Question 448476
<pre>
7th term = (6th term)*r
8th term = (7th term)*r

a<sub>7</sub> = a<sub>6</sub>*r
a<sub>8</sub> = a<sub>7</sub>*r

a<sub>7</sub> = 8*r
8 = a<sub>7</sub>*r

Substitute 8*r for a<sub>7</sub> 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:

a<sub>7</sub> = 8*(±1)

So a<sub>7</sub> 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(xy) = sqrt(8*8)=sqrt(8^2)=8}}}

You'll have to ask your teacher.

Edwin</pre>