Answer
In order for a sequence to be geometric, the quotient of all consecutive terms must be constant.
Hence here: $\frac{a_{n+1}}{a_n}=\frac{(-5)^{n+1}}{(-5)^n}=-5$, thus it is a geometric sequence.
$a_1=-5$
$a_2=25$
$a_3=-125$
$a_4=625$
Work Step by Step
In order for a sequence to be geometric, the quotient of all consecutive terms must be constant.
Hence here: $\frac{a_{n+1}}{a_n}=\frac{(-5)^{n+1}}{(-5)^n}=-5$, thus it is a geometric sequence.
$a_1=(-5)^1=-5$
$a_2=(-5)^2=25$
$a_3=(-5)^3=-125$
$a_4=(-5)^4=625$
