SOLUTION: Use the geometric mean to find the 7th term in a geometric sequence if the 6th term is 8 and the 8th term is 8

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Question 448476: Use the geometric mean to find the 7th term in a geometric sequence if the 6th term is 8 and the 8th term is 8
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
7th term = (6th term)*r
8th term = (7th term)*r

a7 = a6*r
a8 = a7*r

a7 = 8*r
8 = a7*r

Substitute 8*r for a7 in the second equation:

8 = (8*r)*r
8 = 8rČ
Divide through by 8
 1 = rČ
rČ = 1
 r = ±1

So there are two solutions:

a7 = 8*(±1)

So a7 is either 8 or -8.

Maybe your teacher only wanted the positive solution.
You'll have to ask.

Or maybe your teacher wanted you to just use the formula
for the geometric mean:

geometric_mean_of_x_and_y+=+sqrt%28xy%29+=+sqrt%288%2A8%29=sqrt%288%5E2%29=8

You'll have to ask your teacher.

Edwin