution
Detailed explanation
\(S _{21}=\frac{21}{2}\left[20 ar +20.10\,ar ^{2}\right]\) \(=21\left[10\,ar +100\,ar ^{2}\right]\) \(=21 . a _{11}\)
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