boggsgrace90 boggsgrace90
  • 25-01-2019
  • Mathematics
contestada

What is the sum of the geometric sequence −4, 24, −144, ... if there are 8 terms?

Respuesta :

rejkjavik rejkjavik
  • 25-01-2019

Answer:

The sum of 8 geometric sequence is 959780

Step-by-step explanation:

We are given

this sequence is geometric

-4 , 24 , -144

First term is -4

so, [tex]a_1=-4[/tex]

now, we can find common ratio

[tex]r=\frac{24}{-4}=-6[/tex]

we can use formula

[tex]S_n=a_1(\frac{1-r^n}{1-r} )[/tex]

n=8

now, we can plug values

[tex]S_8=-4(\frac{1-(-6)^{8}}{1+6} )[/tex]

now, we can simplify it

and we get

[tex]S_8=959780[/tex]

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