If the product of five numbers in GP is 1024, then the middle number is
If the product of five numbers in GP is 1024, then the middle number is
A) 8
B) 4
C) 2
D) None
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Correct option is (B) 4
Let \(\frac a{r^2},\frac ar,a,ar,ar^2\) are required five numbers in G.P.
\(\therefore\) Their product = 1024
\(\Rightarrow\frac a{r^2}.\frac ar.a.ar.ar^2=1024\)
\(\Rightarrow a^5=1024=2^{10}\)
\(=(2^2)^5=4^5\)
\(\therefore a=4\)
Hence, the middle number is 4.
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