How to find the general formula of arithmetic sequence?

How to find the general formula of arithmetic sequence?

Find A1 and D

Formula proof of the sum of the first n terms of arithmetic sequence

a1=a1
a2=a1+d
a3=a1+2d
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an=a1+(n-1)×d
Sn = Na1 + [n (n-1) D] / 2

If I give you a general term formula, how can I prove that a sequence is an arithmetic sequence, for example, a column
The constant is - 3

The general formula is: an
If an-a (n-1) = A and a is a constant, it can be proved to be an arithmetic sequence
For example, a (n + 1) = 8
An=6
A(n-1)=4
A(n+1)-An=An-A(n-1)=2
Only in this way can it be proved