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  4. The two geometric means between the numbers 1 and 64 are:

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Q. The two geometric means between the numbers 1 and 64 are:

KEAMKEAM 2002

Solution:

Let the GP series be $ 1,{{G}_{1}},{{G}_{2}},64 $ Here, $ a=1,\text{ }n=4,\text{ }l=64 $ $ \therefore $ $ 64={{(r)}^{3}} $ $ \Rightarrow $ $ r=4 $ $ \therefore $ $ {{G}_{1}}=4 $ and $ {{G}_{2}}={{1.4}^{2}}=16 $