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, $n^{\text {th }}$ term is given by " $a_n=6 n+2$ ". 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 $d = 6.$
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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