Me

Sequences Cambridge IGCSE Mathematics revision

Not started

Learn it

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

  1. 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.
  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.
  3. 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.

  1. The difference is 5 each time, so the rule starts 5n.
  2. When n = 1, 5n = 5, but the first term is 4, so subtract 1.
  3. 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.
5 questions, about 2 minutes.

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.

  1. What is the next term of 7, 11, 15, 19?
    • 21
    • 22
    • 23 (the answer)
    • 24

    Add 4.

  2. What is the nth term of 2, 4, 6, 8?
    • n + 2
    • 2n (the answer)
    • n²
    • 2n + 2

    It is the two times table.

  3. What is the 5th term of the sequence with nth term n² − 1?
    • 9
    • 24 (the answer)
    • 25
    • 26

    5² − 1.

  4. What is the nth term of 10, 7, 4, 1?
    • 3n + 7
    • 10 − n
    • 13 − 3n (the answer)
    • 7n + 3

    It goes down by 3, and 13 − 3 = 10.

  5. What is the nth term of 1, 4, 9, 16?
    • 3n − 2
    • 2n
    • n² (the answer)
    • n + 3

    They are the square numbers.

Things you can type

Or go straight to

Or browse a shelf