The recursive formula, an = an-1 - 12 with a0 = 84 describes the amount of water left, in gallons, in a bathtub n after the drain stopper was pulled

Question

The recursive formula, an = an-1 - 12 with a0 = 84 describes the amount of water left, in gallons, in a bathtub n after the drain stopper was pulled. Find a5, he amount of water left in the tub after 5 minutes.

Answer 1

Hi Svetlana N.,

With the recursive formula of a_n = a_n-1 - 12, and a₀ = 84;

For:

n = 1: a₁ = a₀ - 12 = 84 - 12 = 72

n = 2: a₂ = a₁ - 12 = 72 - 12 = 60

n = 3: a₃ = a₂ - 12 = 60 - 12 = 48

n = 4: a₄ = a₃ - 12 = 48 - 12 = 36

n = 5: a₅ = a₄ - 12 = 36 - 12 = 24

∴ a₅ = 24

I hope this helps, Joe.

Answer 2

a₅ = a₁ + (n - 1)d, learn/use this formula

a₅ = 72 + (4)(-12)

Can you solve for a₅ and answer?