Question

A new movie is released each year for 14 years to go along with a popular book series. Each movie is 2 minutes longer than the last to go along with a plot twist. The first movie is 70 minutes long. Use an arithmetic series formula to determine the total length of all 14 movies. A. 2,058 minutes B. 1,162 minutes C. 294 minutes D. 166 minutes

Answer 1

Answer:

B

Step-by-step explanation:

If you use the general equation for an arithmetic sequence,

$a_{n}=a_{1}+d(n-1)$,

where aₙ is the number of minutes for movie n,

a₁ is the length of the first movie in minutes, and

d is the difference between each movie, in minutes

Our sequence is this:

$a_{n}=70+2(n-1)$

If we want the length of the second movie (we already know the length of the first), we fill in n with 2:

$a_{2}=70+2(2-1)$

which gives us a length of 72.  Now for the length of movie n = 3:

$a_{3}=70+2(3-1)$

which gives us a length of 74.  Now for the length of movie n = 4:

$a_{4}=70+2(4-1)$

which gives us a length of 76.  One more and I'm sure you'll notice the pattern:

$a_{5}=70+2(5-1)$

which gives us a length of 78.  Now we will find the length of the 14th movie and add up by 2's all the way up to that number of minutes:

$a_{14}=70+2(14-1)$

which gives up a length of 96 minutes.  We will add up by 2's from 70 to 96:

$70+72+74+76+78+80+82+84+86+88+90+92+94+96=1,162 min$

Answer 2

The total length of all 14 movies is 1,162 minutes.

What is arithmetic series?

The arithmetic series is a series in which the numbers are in the order of some common difference. The difference between any two consecutive numbers is constant.

$\rm a_{n} = a_{1} + d(n-1)$

From an arithmetic series

$\rm a_{n} = a_{1} + d(n-1)$

where aₙ is the number of minutes for movie n,

a₁ is the length of the first movie in minutes, and

d is the difference between each movie, in minutes

$\rm a_{n} = 70+ 2(n-1)$

for the length of the movie n = 2

$\rm a_{n} = 70+ 2(2-1)$ = 72

which gives us a length of 72.  

Now for the length of the movie n = 3

$\rm a_{n} = 70+ 2(3-1)$ = 74

which gives us a length of 74.  

Now for the length of the movie n = 4

$\rm a_{n} = 70+ 2(4-1)$ = 76

which gives us a length of 76.  

Now we will find the length of the 14th movie

$\rm a_{n} = 70+ 2(14-1)$

which gives up a length of 96 minutes.  

We will add up by 2's from 70 to 96

$70+72+74+76+78+80+82+84+86+88+90+92+94+96$

=  1,162 minutes

Thus, the total length of all 14 movies is 1,162 minutes.

Learn more about arithmetic series;

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