FIND THE RULE
Patterns, what comes next?
Given a number sequence, guess the next term. Covers arithmetic, geometric, Fibonacci, squares and more, with random quizzes and revealed rules.
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Solution animation · visualize the rule
Sequence: 4, 9, 16, 25, 36 …
What is this?
Observe the relationship between terms (fixed step, doubling, sum of previous two, squares…) and find the next one. Click “Show rule” for the derivation.
示例与注意事项Example & notes
一个例子A worked example
数列 2、5、10、17、? ：相邻差是 3、5、7，下一个差是 9，所以答案是 26——页面用柱状图标出差值变化。Sequence 2, 5, 10, 17, ? — the differences are 3, 5, 7, so the next is 9 and the answer is 26, with bars showing the change.
注意事项Things to watch
- 先看相邻差；差再差（二阶差）保持恒定，多半是等差类变体。Look at first differences; a constant second difference usually means a quadratic pattern.
- 比值恒定才是等比，别把等比当等差（2、4、8 与 2、4、6 完全不同）。A constant ratio means geometric — do not confuse 2, 4, 8 with 2, 4, 6.
- 规律题有时不唯一，能自圆其说即可，但要写清假设。Pattern puzzles can have several answers; any consistent rule works if you state the assumption.
相关问答More Q&A
能出题练习吗？Can it generate practice?
可以，覆盖等差、等比、平方数、斐波那契与交替规律等常见类型。Yes — arithmetic, geometric, square, Fibonacci and alternating patterns are all included.
答案唯一吗？Is the answer unique?
常见题型有唯一解；开放题型会给出一组合理解释并说明依据。Standard forms have a unique answer; open forms show one justified solution.