finite geometric series ,2 different formulas?

Question

Are both formulas the same?Do they have different use?Is there something else i am missing here? I do not ask for the proof of the formulas.

i see both of them online on various resources, for example try typing in google images '' geometric series''

Answer 1

Yes they are the same just multiply the top and bottom by $-1$ to move from one formula to another. $a_1$ corresponds to $a$ here.

Answer 2

Hint: Write $$\frac{a(r^n-1)(-1)}{(r-1)(-1)}$$