Question

use the geometric mean find the 7th term in a geometric sequence if the 6th is term and the 8th term is 32.

Answer 1

please help

Answer 2

\[a_6=a_o r^5\]
\[a_7=a_o r^6\]
\[a_8=a_o r^7\]
a geomtric mean is defined as: given 2 value, m,n, the geoMean is sqrt(nm)

see if we can get the value of a7 from \(\sqrt{a_o r^5 ~a_o r^7}\)

\(\sqrt{(a_o)^2 r^{5+7}}\)

\(a_o\sqrt{r^{12}}\)

\(a_o~r^{12/2}\)

\(a_o~r^{6}\)

seems to work out just fine