Having the first term of the sequence
a(0)=3
a(1)=3+5=8
We realized that
a(1)=a(0)+2⋅2+1
We also have :
a(2)=a(1)+2⋅3+1=8+7=15
a(3)=a(2)+2⋅4+1=15+9=24
From above we can realize that each term is the sum of the previous
term and 2*(sequence coefficient added to 1) and 1
So the nth term will be:
a(n)=a(n−1)+2⋅(n+1)+1
