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?

600

Step-by-step 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.