Respuesta :
You can use two methods. First is to calculate the answer manually since summation is only of 4 terms. Second is to use the formula for evaluating geometric series.
The sum of given geometric series is given by:
Option C: 40
What is a geometric series and what is its sum expressed as?
A geometric series is sum of terms which are multiple of previous terms with factor as single unique constant used in whole series.
For example,
[tex]a + a \times r + a \times r \times r + a \times r \times r \times r[/tex] is a geometric series since each next series is r times the previous series(assuming r is constant).
Sum of such series with product constant 'r' and initial term 'a' till n terms is given by:
[tex]S_n = \dfrac{a(1-r^n)}{1-r}[/tex]
How to apply the formula of sum of geometric series in given series?
The given series is [tex]S = \sum_{n=1}^4 (-2)(-3)^{n-1}[/tex]
The first term of this series is -2 times -3 raised to the power of 0 which results to -2, thus, a= -2
It is clearly visible that each term will have one more -3 multiplied in comparison to previous term. Thus, r = -3
Since there will be 4 sum in the series, thus n = 4
Putting these values in the formula for sum of geometric series, we get:
[tex]S_4 = \dfrac{(-2)(1-(-3)^4)}{1-(-3)} = \dfrac{-2 \times -80}{4} = 40[/tex]
Thus, the sum of given geometric series is 40.
We can manually check this by:
S = -2 + 6 - 18 + 54 = 40
Thus, Option C: 40 is correct.
Learn more about sum of geometric series here:
https://brainly.com/question/2501276
