How do I know whether a sequence is arithmetic or geometric?

Arithmetic sequences add or subtract the same amount each step, so they use a common difference d. Geometric sequences multiply by the same factor each step, so they use a common ratio r.

How do I find the 15th term quickly?

Enter a1, the common difference or ratio, and n = 15. The calculator applies the standard nth-term formula directly, so you do not have to list all 15 terms by hand.

Why does the geometric sum change when r = 1?

When r = 1 every term stays equal to a1, so the finite sum is just n copies of the same number. That is why the calculator switches to Sn = n · a1 for that case.

Does this calculator handle infinite series or detect other patterns?

No. This tool is only for finite arithmetic and geometric sequences with values you already know. It does not test convergence, work with infinite-series rules, or identify arbitrary patterns automatically.

Arithmetic & Geometric Sequence Calculator

Find the nth term and the finite sum of an arithmetic or geometric sequence without mixing up the formulas. Choose the pattern first, enter a1, d or r, and n, then confirm the result with a first-terms preview.