Good Learning Co.
SavannahYear 8
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MathsAlgebra: expressions and equations28 min★★★ difficulty

Sequences and nth-term rules

A sequence rule lets you jump to the 100th term without writing the other 99.

Part of your national curriculum
  • Algebra: Generate terms of a sequence from a term-to-term or a position-to-term rule

Lesson overview

What you'll learn in this lesson

Generate terms of a sequence from a term-to-term or a position-to-term rule

Key learning points

  • • Two kinds of rule
  • • Finding the nth term
  • • Checking

This lesson at a glance

  • 28 minutes
  • 14 parts to scroll through
  • 3 quick checks
  • Marked quiz at the end
  • Gentle pace: short sittings with pauses

Words to know

generatesequenceterm-to-termposition-to-termfinding

Scroll down — the lesson carries on below

Part 1 of 14 · Discover7%
1

Watch & discover

Part 1 of 14

Watch first

Sequences and nth-term rules

An English teaching video on this topic from mathantics. Watch it, then scroll down for the lesson.

In a nutshell

Generate terms of a sequence from a term-to-term or a position-to-term rule

2

Learning cycle

Part 2 of 14

Learning cycle 1 of 2

Part 1 · Two kinds of rule

A short piece of teaching, then a check to make sure it has landed.

3

Explore the idea

Part 3 of 14

Learn

Two kinds of rule

A term-to-term rule tells you what to do to the previous term ('add 4'). A position-to-term rule works out any term directly from its position number.

4

Explore the idea

Part 4 of 14

Learn

Finding the nth term

For a linear sequence, the common difference is the coefficient of n. For 5, 9, 13, 17 the difference is 4, so start with 4n, then adjust: 4n + 1.

5

Quick check

Part 5 of 14

Quick check

What is the nth term of 3, 7, 11, 15?

6

Reset break

Part 6 of 14

Pause

That's sitting 1 of 2 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now
7

Quick check

Part 7 of 14

Quick check

Using 4n − 1, what is the 10th term?

8

Learning cycle

Part 8 of 14

Learning cycle 2 of 2

Part 2 · Checking

A short piece of teaching, then a check to make sure it has landed.

9

Explore the idea

Part 9 of 14

Learn

Checking

Substitute n = 1 and n = 3 back in. If both match the sequence, the rule is right — testing one term is not enough.

10

Quick check

Part 10 of 14

Quick check

'Add 6 to the previous term' is which kind of rule?

11

Challenge round

Part 11 of 14

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

12

Challenge round

Part 12 of 14

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

A ____ rule tells you what to do to the previous term ('add 4').

A ____ rule works out any term directly from its position number.

For a linear ____, the common difference is the coefficient of n.

13

Mastery quiz

Part 13 of 14

Marked quiz

End of lesson quiz: Sequences and nth-term rules

3 questions, marked with the reasoning shown. No timer.

  1. 1. What is the nth term of 3, 7, 11, 15?

  2. 2. Using 4n − 1, what is the 10th term?

  3. 3. 'Add 6 to the previous term' is which kind of rule?

14

Lesson round-up

Part 14 of 14

Lesson round-up

Ready when you are

Quiz score

Not sat

Games

Not played

Points this lesson

0

Best run

0 in a row

Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?

Ask Luna

Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

The cost of a school trip

A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.

If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.

The school decides to charge £20 and to use anything left over for a second trip later in the year.

Written for Good Learning Co.

Reading questions

  1. Work out the total cost of the trip if 50 pupils go.
  2. Show why the price per pupil falls when more pupils go, using numbers.
  3. At £20 each, how many pupils must go before the trip makes money? Show your working.

  • Working out

    Working out

    Do the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.

    10–15 questions

  • Worked example, explained

    Writing

    Copy one question out and write underneath, in words, why each step works.

    1 question, 4–5 sentences

  • Problem in words

    Working out

    Write your own real-life problem that uses today's method, then solve it.

    1 problem + solution

Saved as you type.

Part 1 of 14 · Watch & discover

How this is going

  • Not looked at yet

    Generate terms of a sequence from a term-to-term or a position-to-term rule

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