Answer:
[tex]\boxed{\text{12 h 20 min}}[/tex]
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
[tex]S_{n} & = & \dfrac{n(a_{1} + a_{n})}{2}[/tex]
So
[tex]\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}}[/tex]
