The second formula is actually ... an = a1 + (n - 1) d
Set the formulas equal to each other
nd + a0 = a1 + (n - 1) d simplify
nd + a0 = a1 + nd - d subtract nd from both sides
a0 = a1 - d add d to both sides
a0 + d = a1 which would be technically correct in your class formula when n= 1
So......the second formula becomes
a0 + d + (n - 1) d =
a0 + d + nd - d =
a0 + nd ........which is the one you used in class
I think the main difference is that your class uses a0 for the first term, so that a1 is actually the first generated term of the series [i.e., the second term]
I believe it's more common for a1 to be represented as the first term....thus, the ACT formula is actually preferred
