Number series: a checking order that works
Almost every series is built from one of a handful of structures. Testing them in a fixed order is faster than staring at the numbers.
Check differences first
Subtract consecutive terms. A constant difference is arithmetic; a difference that itself forms a pattern usually means a second-order rule, such as adding successive even numbers.
Then ratios and squares
Divide consecutive terms for a geometric pattern. If neither works, ask whether the terms are squares, cubes, or squares offset by a constant.
Then alternation
Some series interleave two sequences. Read every second term and check each strand separately before concluding that a series is irregular.
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Questions people ask
Is a calculator allowed?
No. Items are built for mental arithmetic and the numbers stay small deliberately.
What if two rules fit?
Prefer the simpler one that explains every term, not just most of them.