SOLUTION: The first term of a geometric progession is 75 and the third term is 27.Find the two possible values for the fourth term.

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Question 1186566: The first term of a geometric progession is 75 and the third term is 27.Find the two possible values for the fourth term.
Answer by ikleyn(52894) About Me  (Show Source):
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The first term of a geometric progession is 75 and the third term is 27.
Find the two possible values for the fourth term.
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Take the ratio  a%5B3%5D  to  a%5B1%5D  and get the square of the common ratio

    a%5B3%5D%2Fa%5B1%5D = r%5E2 = 27%2F75 = 9%2F25.


THEREFORE,  for the common ratio "r", you have two values  r = sqrt%289%2F25%29 = +/- 3%2F5.


It gives two possible values for the fourth term


    a%5B4%5D = a%5B3%5D%2Ar = 27%2A%283%2F5%29 = 81%2F5,  if  r = 3%2F5,

and


    a%5B4%5D = a%5B3%5D%2Ar = 27%2A%28-3%2F5%29 = -81%2F5,  if  r = -3%2F5.

Solved.