Question

What is the sum of the geometric sequence -4, 24, -144, if there are 6 terms

Answer 1

Answer:

The sum is $26,660$

Step-by-step explanation:

we know that

The formula of the sum in a geometric sequence is equal to

$S=a1[\frac{1-r^{n}}{1-r}]$

where

a1 is the first term

r is the common ratio  

n is the number of terms

we have

a1=-4, a2=24, a3=-144

Find the value of r (common ratio)

r=a2/a1

r=24/(-4)=-6

so

a1=-1

r=--6

n=6

substitute in the formula

$S=(-4)[\frac{1-(-6)^{6}}{1-(-6)}]$

$S=(-4)[\frac{1-(-6)^{6}}{7}]$

$S=26,660$