Find the Sum of the Series -2 , 6 , -18 , 54 , -162

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by ${\displaystyle -3}$ gives the next term. In other words, ${\displaystyle a_n=a_1{r}^{n-1}}$.

Geometric Sequence: ${\displaystyle r=-3}$

This is the form of a geometric sequence.

Substitute in the values of ${\displaystyle a_1=-2}$ and ${\displaystyle r=-3}$.

This is the formula to find the sum of the first ${\displaystyle n}$ terms of the geometric sequence. To evaluate it, find the values of ${\displaystyle r}$ and ${\displaystyle a_1}$.

Replace the variables with the known values to find ${\displaystyle S_5}$.