Nth-Term Rules
Find the nth-term expression for an arithmetic sequence by identifying the common difference and the zero-term, and use it to determine any term in the sequence or test whether a given number belongs to the sequence
Lesson
Set out your lesson
Find an arithmetic sequence's nth-term rule, calculate a distant term, and test membership with a valid position.
Before teaching
Use this short check, then start teaching.
First use Generating Sequences. Ask the learner to explain the difference between a position and a value. Ask them to substitute n = 2 into 3n + 1. Expect 7. If substitution is insecure, return to Substituting into Formulae. Solving Linear Equations is an absent soft prerequisite; the limited undoing method required here is taught below, not assumed.
Check readiness directly. Prerequisite availability is not attainment.
Share and support
Compare teaching approaches
Teaching approaches
Gakuva’s recommended starting approach is selected. You can still compare every option.
1 approach
Find an arithmetic sequence's nth-term rule, calculate a distant term, and test membership with a valid position.
Find an arithmetic sequence's nth-term rule, calculate a distant term, and test membership with a valid position.
Family records and proof options
Keep a record of your learning
Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Find 1 Starting from 5/3, Assessment Variation
Before you open · source notes
Find 1 Starting from 5/3, Assessment Variation supports nth-term rules. 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 “Find 1 Starting from 5/3, Assessment Variation” in their own words.
Opening this link does not save learning or assess mastery.
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. “Find 1 Starting from 5/3, Assessment Variation.” 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
- Derive the nth-term rule for an arithmetic sequence such as 3, 7, 11, 15, … as 4n − 1
- Use an nth-term formula to find the 50th or 100th term without listing all preceding terms
- Determine whether a given number (e.g., 99) is a term in a specified arithmetic sequence
“If your child is given the sequence 4, 7, 10, 13…, can they find a formula for the nth term — and use it to check whether, say, 100 is in the sequence?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Algebra
- Age range
- Ages 11–14
Standards