SOLUTION: if the value of A1= 1/2 and A9=64. what is the value of r in geometric sequence

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Question 979571: if the value of A1= 1/2 and A9=64. what is the value of r in geometric sequence
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!

Since we are given the geometric progression,  we have

a%5B1%5D = 1%2F2,

a%5B9%5D = a%5B1%5D%2Ar%5E%289-1%29 = a%5B1%5D%2Ar%5E8 = 64,

where  r  is the  common ratio  of the progression.

It implies that  r%5E8 = a%5B9%5D%2Fa%5B1%5D = 64:1%2F2 = 128 = 2%5E7.


Hence,  r = root%288%2C+2%5E7%29 = 2%5E%287%2F8%29 = 2^(7/8).