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a1 = -2 r=-2 Sn=22 Determine the number of terms of n in the series

Sagot :

MrRoyalidn

A series can be an arithmetic series or geometric series

The series is undefined

How to determine the number of terms?

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

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