If the first term of an A.P. is a and nth term is b, then its common difference is

Here, we are given the first term of the A.P. as a and the nth term (an) as b. So, let us take the common difference of the A.P. as d.

Now, as we know,

$a_{n}=a+(n-1) d$

On substituting the values given in the question, we get.

$b=a+(n-1) d$

$(n-1) d=b-a$

$d=\frac{b-a}{n-1}$

Therefore, $d=\frac{b-a}{n-1}$

Hence the correct option is (b).