Start with a rule
Here is your puzzle: using n × (n + 1), starting at n = 1, what comes after 2, 6, 12, 20? Take a moment before reading on. There is no clock to beat.
An unrestricted number sequence can have many possible continuations. This puzzle gives you its rule, so you can test one specific idea rather than guess what the author intended.
Look at the building blocks
Write the first four terms as products: 1 × 2, 2 × 3, 3 × 4, and 4 × 5. Each term multiplies a number by the number immediately after it.
The next product is 5 × 6, which makes 30. You can check it a second way: the gaps are 4, 6, 8, and then 10. Adding 10 to 20 gives the same answer.
Make a puzzle of your own
Choose a starting value for n and write three consecutive products using the same rule. Give a friend both the terms and the rule, then ask for the next product.
Try explaining why your answer works without saying “it just looks right.” Finding a pattern is fun; explaining it gives someone else a way to follow your thinking.
Sources, credits & transparency
Original creative or practical content; no external factual claims are used as evidence.
Development reference photograph · Unsplash. Reference use; provenance and final image approval pending; see public/images/manifest.json.
Created with AI assistance. Approved for publication by the SparkKindly site owner on 19 October 2026. Primary sources and puzzle reasoning were checked with AI assistance; no independent specialist review is claimed.