Problem:
Consider the sequence defined recursively by u1​=a (any positive number) and un+1​=−1/(un​+1),n=1,2,3,…. For which of the following values of n must un​=a?
Answer Choices:
A. 14
B. 15
C. 16
D. 17
E. 18
Solution:
Note that u1​=a,u2​=a+1−1​,u3​=a+1−1​+1−1​=a−(a+1)​, and u4​= −a(a+1)​+1−1​=−1−a​=a. Hence a=u1​=u4​=u7​=⋯=u16​. Use a=1 to show unâ€‹î€ =a for the other given values of n.