Question

In a geometric sequence, a5=8 and a7=32. use the geometric mean to find the value of a6.

Answer 1

since a5, a6 and a7 are geometric progression
therefore
\[a_6^2= a_5 \times a_7 \]
\[a_6^2= 8 \times 32 =256 \rightarrow a_6= \sqrt{256}\]
\[a_6= \pm16\]
since 8 and 32 are positive numbers
therefore \[a_6= 16\]

Answer 2

thank you! @dpasingh