How to Use the Arithmetic & Geometric Sequence Calculator
Wondering what the 100th or 1000th term of a sequence would be without adding or multiplying your way there one step at a time? Choose the sequence type (arithmetic or geometric), enter the first term, the common difference or ratio, and the term number you want, and this calculator instantly gives you the nth term and the sum of the first n terms.
An arithmetic sequence has a constant difference between consecutive terms, and its nth term is found with an = a1 + (n-1)d. A geometric sequence has a constant ratio between consecutive terms, using an = a1 × r^(n-1). The sum formulas are Sn = n/2 × (2a1 + (n-1)d) for arithmetic sequences, and, when the ratio isn't 1, Sn = a1 × (1-r^n)/(1-r) for geometric sequences.
Geometric sequences grow extremely fast once the absolute value of the ratio exceeds 1, so this calculator supports term numbers up to 100,000 and shows an error message if the result approaches infinity. Useful for sequence homework, verifying number patterns, or working with compounding growth like interest or population increase.
Frequently Asked Questions
An arithmetic sequence has a constant difference between consecutive terms (the common difference), while a geometric sequence has a constant ratio between consecutive terms (the common ratio). For example, 2, 4, 6, 8 is arithmetic with common difference 2, and 2, 4, 8, 16 is geometric with common ratio 2.
Yes, this calculator treats the first term as n=1. So entering n=1 simply returns the first term itself.