Let a 1 , a 2 , a 3 , … be a G.P. of increasing positive terms such that a 2 · a 3 · a 4 = 64 and a 1 + a 3 + a 5 = 813 7 . Then a 3 + a 5 + a 7 is equal to: [2026}

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Solution

Q.
Let $a_{1}, a_{2}, a_{3}, \dots$ be a G.P. of increasing positive terms such that $a_{2} \cdot a_{3} \cdot a_{4} = 64 and a_{1} + a_{3} + a_{5} = \frac{813}{7} .$ Then $a_{3} + a_{5} + a_{7}$ is equal to: [2026]

1 3256

2 3244

3 3248

4 3252

Ans.
(4)

$a r \cdot a r^{2} \cdot a r^{3} = 64$

$a^{3} r^{6} = 64 \Rightarrow a r^{2} = 4$

$a + a r^{2} + a r^{4} = \frac{813}{7}$

$r^{2} = 28$

$a r^{2} + a r^{4} + a r^{6} = ?$

$a r^{2} (1 + r^{2} + r^{4}) = 4 (1 + 28 + 784) = 3252$

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