ANSWER:
4th option: -5208
STEP-BY-STEP EXPLANATION:
A geometric sequence is formed by multiplying a term by a number called the common ratio r to get the next term. The formula for a sum of a geometric sequence is:
[tex]S_n=\frac{a_1\left(1-r^n\right)}{1-r}[/tex]
Where a1 is the first term, r is the commom ratio, and n is the number of the term.
The value of r is found as follows:
[tex]r=\frac{-10}{2}=\frac{50}{-10}=-5[/tex]
We substitute in the main formula, like this:
[tex]\begin{gathered} S_n=\frac{2\cdot\left(1-\left(-5\right)^6\right?}{1-\left(-5\right)}=\frac{2\cdot\left(1-15625\right)}{1+5}=\frac{2\cdot\left(-15624\right)}{6} \\ S_n=-5208 \end{gathered}[/tex]
The sum of the geometric series is equal to -5208
