Question

4. In a geometric sequence, ag = 64 and a 10 = 0.25.Use the geometric mean to find the value of ag.3216

Answer 1

We are asked to determine the term between the 8th and 10th terms of the geometric sequence. To do that we need to have into account that in a geometric sequence the term between two given terms is equivalent to the geometric mean of the two terms. The geometric terms between the two terms is given by:

`G_m=\sqrt[]{a_1a_2}`

Replacing the values:

`\begin{gathered} G_m=\sqrt[]{(64)(0.25)}_{} \\ G_m=\sqrt[]{16} \\ G_m=4 \end{gathered}`

Therefore, the 9th term is 4.