A series can be an arithmetic series or geometric series
The series is undefined
The given parameters about the geometric series are:
a1 = -2 --- the first term
r=-2 --- the common ratio
Sn=22 --- the sum of n terms
The sum of n terms of a geometric series is represented as:
[tex]S_n = \frac{a(r^n - 1)}{(r-1)}[/tex]
Substitute known values
[tex]22 = \frac{-2((-2)^n -1)}{(-2-1)}[/tex]
This gives
[tex]22 = \frac{-2((-2)^n -1)}{(-3)}[/tex]
Divide both sides by -2
[tex]-11 = \frac{((-2)^n -1)}{(-3)}[/tex]
Multiply both sides by -3
[tex]33 = (-2)^n -1[/tex]
Add 1 to both sides
[tex](-2)^n = 34[/tex]
Take the natural logarithm of both sides
[tex]n\ln(-2) = \ln(34)[/tex]
Solve for n
[tex]n= \frac{\ln(34)}{\ln(-2) }[/tex]
The above number is a complex number.
Hence, the series is undefined
Read more about geometric series at:
https://brainly.com/question/12006112
