Question

A new movie is released each year for 12 years to go along with a popular book series. Each movie is 3 minutes longer than the last to go along with a plot twist. The first movie is 65 minutes long. Use an arithmetic series formula to determine the total length of all 12 movies. 244.5 minutes

Answer 1

Answer:

$S_n=978\ minutes$

Step-by-step explanation:

Arithmetic sequences have the following form

$a_n=a_1+d(n-1)$

Where

$a_1$ is the first term of the series

d is the common difference between consecutive terms.

$a_n$ is the nth term.

The formula to find the sum Sn of the first n terms of an arithmetic series is:

$S_n=\frac{a_1+a_n}{2}*n$

In this case $n=12$, $d=3$, $a_1=65$

$a_{12}=65+3(12-1)$

$a_{12}=98$

Then:

$S_n=\frac{65+98}{2}*12$

$S_n=978\ minutes$

You can also find the sum through the following series

$S_n=\sum_{n=1}^{n=12}a_1+d(n-1)$

$S_n=\sum_{n=1}^{n=12}65+3(n-1)$

$S_n=\sum_{n=1}^{n=12}65+3(n-1)\\\\S_n=978$

Answer 2

The total length of all 12 movies using the concept of an arithmetic progression is 978 min

What is an arithmetic progression?

It is a series of numbers where the difference between two consecutive terms is equal.

Formula to find the sum of an arithmetic progression is

$Sn = \frac{n}{2} (2a + (n-1)d)$

Where Sn = sum of arithmetic series

a = first term of the series

n = total terms of the series

d = common difference

It is given that

a = 65

n =12

d =3

$Sn = \frac{12}{2} (2*65 + (12-1)*3)$

$Sn = 978min$

Therefore, the total length of all 12 movies is 978 min.

To get more about arithmetic progression visit:

https://brainly.com/question/18828482