SOLUTION: The 3rd term of a G.P is 360 and the 6th term is 1215.Find the 1st term and the common ratio

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Question 760241: The 3rd term of a G.P is 360 and the 6th term is 1215.Find the 1st term and the common ratio
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
DEFINITIONS: b%5B1%5D = first term, and r = common ratio
FORMULAS: b%5Bn%5D=r%2Ab%5Bn-1%5D and b%5Bn%5D=b%5B1%5D%2Ar%5E%28n-1%29

So b%5B3%5D=b%5B1%5D%2Ar%5E2, and b%5B6%5D=b%5B1%5D%2Ar%5E5.
Then b%5B6%5D%2Fb%5B3%5D=b%5B1%5D%2Ar%5E5%2Fb%5B1%5D%2Fr%5E2 --> b%5B6%5D%2Fb%5B3%5D=r%5E5%2Fr%5E2 --> b%5B6%5D%2Fb%5B3%5D=r%5E3

system%28b%5B6%5D%2Fb%5B3%5D=r%5E3%2Cb%5B6%5D%2Fb%5B3%5D=%283%2F2%29%5E3%29 --> highlight%28r=3%2F2%29

system%28b%5B3%5D=360%2Cb%5B3%5D=b%5B1%5D%2Ar%5E2%2Cr=3%2F2%29 --> 360=b%5B1%5D%2A%283%2F2%29%5E2 --> 360=b%5B1%5D%2A%289%2F4%29 --> b%5B1%5D=360%2A%284%2F9%29 --> highlight%28b%5B1%5D=160%29