Given, an=3n2+5
Put n=1, a1=3(1)2+5=8
Put n=2, a2=3(2)2+5=3(4)+5=17
Put n=3, a3=3(3)2+5=3(9)+5=27+5=32
So, the series is :
8, 17, 32, ...
Here,
a2−a1=17−8=9
a3−a2=32−17=15
a2−a1≠a3−a2
Since the difference between the consecutive terms of the series is not same, the formula does not represent the nth term of an AP.