How to find the sequence 7,9,13,19 by guessing ideas (analysis method) The general term formula of Is there any formula or something like that An = an + BN and so on

How to find the sequence 7,9,13,19 by guessing ideas (analysis method) The general term formula of Is there any formula or something like that An = an + BN and so on

The rule is a (n + 1) = a (n) + 2n
The general term formula can be obtained by superposition method
Direct observation
a1=7=7+0*1
a2=9=7+1*2
a3=13=7+2*3
a4=19=7+3*4
∴ a(n)=7+n(n-1)