Answer
Geometric
Sum: $\dfrac{2^{50}-1}{3}$
Work Step by Step
We are given the sequence:
$-1,2,-4,8,....$
Compute the ratio between two consecutive terms:
$\dfrac{2}{-1}=-2$
$\dfrac{-4}{2}=-2$
$\dfrac{8}{-4}=-2$
As the ratio between any consecutive terms is constant, the sequence is geometric.
Its elements are:
$a_1=-1$
$r=-2$
We determine the sum of the first 50 terms:
$S_n=a_1\cdot\dfrac{1-r^n}{1-r}$
$S_{50}=(-1)\cdot\dfrac{1-\left(-2\right)^{50}}{1-(-2)}=\dfrac{2^{50}-1}{3}$
