The answers says the generator matrix of the Markov process is
$Q(n, n + 1) =150$ for all $n\geq0$;
$Q(n, n-1) = 50n$ for all $n\geq 1$;
$Q(n, n) = 50(n + 3)$ for all $n\geq 0$
While in the problem it says: The raindrops hit the piece of terrain at times of a Poisson process with rate $150$ per second. Independent of this Poisson process, it takes an exponentially distributed time with mean $20$ millisecond ($0.02$ seconds) for each raindrop to reach the down-pipe. Let $X_t$ be the number of raindrops on the terrain at time $t$, which have not reached the down-pipe.
So I am not sure why $Q(n, n-1) = 50n$ but not $50$?
I know it takes each drop $0.02$ seconds, but isn't it $Q(3,2) = Q(4,3)$ because the change is one drop anyway?
Also how can you get $Q(n, n) = -50(n + 3)$ for all $n\geq 0$?