Answer
Oscillates and diverges.
Work Step by Step
The general form of geometric series is written as:
$\Sigma_{n=0}^{\infty} ar^n=a+ar+ar^2+ar^3+.......=\dfrac{a}{1-r}~~~~(1)$
when $|r| \lt 1$, then the sequence converges.
Here, we are given the geometric series $(-2.5)^{n}$
On comparing the above equation with the equation (1), we get
$a=1$ and $r=-2.5$
This implies that the common ratio $|r|=|-2.5| \gt 1$ , so the sequence diverges.
Hence, we conclude that the sequence increase and decrease and the every term of the sequence shows an alternate pattern. This means that the given sequence oscillates and diverges.
