Question

A new movie is released each year for 8 years to go along with a popular book series. Each movie is 5 minutes longer than the last to go along with a plot twist. The first movie is 75 minutes long. Use an arithmetic series formula to determine the total length of all 8 movies.

Answer 1

Answer:

The total length of all 8 movies is 740 minutes

Step-by-step explanation:

* Lets revise the arithmetic series

- In the arithmetic series there is a constant difference between  

 each two consecutive numbers  

- Ex:  

# 2 , 5 , 8 , 11 , ………………………. (constant difference is 3)

# 5 , 10 , 15 , 20 , ………………………… (constant difference is 5)

# 12 , 10 , 8 , 6 , …………………………… (constant difference is -2)

* General term (nth term) of an Arithmetic series:  

- If the first term is a and the common diffidence is d, then

 U1 = a , U2 = a + d , U3 = a + 2d , U4 = a + 3d , U5 = a + 4d  

 So the nth term is Un = a + (n – 1)d, where n is the position of the

  number in the series

- The formula to find the sum of n terms is

  Sn = n/2 [a + l] , where l is the last term in the series

* Lets solve the problem

- A new movie is released each year for 8 years to go along with a

 popular book series

∴ n = 8

- Each movie is 5 minutes longer than the last

∴ d = 5

- The first movie is 75 minutes long

∴ a = 75

- To find the total length of all 8 movies find the sum of the 8 terms

∵ Un = a + (n - 1)d

∵ The last term l is u8

∵ a = 75 , d = 5 , n = 8

∴ l = 75 + (8 - 1)(5) = 75 + 7(5) = 75 + 35 = 110

∴ l = 110

∵ Sn = n/2 [a + l]

∴ S8 = 8/2 [75 + 110] = 4 [185] = 740 minutes

* The total length of all 8 movies is 740 minutes