# The first term of a geometric sequence is 4 and the multiplier, or ratio, is –2. What is the sum of the first 5 terms of the sequence?

##### 2 Answers

Aug 4, 2018

#### Explanation:

#"the sum to n terms of 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"#

#"here "a=4" and "r=-2#

#S_5=(4((-2)^5-1))/(-2-1)#

#color(white)(S_5)=(4(-32-1))/(-3)=(-132)/(-3)=44#

#"Alternatively"#

#"listing the first five terms of the sequence"#

#4,-8,16,-32,64#

#S_5=4-8+16-32+64=44#

Aug 4, 2018

#### Explanation:

The sum of first

#color(blue)(S_n=(a_1(1-r^n))/(1-r)#

Where ,

We have ,

So, the sum of first