How can you tell they’ve got it: Nth-Term Rules?

If they’ve got it, you’ll see things like: 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. Or just try it together: 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?

Mathematics Algebra Ages 12–14

Nth-Term Rules

Your child can find a formula for the nth term of a sequence, like 4n − 1 for 3, 7, 11. They use it to find the 50th term.

In curriculum terms

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

Ages are typical, not deadlines — follow your child’s pace. How to help at home →

How to tell they’ve got it

Tick these off as you see them — no test required.

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

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Try this together

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?

Where this sits on the map

Stuck here? Check the skills it builds on first. Confident? Here’s what it unlocks.

Builds on

Generating Sequencesages 11–14Finding nth term requires experience generating and classifying sequences first

Solving Linear Equationsages 11–14Testing whether a number is in a sequence requires solving a linear equation

Nth-Term Rulesthis skill · ages 12–14

Unlocks

Nothing on the map depends on this yet.

solid = must come firstdashed = helps

Curriculum alignment

Where this fits in the official school curriculum — our best automated guess, not yet checked by a person.

This skill sits beyond Year 6 in the Australian Curriculum, so no F–6 code is matched. It also sits beyond the NSW K–6 syllabuses. It also sits beyond Level 6 in the Victorian Curriculum.

Nearby on the map

Factorising Expressionsages 12–13 Linear Function Graphsages 12–14 Plotting Linear Graphsages 12–14 Simple formulaeages 12–14

All Algebra skills →