How do I answer this arithmetic sequence question?

Question

Calculate the number of terms in the arithmetic sequence

$$a, a + d, a + 2d,\cdots, a + (n-1)d.$$

I don't have a problem answering this question with an integer sequence but I'm a bit lost with what to do for the general formula.

Answer 1

The $a$ is fixed, so it doesn't tell us anything about the number of terms. Thus, you may neglect it. What you watch is the coefficient of $d,$ which varies, beginning from $0,$ and increasing by $1$ each step of the way.

In other words you only have to deal with the simpler progression $$0,1,2,3,\cdots, n-2, n-1.$$ Can you tell how many terms there are now?