Question 8
Find the smallest integer $k$ for which the conditions
$(1)$ $a_1,$ $a_2,$ $a_3,$ $\ldots$ is a nondecreasing sequence of positive integers
$(2)$ $a_n = a_{n-1} + a_{n-2}$ for all $n \gt 2$
$(3)$ $a_9 = k$
are satisfied by more than one sequence.
$(1)$ $a_1,$ $a_2,$ $a_3,$ $\ldots$ is a nondecreasing sequence of positive integers
$(2)$ $a_n = a_{n-1} + a_{n-2}$ for all $n \gt 2$
$(3)$ $a_9 = k$
are satisfied by more than one sequence.