JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(S_{n}\) be the sum of the first \(n\) terms of an arithmetic progression. If \(S_{3 n}=3 S_{2 n}\), then the value of \(\frac{S_{4 n}}{S_{2 n}}\) is:
- A \(4\)
- B \(6\)
- C \(8\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(6\)
Step-by-step Solution
Detailed explanation
Let a be first term and \(d\) be common diff. of this A.P. Given \(\mathrm{S}_{3 \mathrm{n}}=3 \mathrm{~S}_{2 \mathrm{n}}\) \(\Rightarrow \frac{3 n}{2}[2 a+(3 n-1) d]=3 \frac{2 n}{2}[2 a+(2 n-1) d]\) \(\Rightarrow 2 a+(3 n-1) d=4 a+(4 n-2) d\) \(\Rightarrow 2 a+(n-1) d=0\)…
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