How do you find the nth to the quadratic sequence of 3,8,15,24,35

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

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step-by-step explanation: