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If Each Term of a G.P. is Raised to the Power X, Show that the Resulting Sequence is Also a G.P. - Mathematics

Sum

If each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.

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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.

Concept: Simple Applications - Geometric Progression
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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 11 Geometric Progression
Exercise 11 (C) | Q 6 | Page 156
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