Geometric Sequences

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Description of Levels

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Level 1 - Find the next term of these geometric sequences

Level 2 - Find a given term of these geometric sequences

Level 3 - Mixed questions about geometric sequences and their sums

Level 4 - Sum of infinite convergent geometric sequences

Missing Terms - Find the missing terms of arithmetic, geometric and Fibonacci-type sequences in this self marking quiz.

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

Arithmetic Sequences - A similar exercise on arithmetic sequences.

Sigma - Practise using the sigma notation to find the sum of various number series.

More on this topic including lesson Starters, visual aids and investigations.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Geometric Sequences

Here is a reminder of some facts that may help you answering the questions in this exercise.

An geometric sequence, sometimes called a geometric progression, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed number called the common ratio. For example, the sequence 5, 10, 20, 40, ... is a geometric sequence with common ratio 2.

The first term of the sequence can be written as u₁

The n^th term of the sequence can be written as u_n

The common ratio is usually written as r

The formula for finding the n^th term is u_n=u₁r^(n-1)

The excellent video above is from Corbettmaths.

The formula for finding the sum of $n$ terms is:

$$ S_n = \dfrac{u_1(r^n-1)}{r-1}$$

The sum of an infinite geometric sequence is:

$$ S_\infty = \dfrac{u_1}{1-r}, \quad |r| \lt 1 $$

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Geometric Sequences

An exercise on geometric sequences including finding the nth term and the sum of n terms.

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Geometric Sequences