Problem:
Suppose that (un) is a sequence of real numbers satisfying un+2=2un+1+un, and that u3=9 and u6=128. What is u5?
Answer Choices:
A. 40
B. 53
C. 68
D. 88
E. 104
Solution:
Note that u5=2u4+9 and 128=u6=2u5+u4=5u4+18. Thus u4=22, and it follows that u5=2⋅22+9=(B)53.
The problems on this page are the property of the MAA's American Mathematics Competitions