Respuesta :
Answer:
See below.
Step-by-step explanation:
The common ratio = -10/4 = -5/2 and the first term is 4.
The sigma notation is:
n=6
∑ 4(-5/2)^n-1. (answer).
n=1
Answer:
[tex]\sum_{n=1}^{n=6} 4(\frac{-5}{2} )^{n-1}[/tex]
Step-by-step explanation:
We are given the geometric series [tex]4 + -10+ 25+ -62.5+ 156.25+ -390.625[/tex]
General geometric series is of the form
[tex]a, ar, ar^2, ar^3, ar^4,\text{ and so on}[/tex], where a is the first term and r is the common ration.
The common ratio for given geometric series is [tex]\frac{\text{Second Term}}{\text{First Term}}[/tex] = [tex]\frac{-10}{4} = \frac{-5}{2}[/tex]
[tex]a = 4\\r = \frac{-5}{2}[/tex]
To write the series in summation form we use:
[tex]\sum_{k=0}^{k=n} a(r)^{k}[/tex]
Thus, the given geometric series is
[tex]\sum_{n=1}^{n=6} 4(\frac{-5}{2} )^{n-1}[/tex]
