About Sequences & Chains puzzles
Sequences and Chains are the classic aptitude-test format, done properly. You are shown a run of numbers with a gap, and the step between terms is what you have to recover. Sometimes it is constant, sometimes it grows, sometimes it alternates between two operations, and sometimes the sequence is really two interleaved sequences pretending to be one.
The universal first move is to write the differences underneath. A constant difference means arithmetic progression and you are done. A difference that itself forms a neat pattern means you are one level deep and should take differences again. A difference that swings wildly usually means the sequence is multiplicative, so switch to ratios instead. This ladder — differences, second differences, ratios — resolves the overwhelming majority of chains you will meet, here or in an exam hall.
The chains in later packs are built to defeat the ladder on the first pass. Interleaved sequences are the favourite trick: odd positions climb by three while even positions double, and the combined list looks like noise until you separate them. Once you have been caught by that once, you will check for it forever, which is exactly the point.
This world maps more directly onto standardised tests than any other on Numerly. If you are preparing for one, these are the packs to grind.
How to solve Sequences & Chains
- Write the differences between consecutive terms before theorising.
- If differences look random, try ratios — the sequence may be multiplying.
- Split odd and even positions into two lists to expose interleaved sequences.
- Extend your rule backwards to the first term as a free correctness check.
Skill trained: Pattern extrapolation and difference analysis.