Answer:
S = -9,372 ⇒ 1st answer
Step-by-step explanation:
* Lets revise the geometric series
- There is a constant ratio between each two consecutive numbers
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
* General term (nth term) of a Geometric series:
U1 = a , U2 = ar , U3 = ar2 , U4 = ar3 , U5 = ar4
Un = ar^(n-1), where a is the first term, r is the constant ratio between
each two consecutive terms
- The sum of first n terms of a geometric series is calculate from
[tex]S_{n}=\frac{a(1-r^{n})}{1-r}[/tex]
* Lets solve the problem
∵ The series is geometric
∵ a1 = -12
∴ a = -12
∵ a5 = -7500
∵ a5 = ar^4
∴ -7500 = -12(r^4) ⇒ divide both sides by -12
∴ 625 = r^4 take root four to both sides
∴ r = ± 5
∵ r = 5 ⇒ given
∵ [tex]Sn=\frac{a(1-r^{n})}{1-r}[/tex]
∵ n = 5
∴ [tex]S_{5}=\frac{-12[1-(5)^{5}]}{1-5}=\frac{-12[1-3125]}{-4}=3[-3124]=-9372[/tex]
* S = -9,372
