Find s for the given geometric series. round answers to the nearest hundredth, if necessary. a1 = –12, a5 = –7,500, r = 5 question 4 options: –9,372 –6,252 –1,872 –18,780

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

* 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

∵

∵ n = 5

∴

* S = -9,372

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i