Question

If a, x, and b are consecutive terms of a geometric sequence, then x is called the geometric mean of a and b. Find the geometric mean of 2 and 8.

Answer 1

geometric mean is
\[\sqrt{ab}\]

Answer 2

I thought it had the formula tn = ar^n-1

Answer 3

so in your case it would be
\[\sqrt{2\times 8}=\sqrt{16}=4\]

Answer 4

if you have a geometric sequence
\[2,2r, 2r^2,...\] and you know that
\[2r^2=8\] that means
\[r^2=4\]
\[r=2\] and so the middle term
\[2r=4\]

Answer 5

ohhh, i see. thanks!

Answer 6

yw