If five geometric means are inserted between 8 and 5832, the fifth term in the geometric series is:

648

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832

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1168

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1944

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Solution

The correct option is A 648
Denote the terms in the geometric progression by
$a_{1} = 8, a_{2} = 8 r, . . . . . . ., a_{7} = 8 r^{6}$ = 5832.
$∴ r^{6} = 729;$
$∴ r = 3$ and $a_{5} = 8 r^{4}$ = 648

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