I've been pondering about this for a bit now and I just can't find the answer. The information given states "In this class, we used the formula: an=dn+a0." However, for the A.C.T., we'll use the explicit formula an=a+(n-1)*d. The question asks to explain the logic in how the formulas are the exact same thing and to find out how to convert them between one another arithmetically.
Hopefully this has enough info. Thanks.
+129847 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
+129847 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
