Why Does Geometric Sequence General Term Formula Use n, Not n-1?

[L²Cc]

do you have an explanation to why sometimes the general term formula for geometric sequence is not raised to n-1 but to simply n?

 

[courtrigrad]

because you could have $$\sum_{n=0}^{\infty} ar^{n}$$ or $$\sum_{n=1}^{\infty} ar^{n-1}$$

Or $$\sum_{n=k}^{\infty} ar^{n-k}$$

 

[L²Cc]

oh ok...so from what I understood, if the sequence starts at zero then the formula raised to n because if it was n-1 then it will read -1, right?

 

[courtrigrad]

that is correct

 

[L²Cc]

all right thank you!