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