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
- 17 parts to scroll through
- 3 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 17
Visual introductionPicture this
Sequences and nth-term rules
A sequence rule lets you jump to the 100th term without writing the other 99.
In a nutshell
Generate terms of a sequence from a term-to-term or a position-to-term rule
Learning cycle
Part 2 of 17
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.
Explore the idea
Part 3 of 17
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.
Reset break
Part 4 of 17
Pause
That's sitting 1 of 4 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.
Explore the idea
Part 5 of 17
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.
Quick check
Part 6 of 17
Quick check
Part 7 of 17
Reset break
Part 8 of 17
Pause
That's sitting 2 of 4 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.
Learning cycle
Part 9 of 17
Learning cycle 2 of 2
Part 2 · Checking
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 17
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.
Quick check
Part 11 of 17
Reset break
Part 12 of 17
Pause
That's sitting 3 of 4 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.
Challenge round
Part 13 of 17
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
Challenge round
Part 14 of 17
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.
Challenge round
Part 15 of 17
Game · Recall cards
What is the nth term of 3, 7, 11, 15?
Card 1 of 3
Mastery quiz
Part 16 of 17
Marked quiz
End of lesson quiz: Sequences and nth-term rules
3 questions, marked with the reasoning shown. No timer.
1. What is the nth term of 3, 7, 11, 15?
2. Using 4n − 1, what is the 10th term?
3. 'Add 6 to the previous term' is which kind of rule?
Lesson round-up
Part 17 of 17
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 LunaPart 1 of 17 · 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