Question

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

Answer 1

Answer:

$\boxed{\text{12 h 20 min}}$

Step-by-step explanation:

1. Find the eighth term

You have an arithmetic sequence. It starts at 75 and each successive term is 5 more than the one preceding it

The general formula for the nth term (aₙ) is

aₙ = a₁ + (n - 1)d

where a₁ is the first term and d is the common difference (5) between consecutive terms.  Thus,

a₈ = 75 + (8 - 1) × 5 = 75 + 7 × 5 = 75 + 35 = 110

2. Find the sum

The formula for sum of the first n terms of an arithmetic sequence is

$S_{n} & = & \dfrac{n(a_{1} + a_{n})}{2}$

So

$\begin{array}{rcl}S_{8}& = & \dfrac{8(75 +110)}{2}\\& = & 4 \times 185\\& = & \text{740 min}\\& = & \textbf{12 h 20 min}\\\end{array}\\\text{The total length of all eight movies is }\boxed{\textbf{12 h 20 min}}$