MathsYears 12–13Sequences and Series

Geometric sequences and series

Find nth terms, sums and sums to infinity of geometric sequences; convergence conditions

What you'll learn

  1. 1

    Imagine a bouncing ball that comes up half as high each time it bounces. The heights form a sequence: 100cm, 50cm, 25cm, 12.5cm… That's a geometric sequence!

  2. 2

    In a geometric sequence, what do we multiply by each time?

  3. 3

    Drag the slider to change the common ratio and see how the sequence grows or shrinks.

  4. 4

    Find the 5th term of a geometric sequence where first term a = 3 and common ratio r = 2.

  5. 5

    What is the 4th term of a geometric sequence with a = 5 and r = 3?

  6. 6

    Explore the formula for the nth term: a × r^(n-1). Type in a = 2, r = 3, n = 4 to find the 4th term.

  7. 7

    Which formula gives the nth term of a geometric sequence?

Practise Geometric sequences and series with Whizlo

Free AI-tutored lessons, unlimited practice questions, and progress tracking for ages 16–18. Aligned to the UK National Curriculum.