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If $3^{2 \sin 2 θ - 1}, 14, 3^{4 - 2 \sin 2 θ}$ are first three terms of an A.P., then its fifth term is given by

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Detailed Solution

We have $\frac{t}{3} + \frac{81}{t} = 28$ where $t = 3^{2 \sin 2 θ}$

$\Rightarrow t^{2} - 84 t + 243 = 0 \Rightarrow t = 3, 81$

But $1 / 9 \leq t \leq 9$ . Thus, $t = 3 .$

$∴ a_{1} = 1, d = 13 \Rightarrow a_{5} = a_{1} + 4 d = 53$

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