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

Question

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

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Answer

In the given problem, $n^{th}$ term is given by $"a_n= 6n + 2"$. To find the common diffrence 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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