Question

Aimee started a business making picture frames. On the first day that she was in business, she made 3 picture frames. She then increased the number made by 2 per day. Which recursive sequence correctly shows the number of picture frames that Aimee made after n days?

a) a₁ = 3, aₙ = aₙ₋₁ + 2
b) a₁ = 3, aₙ = aₙ₋₁ - 2
c) a₀ = 3, aₙ = a₀ + 2
d) a₀ = 3, aₙ = a₀ + 2n

Answer 1

Aimee increases her picture frame production by 2 each day, starting with 3 on the first day. The correct recursive sequence for this pattern is a₁ = 3, aₙ = aₙ₋₁ + 2, which indicates a linear growth.

Step-by-step explanation:

Aimee's business of making picture frames shows a linear increase in production as time progresses. On the first day, she produced 3 frames. From the second day onward, she increased her production by 2 frames per day. This situation can be represented by a recursive sequence.

The correct option for the recursive sequence is: a)a₁ = 3, aₙ = aₙ₋₁ + 2.

This means that the first term of the sequence, a₁, is 3 (for the first day). n terms thereafter are derived by taking the previous day's production (aₙ₋₁) and adding 2 to it.

This sequence properly reflects the increasing number of picture frames made each day following the pattern Aimee has set for her business.