SOLUTION: if the 3rd term of a G.P. is the square of its first term and its 5th term is 64, find its first term and the common ration.

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Question 401429: if the 3rd term of a G.P. is the square of its first term and its 5th term is 64, find its first term and the common ration.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B3%5D+=+a%5B1%5D%2Ar%5E2+=+%28a%5B1%5D%29%5E2==> a%5B1%5D++=r%5E2.
Now a%5B5%5D+=+a%5B1%5D%2Ar%5E4+=+64==> r%5E2%2Ar%5E4+=+r%5E6+=+64 ==> r = -2, 2.
==> a%5B1%5D+=+4.
Incidentally there are two G.P.'s that satisfy the initial conditions.