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# Edexcel A-level Maths Geometric sequences

In a geometric sequence, all terms are multiplied or divided by the same value. For example, the sequence 2, 4, 8, 16, ... is geometric, as each term is twice the previous term.

The term to term rule in a geometric sequence is multiplying or dividing by the same value, also known as the common ratio (r). The common ratio is determined by dividing one term by the previous term.

The nth term, or general term, of a geometric sequence is given by a formula (see image).

A geometric sequence (i.e. a list of terms) can also be represented as a geometric series (a sum of terms). Sigma notation (see image) is used to calculate the sum of a finite number of terms of a geometric sequence.

An infinite series has an infinite number of terms. The partial sum (Sā) of these terms is the sum of the first n terms. If Sā approaches a finite limit (known as the sum to infinity), the series is convergent. In a geometric series, if |r|< 1, the sum to infinity can be calculated with a formula (see image).

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Determine whether the sequence 1, 0, 1, 0, ... is geometric. Give reasoning for your answer.

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What is the name given to the value each term in a geometric sequence is multiplied/divided by?

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Obtain the common ratio of the geometric sequence 1.5, 13.35, 118.815, ....

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What are the next three terms of the geometric sequence 12, 6, 3, ...?

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Find the 7th term of the geometric sequence 8, 4, 2, ....

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Obtain the 6th term of the geometric sequence ā3.7, ā4.81, ā6.253, ... .

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What is the 11th term of the geometric sequence with the 7th term 18.225 and the common ratio 1.5?

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Calculate the sum of the first three terms of the geometric sequence 8, 24, 72, ... .

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Obtain the sum of the first five terms of the geometric sequence 2.4, ā1.2, 0.6, ā0.3, ... .

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If |r| > 1, a geometric series is convergent. True or false? Explain your answer.

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Determine the sum to infinity of the geometric series 8 ā 4 + 2 ā 1 ... .

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Find the sum to infinity of the geometric series 4.6 + 3.68 + 2.944 + ... .

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