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JEE Mains · Maths · STD 11 - 8. sequence and series
If \(3^{2 \sin 2 \alpha-1},14\) and \(3^{4-2 \sin 2 \alpha}\) are the first three terms of an \(A.P.\) for some \(\alpha\), then the sixth term of this \(A.P.\) is
- A \(66\)
- B \(65\)
- C \(81\)
- D \(78\)
Answer & Solution
Correct Answer
(A) \(66\)
Step-by-step Solution
Detailed explanation
Given that \(3^{4-\sin 2 \alpha}+3^{2 \sin 2 \alpha-1}=28\) Let \(3^{2} \sin 2 \alpha=t\) \(\frac{81}{t}+\frac{t}{3}=28\) \(t=81,3\) \(3^{2 \sin 2 \alpha}=3^{1}, 3^{4}\) \(2 \sin 2 \alpha=1,4\) \(\sin 2 \alpha=\frac{1}{2}, 2(\) rejected \()\) First term…
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