--- title: "Linear number sequences" description: "Generate and describe linear number sequences, including those with negative and decimal steps; identify the term-to-term rule" canonical: https://lightmysky.com/learn/mathematics/linear-number-sequences-mt_hBZwbst0ow source: https://lightmysky.com/learn/mathematics/linear-number-sequences-mt_hBZwbst0ow.md retrieved: 2026-10-19 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Linear number sequences Generate and describe linear number sequences, including those with negative and decimal steps; identify the term-to-term rule Subject: Mathematics · Area: Algebra · Ages 10 to 11 Page: https://lightmysky.com/learn/mathematics/linear-number-sequences-mt_hBZwbst0ow ## Ready when they can - Continue the sequence 2.5, 4.0, 5.5, ... and state the rule as 'add 1.5' - Generate terms of a sequence that crosses zero (e.g. 3, 1, −1, −3, ...) - Describe the term-to-term rule for a given linear sequence and predict the 10th term ## Lesson: Linear number sequences A sequence is a list of numbers written in order. In a linear sequence, you use the same rule every time to get from one number to the next. *(drawing: Each number is 4 more than the last. The rule is 'add 4'.)* **Example.** Mia writes 2.5, 4.0, 5.5, 7.0. She checks the gaps: 4.0 minus 2.5 is 1.5, 5.5 minus 4.0 is 1.5, 7.0 minus 5.5 is 1.5. Every gap is the same, so the rule is 'add 1.5'. **Example.** Think about a cold day. The temperature is 3, then 1, then -1, then -3. Each step goes down by 2. Even when the numbers cross past zero, the rule stays the same: subtract 2. **Tip.** To find a term far down the list, you do not need to write out every number. Just keep applying the rule from the term before it, again and again. **Recap.** A linear sequence always uses the same add or subtract rule, even when the numbers are decimals or cross zero. ## Practice 17 questions on this page, each with its working shown. ## Needs first - [Generating a pattern from a rule](https://lightmysky.com/learn/mathematics/generating-a-pattern-from-a-rule-mt_A-FyLLLLzy) - [Negative Numbers Across Zero](https://lightmysky.com/learn/mathematics/negative-numbers-across-zero-mt_RVK655t391) ## Opens up - [Generalising with repeated reasoning](https://lightmysky.com/learn/mathematics/generalising-with-repeated-reasoning-mt_iyovKgZC1q) - [Generating Sequences](https://lightmysky.com/learn/mathematics/generating-sequences-mt_yXO7lQ9Yn7)