# Write the expression of the common difference of an A.P. whose first term is a and nth term is b.

Question:

Write the expression of the common difference of an A.P. whose first term is a and nth term is b.

Solution:

Here, we are given

First term = a

Last term = b

Let us take the common difference as d

Now, we know

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

So,

For the last term (an),

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

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

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

Therefore, common difference of the A.P. is $d=\frac{b-a}{n-1}$