Answer:
[tex]a_n= 4(-5)^{(n-1)}[/tex]
-10416
Step-by-step explanation:
a = 4
r = -5
geometric series: [tex]a_n=ar^{(n-1)} = 4(-5)^{(n-1)}[/tex]
Determine which term = -12500:
[tex]a_n=-12500[/tex]
[tex]4(-5)^{(n-1)}=-12500[/tex]
[tex](-5)^{(n-1)} = -3125[/tex]
[tex](5)^{(n-1)} = 3125[/tex]
[tex](n-1)ln(5) = ln(3125)[/tex]
[tex]n-1 = ln(3125)/ln(5) = 5[/tex]
[tex]n = 5 + 1 = 6[/tex]
[tex]a_6=-12500[/tex]
Using geometric sum series formula: [tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
Therefore, [tex]S_6=\frac{4(1-(-5)^6)}{1-(-5)} =\frac{-62496}{6} =-10416[/tex]
