# Zero-based numbering vs. one-based numbering for sequences

What are the advantages of using one over the other? I mean this in the context of sequences and series. For example, should we let the geometric sequence start from $n=0$ or $n=1$ to get $a_n = a_0r^n$ or $a_n = a_1r^{n-1}$, respectively? Another example is the arithmetic sequence, which changes from $a_0 + dn$ to $a_1 + d(n-1)$ based on which number we start with (0 or 1).

• The only advantage of the former, as far as I know, is shorter expressions – Yuriy S Jul 10 '16 at 14:17
• In Taylor series $\sum_0^\infty b_n(x-a)^n$ is the natural way to proceed. – André Nicolas Jul 10 '16 at 14:19