Question

$n^{th}$ term of a sequence is $2n+1.$ Is this sequence an A.P.?If so find its first term and common difference.

Answer 1

We know that $n^{th}$ term of an A.P is given by,
$a_n=a+(n-1)d$
Now, equating it with the expression given we get,
$2n+1=a+(n-1)d$
$2n+1=a+nd-d$
$2n+1=nd+(a-d)$
Equating both sides we get,
$d=2$ and $a-d=1$
So we get,
$a=3$ and $d=2$
So the first term of this sequence is $3,$ and common difference is $2.$