Find r and a1 for the geometric sequence: a3 = 5, a8 = 1/625

johnathanpbICa

johnathanpbICa

Answered question

2022-11-23

Find r and a1 for the geometric sequence: a3 = 5, a8 = 1/625

Answer & Explanation

Charlize Hendricks

Charlize Hendricks

Beginner2022-11-24Added 8 answers

For a geometric series:
XXX a m = a n r n - m

We will use this general formula in two forms
XXX a 8 = a 3 r 5
and
XXX a 1 = a 3 r - 2

We are told a 8 = 1 625 and a 3 = 5
Therefore
XXX 1 625 = 5 r 5

XXX r 5 = 1 5 625 = 1 5 5 4 = 1 5 5

XXX r = 1 5

and since a 1 = a 3 r - 2
XXX a 1 = 5 ( 1 5 ) - 2 = 5 5 2 = 125

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