If the product of five numbers in G.P is 1024, then the middle number is
If the product of five numbers in G.P is 1024, then the middle number is
A) 2
B) 8
C) 4
D) 16
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Correct option is (C) 4
Let \(\frac a{r^2},\frac ar,a,ar,ar^2\) be required 5 numbers in G.P.
Given that product of these 5 numbers is 1024.
\(\therefore\) \(\frac a{r^2}.\frac ar.a.ar.ar^2=1024\)
\(\Rightarrow a^5=1024=2^{10}\)
\(=(2^2)^5=4^5\)
\(\Rightarrow\) a = 4
Hence, middle number is a = 4.
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