How do I find the common difference if the first term is unknown?

Question

Given the formula: $A_n = A_1+ (n-1)d$

I'm trying to look for $d$, if given the the second and $17^{\text{th}} $ terms, namely $37$ and $82$.

I can't seem to figure out where to start; if $A_1$ were at least given I might have a starting point, but here I'm completely lost now that both are missing.

Answer 1

Hint: $$a_{17} - a_2 = 45 = 16d - d = 15d$$

Answer 2

The $n$th term of an arithmetic sequence is

$$a+(n-1)d$$ where $a$ is the first term and $d$ is the common difference between each term.

You have:

$$a+16d=82\tag1$$ $$a+d=37\tag2$$ When we perform $(1)-(2)$, what do we get?