How to Use the Arithmetic Sequence Term Finder
An arithmetic sequence increases or decreases by a fixed amount, called the common difference, between neighboring terms. The general term formula is aₙ = a₁ + (n-1)d. This calculator works backward: given a value you know appears somewhere in the sequence, it finds exactly which term number that value belongs to, using n = (value - a₁) / d + 1.
For example, a sequence starting at 3 with a common difference of 4 runs 3, 7, 11, 15, 19, 23, 27, and so on. To find which term equals 23, the formula gives n = (23-3)/4+1 = 6 — the 6th term. Solving this by hand is easy to get wrong, especially with larger numbers, so this tool gives you an instant, error-free answer.
If the value you enter never actually appears in the sequence (it doesn't land on a multiple of the common difference away from the first term), the calculator shows a clear message instead of a wrong answer. It also handles the special case where the common difference is 0, meaning every term is identical to the first term. This kind of reverse lookup is useful well beyond homework — analyzing evenly spaced data, billing cycles, or step counters often boils down to the same math.
Frequently Asked Questions
Yes. A negative common difference means the sequence decreases, and the same formula still finds the term number.
A message tells you the value isn't a term in this sequence, since only values spaced by the common difference exist as terms.
Every term equals the first term. If your target matches the first term, every position works; otherwise no term matches.