Geometric sequences application

[VCE_2012]

Hi guys, please explain why in certain applications for Geo sequences why (n-1) is sometimes counted as the (th) day or (other) and sometimes (n) represents the (th) day or (other).
I noticed it largely in compound interest: is this true 'a' does not equal [t[/1]? Because 'a' means the value after one year; but in fact after one year it has already been affected by r... i also realize this in a problem where a ball is dropped from a height of 2m and after each bounce the height decreases by 3/4... a=2m but [t][/1]= (3/4)(2).
Also, how can i tell if days or other entities are represented by 'n' or 'n-1'?  Or is it based on the fact that 'a' does not = to [t][/1] "kind of thing"...
Enlighten me...