SOLUTION: Find the common ratio, given that it is negative, of a GP whose first term is 8 and whose 5th term is ½.

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Question 1205019: Find the common ratio, given that it is negative, of a GP whose first term is 8 and whose 5th term is ½.
Answer by ikleyn(52788) About Me  (Show Source):
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Find the common ratio, given that it is negative, of a GP whose first term is 8 and whose 5th term is ½.
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Let "r" be the common ratio, which is an unknown value in this problem.


First term of the GP is 8; 5th term is  8%2Ar%5E%285-1%29 = 8%2Ar%5E4, according to the formula
of the n-th term of a GP.


So, 8%2Ar%5E4 = 1%2F2.


Divide both sides bt 8:  r%5E4 = 1%2F16.


Take the root of degree 4 of both sides.  In real numbers, you will get

    r = +/- 1%2F2.


We are given that common ratio value is negative, so from two values 1%2F2 and -1%2F2
we select the ANSWER  r = -1%2F2.

Solved.

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For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.