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Question
If each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.
Solution
Let a1, a2, a3, ................., an, .......... be a G.P. with common ratio r.
`=> (a_(n + 1))/a_n = r` for all n ∈ N
If each term of a G.P. is raised to the power x, we get the sequence `a_1^x, a_2^x, a_3^x, ............, a_n^x,.........`
Now, `(a_(n + 1))^x/(a_n)^x = ((a_(n + 1))/a_n)^x = r^x` for all n ∈ N
Hence, `a_1^x, a_2^x, a_3^x, ............, a_n^x,.........` is also a G.P.
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