Write the common difference of an A.P.

Question:

Write the common difference of an A.P. whose nth term is an = 3n + 7.

Solution:

In the given problem, nth term is given by,

.

To find the common difference of the A.P., we need two consecutive terms of the A.P.

So, let us find the first and the second term of the given A.P.

First term,

$a_{1}=3(1)+7$

$=3+7$

$=10$

Second term $(n=2)$

$a_{2}=3(2)+7$

$=6+7$

$=13$

Now, the common difference of the A.P. $(d)=a_{2}-a_{1}$

$=13-10$

$=3$

Therefore, the common difference is $d=3$.