Question

Enter the finite geometric series from its given description, and then enter its sum.

Answer 1

Answer:

$a_n= 4(-5)^{(n-1)}$

-10416

Step-by-step explanation:

a = 4

r = -5

geometric series:  $a_n=ar^{(n-1)} = 4(-5)^{(n-1)}$

Determine which term = -12500:

$a_n=-12500$

$4(-5)^{(n-1)}=-12500$

$(-5)^{(n-1)} = -3125$

$(5)^{(n-1)} = 3125$

$(n-1)ln(5) = ln(3125)$

$n-1 = ln(3125)/ln(5) = 5$

$n = 5 + 1 = 6$

$a_6=-12500$

Using geometric sum series formula: $S_n=\frac{a(1-r^n)}{1-r}$

Therefore, $S_6=\frac{4(1-(-5)^6)}{1-(-5)} =\frac{-62496}{6} =-10416$