Question

Can the following expression be $n^{th}$ term of an AP?
If true then enter $1$ and if false then enter $0$.

$3n^2+5$

Answer 1

We have
$a_n=3n^2+5$

Changing to n to n+1 in $a_n$, we get
$a_{n+1}=3(n+1{)}^2+5$
$\Rightarrow a_{n+1}=3n^2+6n+8$

Common difference $a_{n+1}-a_n=(3n^2+6n+8)-(3n^2+5)=6n+3$

since $a_{n+1}-a_n$ is depends upon $n$ and therefore not a constant.

So, the given sequence is not an AP.