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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.
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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.
RELATED QUESTIONS
Find the 9th term of the series :
1, 4, 16, 64, ...............
Find the third term from the end of the G.P.
`2/27, 2/9, 2/3, .........,162.`
For the G.P. `1/27, 1/9, 1/3, ........., 81`; find the product of fourth term from the beginning and the fourth term from the end.
Q 7
If a, b and c are in G.P., prove that : log a, log b and log c are in A.P.
If a, b and c are in A.P. and also in G.P., show that : a = b = c.
Find the geometric mean between `4/9` and `9/4`
Q 8
The first term of a G.P. is –3 and the square of the second term is equal to its 4th term. Find its 7th term.
Find a G.P. for which the sum of first two terms is – 4 and the fifth term is 4 times the third term.
