Write the sum using summation notation, assuming the suggested pattern continues. 4-24+144-864+

Sn = ∑ 4(-6)^n, from n = 0 to n = n

Step-by-step explanation:

* Lets study the geometric pattern

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)  

- The sum of n terms is Sn = , where

 a is the first term , r is the common ratio between each two

 consecutive terms and n is the numbers of terms

- The summation notation is ∑ a r^n, from n = 0 to n = n

* Now lets solve the problem

∵ The terms if the sequence are:

  4 , -24 , 144 , -864 , ........

∵

∵

∴ There is a constant ratio between each two consecutive terms

∴ The pattern is geometric

- The first term is a

∴ a = 4

- The constant ratio is r

∴ r = -6

∵ Sn =

∴ Sn =

- By using summation notation

∵ Sn = ∑ a r^n , from n = 0 to n = n

∴ Sn = ∑ 4(-6)^n

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step-by-step explanation:

if the rectangular pool has a area of 192 square ft. and length of 15 ft. you must divide 15 into 192. 192 ÷ 15 = about 13 ft.