Question

Each year, a daylily farm sells a portion of their daylilies and allows a portion to grow and divide. The recursive formula

an = 1.5(2n-1)-100
represents the number of daylilies, a, on the farm after n years. After the fifth year, the farmers estimate
they have 2,225 daylilies. How many daylilies were on the farm after the first year?

Answer 1

C. 600

Explanation:

Answer 2

600

Explanation:

We can solve the recursive formula for the previous term in terms of the present one:

a[n-1] = (a[n] +100)/1.5

Working backward, we find ...

a[4] = (a[5] +100)/1.5 = (2225 +100)/1.5 = 1550

a[3] = (1550 +100)/1.5 = 1100

a[2] = (1100 +100)/1.5 = 800

a[1] = (800 +100)/1.5 = 600

There were 600 daylilies on the farm after the first year.