Dipesh is looking at two different options for a new video rental plan. Plan A has a fee of $7.95 plus an additional fee of $1.2
5 per rental. With this plan, the first 2 rentals are free. Plan B has a fee of $5.00 plus an additional fee of $3.90 per rental. With this plan, the first 6 rentals are free. After how many rentals would both options cost the same amount?
2 answers:
Dipesh is looking at two different options for a new video rental plan. Plan A has a fee of $7.95 plus an additional fee of $1.25 per rental. With this plan, the first 2 rentals are free. Plan B has a fee of $5.00 plus an additional fee of $3.90 per rental. With this plan, the first 6 rentals are free. After how many rentals would both options cost the same amount?
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Answer:
<h2> aₙ = 7n - 10</h2>Step-by-step explanation:
The nth term:
So:
a₄ = a₁ + 3d
18 = a₁ + 3d ⇒ 3d = 18 - a₁
a₇ = a₁ + 6d
39 = a₁ + 6d
39 = a₁ + 2(18 - a₁)
39 = a₁ + 36 - 2a₁
39 = 36 - a₁
a₁ = -3
3d = 18 - (-3)
3d = 21
d = 7
So the nth term: