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
, which is rounded to the neartest tenth of a mile.