Counting terms of an arithmetic progression ($n=1+(a_n-a_1)/d$)

Starting at $a_1$ and repeatedly adding a nonzero common difference $d$, a proposed final value $z$ is reached at positionif and only if this expression is a positive integer. For $a_1=7$, $d=3$, and $z=28$, it gives $n=8$. The quotient $21/3=7$ counts increments, while the initial entry adds one to the number of sequence terms. The proposed value $27$ gives $n=1+20/3$, which is not an integer, so it is never reached by these updates. The test also handles decreasing arithmetic progressions; when $d=0$, the repeated value alone cannot determine a length.