I am reading the textbook Introduction to Stochastic Processes with R Book by Robert P. Dobrow, page 126.
For an absorbing Markov chain started in transient state $i$, let $a_i$ be the expected absorption time, the expected number of steps to reach some absorbing state.
I don't understand the below:
The number of transitions from $i$ to an absorbing state is simply the sum of the number of transitions from $i$ to each of the transient states until eventual absorption. The expected number of steps from $i$ to transient state $j$ is $F_{ij}$. It follows that
$$a_i=\Sigma_{k \in T}F_{ik}$$, where T is the set of transient states.
Can anyone help me explain the above?