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igomit [66]
3 years ago
11

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

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
4 0

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

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