The geometric series which result in a sum of -69,905 is: D. [tex]\sum^{9}_{k=0} -\frac{1}{5} (4)^k[/tex]
The standard form of a geometric series.
Mathematically, the standard form of a geometric series can be represented by the following expression:
[tex]\sum^{n-1}_{k=0}a_1(r)^k[/tex]
Where:
- a₁ is the first term of a geometric series.
Also, the sum of a geometric series is given by:
[tex]S=\frac{a_1(1-r^n)}{1-r}[/tex]
For option A, we have:
r = -5, n = 8, a₁ = 1/4 = 0.25
[tex]S=\frac{0.25(1-(-5)^8)}{1-(-5)}[/tex]
S = -24,414.
For option B, we have:
r = 5, n = 12, a₁ = -1/4 = -0.25
[tex]S=\frac{-0.25(1- 5)^{12})}{1-5}[/tex]
S = -15,258789.
For option C, we have:
r = -4, n = 11, a₁ = 1/5 = 0.2
[tex]S=\frac{0.2(1-(-4)^{11})}{1-(-4)}[/tex]
S = -279,620.
For option D, we have:
r = 4, n = 10, a₁ = -1/5 = -0.2
[tex]S=\frac{-0.2(1-4^{10})}{1-4}[/tex]
S = -69,905.
In conclusion, the geometric series which result in a sum of -69,905 is [tex]\sum^{9}_{k=0} -\frac{1}{5} (4)^k[/tex]
Read more on geometric series here: brainly.com/question/12630565
#SPJ1
