If Arithmetic and Geometric Sequences are simply Linear and Exponential functions respectively. Why then do we subtract the n variable by 1 when solving for certain terms in these sequences?
$t_n=d(n-1)+a$
$t_n=a\cdot r^{n-1}$
I've tried exploring this question from a graphing perspective and it's clear this results in the sequence index starting at 1 rather then zero but is that really the only reason? Personally I'd rather start sequence indices at 0 as I've found going back and forth between linear equation techniques and sequence term formulas makes it easy to make off by 1 errors if one isn't careful.