Consider the sequence $(a_n{)}_{n}0,$ which begins $1,5,13,41,121,$dots, defined by $a_n=2a_{n-1}+3a_{n-2}$

with $a_0=1,a_1=5.$ Your friend, Jan, suggests the solution $a_n=\frac{3^{n+1}}{2},$ arguing that the

proposed solution satisfies the recursive equation. However, Jan is not fully correct. Address

Jan's productive ideas and those that are incorrect. NOTE: You do not need to solve the

recurrence relation to answer this question. In fact, just solving the recurrence

relation will not count as answering the question.