If there are 3 geometric means between 4 and 64 then the common ratio is
If there are 3 geometric means between 4 and 64 then the common ratio is
A) 12
B) 15
C) 2
D) 16
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Correct option is (C) 2
Let \(ar,ar^2\;and\;ar^3\) are three geometric means between 4 and 64.
\(\therefore4,ar,ar^2,ar^3,64\) will form a G.P.
\(\therefore ar^4=64\;\&\;a=4\)
\(\Rightarrow4.r^4=64\)
\(\Rightarrow r^4=\frac{64}4\)
\(=16=2^4\)
\(\Rightarrow r=2\)
Hence, common ratio is r = 2.
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