The nth term of an A.P. is 6n + 2.

Question:

The $n$th term of an A.P. is $6 n+2$. Find the common difference.

Solution:

In the given problem, $n$th term is given by " $a_{n}=6 n+2^{*}$. 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 $(n=1)$,

$a_{1}=6(1)+2$

$=6+2$

$=8$

Second term $(n=2)$

$a_{2}=6(2)+2$

$=12+2$

$=14$

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

$=14-8$

$=6$

Therefore, the common difference is $d=6$.

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