Sequence Next Term Finder
Enter the first few terms of a sequence and detect whether it is arithmetic or geometric, then predict the next term.
How it works
Arithmetic if t2 − t1 = t3 − t2 (add d) · Geometric if t2 ÷ t1 = t3 ÷ t2 (multiply by r)
Two of the most common sequences are arithmetic, where each term adds a fixed amount, and geometric, where each term multiplies by a fixed ratio. The calculator checks the differences between consecutive terms first: if they match, it is arithmetic; otherwise it checks the ratios. Once the rule is identified, extending the sequence is just one more addition or multiplication.
Worked example
For 2, 6, 18 the differences are 4 and 12 — not equal, so not arithmetic. The ratios are 6 ÷ 2 = 3 and 18 ÷ 6 = 3 — equal, so it is geometric with ratio 3, and the next term is 18 × 3 = 54.
Frequently asked questions
How does it tell arithmetic from geometric?
It compares consecutive terms two ways. If the differences are equal (t2 − t1 = t3 − t2) the sequence is arithmetic; if the ratios are equal (t2 ÷ t1 = t3 ÷ t2) it is geometric. Arithmetic is checked first.
What if my sequence is neither?
Many sequences follow other rules — quadratic, Fibonacci-style, or no simple pattern at all. The calculator reports "neither" and shows the differences so you can look for a higher-order pattern yourself.
Can it handle decreasing sequences?
Yes. A negative common difference (like 20, 15, 10) is arithmetic, and a ratio between 0 and 1 (like 80, 40, 20) is geometric. Both are detected and extended correctly.
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This calculator is for educational purposes. Double-check important results before acting on them.