# What is the sum of the geometric sequence -3, 18, -108, … if there are 7 terms?

##### 3 Answers

#### Explanation:

#"the sum to n terms for a geometric sequence is"#

#•color(white)(x)S_n=(a(r^(n-1)))/(r-1)#

#"where a is the first term and r the common ratio"#

#a=-3" and "r=(-108)/18=18/(-3)=-6#

#S_7=(-3((-6)^7-1))/(-6-1)#

#color(white)(xx)=(-3(-279936-1))/(-7)#

#color(white)(xx)=(-3xx-279937)/(-7)=-19973#

#### Explanation:

Here,

Let ,first term

common ratio

So, the sum of first n terms is:

-119973

#### Explanation:

We can first see that the ratio between these is