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.


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.

  • $\begingroup$ I get it now thank you I have added my attempt in my edit .I will accept this answer when the site let's me . Tyvm!!! $\endgroup$ – user57928 Oct 10 '18 at 22:37
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    $\begingroup$ Looks good, just make sure that if you're answering this for homework or in an exam or something that you put the appropriate amount of detail in. $\endgroup$ – ConMan Oct 10 '18 at 23:50

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