Show that the the sequence defined by ` T_(n) = 3n^(2) +2 ` is not an AP.

Explanation

We have, `t_n=3n^(2)+2`
On replacing n by `(n-1),` we get
`t_(n-1)=3(n-1)^(2)+2`
`implies t_(n-1)=3n^(2)-6n+5`
`therefore t_n-t_(n-1)=(3n^(2)+2)-(3n^(2)-6n+5)`
`" "=6n-3`
Clearly, `t_n-t_(n-1)` is not independent of n and therefore it is not constant. So, the given sequence is not an AP.