Generating Sequences
Generate terms of a sequence from a term-to-term rule (e.g., 'add 3 each time') or a position-to-term rule (e.g., '2n + 1'), and identify whether a sequence is arithmetic, geometric, or neither
Lesson
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Generate terms from two kinds of rule. Use differences and ratios to classify the shown transitions.
Before teaching
Use this short check, then start teaching.
First use Linear number sequences and Substituting into Formulae. Ask the learner to distinguish position 3 from the value at position 3 in a sequence. If this is unclear, label a position row before calculating. This lesson supplies and explains ratio notation; it does not assume a complete ratio lesson.
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Generate terms from two kinds of rule. Use differences and ratios to classify the shown transitions.
Generate terms from two kinds of rule. Use differences and ratios to classify the shown transitions.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Addition Patterns
Before you open · source notes
Addition Patterns supports generating sequences. Not every worksheet pack.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk the learner to explain one step of “Addition Patterns” in their own words.
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Source, access and review notes
Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-12 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.
Illustrative Mathematics. “Addition Patterns.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.
CC BY-NC-SA 4.0 — link only
Check understanding
- Continue a sequence given a term-to-term rule involving addition, subtraction, or multiplication
- Generate the first five terms from a position-to-term formula such as 3n − 2
- Classify sequences as arithmetic (constant difference), geometric (constant ratio), or other
“Can your child work out the next few terms of a sequence like 5, 8, 11, 14… and explain whether the rule is "add a fixed number each time" or something else?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Algebra
- Age range
- Ages 11–14
Standards