I have to describe a recurrence for $l_n$, the number of lobsters caught in year $n$.
The task says: a hobby fisherman estimates the number of lobsters he will catch in a year as the average of the number he caught in the two previous years.
Describe a recurrence for $l_n$, the number of lobsters caught in year $n$.
I have tried something. It is a homogeneous degree LRR, so the recurrence is: $\displaystyle l_n = \frac{(l_{n-1} + l_{n-2})}{2}$ as it is the average for $2$ years. Have I solved ít correctly?
Hint: if you apply the recurrence to $l_3$ you have $l_3=\frac{l_2+l_1}{2}$. Now apply the same recurrence relation and use the last equation to express $l_4$ as a function of $l_2$ and $l_1$.