The nth term formula is that $a_n = a+(n-1)d$
How does this formula convert to the formula for the number of terms in an arithmetic sequence which is equal to $$\dfrac{\text{last term-first term}}{ \text{common difference}}+1$$
In other words, how can I prove the formula for the number of terms in an arithmetic sequence?
I tried to attempt this but I don't know how to manipulate a formula with a subscript in maths.
Edit: So going on from one of the answers we have $$a_n=a+(n-1)d \Longrightarrow \frac{a_n-a}{d}+1=n$$
So I get it now.
Best Answer
Treat a pronumeral with a subscript as a single unit - if you have $a_n$ then you always move them together and you never split them up, almost as if they were just one symbol like $x$ or $\aleph$.
In this case, you're trying to take $a_n = a + (n-1)d$ and rearrange it to express $n$ in terms of the other values. So start by subtracting $a$ from both sides, then see how to go from there.