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Geometric Sequences

Maths: Edexcel A Level Pure Maths, topic 4.2.5

Geometric Sequences

A geometric sequence is one in which any term divided by the previous term is a constant.

Common ratio

Common ratio

  • This constant is called the common ratio of the sequence.
  • The common ratio can be found by dividing any term in the sequence by the previous term.
Explicit formula

Explicit formula

  • If a1a_1 is the initial term of a geometric sequence and rr is the common ratio, the explicit equation to find a particular term ana_n is:
  • an=a1rn−1a_n = a_1r^{n-1}
Recursive formula

Recursive formula

  • A recursive formula allows us to find any term of a geometric sequence by using the previous term:
  • an=ran−1a_n=ra_{n-1}
  • For n≥2n\geq 2

Test yourself on Geometric Sequences

  • The first term in a geometric sequence is 2, and the common ratio is 3. What is the 5th term?

  • The first term in a geometric sequence is 16 and the common ratio is −13-\frac{1}{3}. What is the 4th term?

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