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Derivation of arithmetic progression's general term formula in senior high school mathematics
In fact, as long as the formula is reasonable and clear, there is no need to prove it.

There is a2=a 1+d,

a3 = a2+d = a 1+d+d = a 1+2d,

a4=a3+d=a 1+3d,

Through observation, the nth term is the first term plus (n- 1) multiplied by the tolerance d,

That is, an = a1+(n-1) × d.

This conclusion can be drawn through students' observation.