Sequences Cambridge IGCSE Mathematics (9–1) revision
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In plain words
A sequence is a list of numbers that follows a rule. The useful thing is a formula for the nth term: give it the position, and it gives you the number. Then you can find the 100th term without writing out the first 99.
Three things to know
- If the sequence goes up by the same amount d each time, the nth term is dn plus or minus something. For 5, 8, 11, 14 the difference is 3, so it starts 3n; 3 × 1 = 3 and you need 5, so it's 3n + 2.
- If the differences aren't the same but the second differences are, the sequence is quadratic (it has n² in it): 2, 5, 10, 17 is n² + 1.
- In a geometric sequence you multiply by the same number each time: 3, 6, 12, 24.
Worked example
Find the nth term of 4, 9, 14, 19.
- The difference is 5 each time, so the rule starts 5n.
- When n = 1, 5n = 5, but the first term is 4, so subtract 1.
- nth term = 5n − 1.
Tips and tricks
- Test your formula on the second or third term, not just the first.
- To see whether a number is in a sequence, set the nth term equal to it and solve. If n is a whole number, it is.
It lands in your notebook with its questions as flashcards.
Sequences: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is the next term of 7, 11, 15, 19?
Add 4.
What is the nth term of 2, 4, 6, 8?
It is the two times table.
What is the 5th term of the sequence with nth term n² − 1?
5² − 1.
What is the nth term of 10, 7, 4, 1?
It goes down by 3, and 13 − 3 = 10.
What is the nth term of 1, 4, 9, 16?
They are the square numbers.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
4 questions, 7 marks. Write your answers on paper, then check them.
Sequences
Cambridge IGCSE Mathematics (9–1) 0980 · 7 marks · papermunch.org
Name ______________________________ Date ______________
Find the nth term of 5, 8, 11, 14.[2]
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3n + 2.
The nth term of a sequence is 3n + 2. Is 50 a term in the sequence? Show your working.[2]
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Yes. 3n + 2 = 50 gives n = 16, a whole number.
Find the nth term of 2, 5, 10, 17.[2]
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n² + 1.
Write down the next term of 3, 6, 12, 24.[1]
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48.
Answers: Sequences
- 1. 3n + 2.
- 2. Yes. 3n + 2 = 50 gives n = 16, a whole number.
- 3. n² + 1.
- 4. 48.