Problem:
Define a sequence of real numbers a1,a2,a3,… by a1=1 and an+13=99an3 for all n≥1. Then a100 equals
Answer Choices:
A. 3333
B. 3399
C. 9933
D. 9999
E. none of these
Solution:
Since an+1=399⋅an for all n≥1, it follows that a1,a2,a3,… is a geometric sequence whose first term is 1 and whose common ratio is r=399. Thus
a100=a1⋅r100−1=(399)99=9933.