MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

Answer:The total length of all 8 movies is 740 minutesStep-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