Question

Check whether $a_n=2n^2+1$ is an AP or not.

Enter 1 if AP or 0 if not an AP.

Answer 1

Given, $a_n=2n^2+1$
Then $a_{n+1}=2{(n+1)}^2+1$
$\therefore a_{n+1}-a_n=2(n^2+2n+1)+1-2n^2-1$
$=2n^2+4n+2+1-2n^2-1$
$=4n+2$ which is not constant
$\therefore$ The above sequence is not an AP