Answer
Geometric
Sum: $0$
Work Step by Step
We are given the sequence:
$\{(-1)^n\}$
Compute the ratio between two consecutive terms:
$\dfrac{a_{k+1}}{a_k}=\dfrac{(-1)^{k+1}}{(-1)^k}=-1$
As the ratio between any consecutive terms is constant, the sequence is geometric.
Its elements are:
$a_1=(-1)^1=-1$
$r=-1$
We determine the sum of the first 50 terms:
$S_n=a_1\cdot\dfrac{1-r^n}{1-r}$
$S_{50}=(-1)\cdot\dfrac{1-\left(-1\right)^{50}}{1-(-1)}=0$