Answer
$\pm \frac{4}{15}$
Work Step by Step
The middle term of three consecutive terms of a geometric sequence can be found using the geometric mean formula:
geometric mean = $\sqrt {\frac{2}{5} \bullet \frac{8}{45}}$
Multiply terms within the radicand first:
geometric mean = $\sqrt {\frac{16}{225}}$
Take the square root:
geometric mean = $\frac{4}{15}$
The missing term could be either the geometric mean or its opposite, so we need to include both positive and negative values:
missing term = $\pm \frac{4}{15}$
