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Q.

Suppose $a_{1}, a_{2}, 2, a_{3}, a_{4}$ be in an arithmetic geometric progression. If the common ratio of the corresponding geometric progression is 2 and the sum of all terms of the arithmetico geometric progression is $\frac{49}{2}$ then a₄ equal to_____

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answer is 16.

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Detailed Solution

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$Let terms be \frac{a - 2 d}{r^{2}}, \frac{a - d}{r}, a, (a + d) r, (a + 2 d) r^{2} a = 2 \begin{array}{l} \frac{2 - 2 d}{4} + \frac{2 - d}{2} + 2 + (2 + d) 2 + (2 + 2 d) 4 = \frac{49}{2} \\ ∴ d = 1 \\ a_{4} = (2 + 2) \times 4 = 16 \end{array}$

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Suppose a1,a2,2,a3,a4 be in an arithmetic geometric progression. If the common ratio of the corresponding geometric progression is 2 and the sum of all terms of the arithmetico geometric progression is 492 then a4 equal to_____