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(an-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?
279
518
600
800

Answer 1

Use the recurrence backwards: a_{n-1} = (a_n + 100)/1.5.

a_5 = 2225
a_4 = (2225+100)/1.5 = 2325/1.5 = 1550
a_3 = (1550+100)/1.5 = 1650/1.5 = 1100
a_2 = (1100+100)/1.5 = 1200/1.5 = 800
a_1 = (800+100)/1.5 = 900/1.5 = 600

Answer: 600.