Geometric Sequences for IGCSE Maths

What You Need to Know

Sequences with a constant ratio between consecutive terms. This subtopic is part of Sequences in the Cambridge IGCSE Mathematics 0580 syllabus (Extended tier only). Understanding geometric sequences is essential for achieving a strong grade in your IGCSE Maths exam.

Understanding Geometric Sequences

A geometric sequence has a constant ratio r between consecutive terms. The nth term formula is Tₙ = ar^(n−1), where a is the first term. The sum of the first n terms is Sₙ = a(rⁿ − 1)/(r − 1) for r ≠ 1. IGCSE Extended tests: finding the nth term, the common ratio, specific terms, and the sum of a geometric series. Real-world applications include compound interest and population growth.

Step-by-Step Method

1. 1

   Find the common ratio r

   Divide any term by the previous one: r = T₂/T₁ = T₃/T₂. Verify it is constant.

2. 2

   Identify the first term a

   The first term is given as the first number in the sequence.

3. 3

   Write the nth term formula

   Tₙ = a × r^(n−1). Substitute a and r.

4. 4

   Find the sum if required

   Sₙ = a(rⁿ − 1)/(r − 1) for r ≠ 1. For |r| < 1, the sum to infinity is S∞ = a/(1−r).

5. 5

   Verify and interpret

   Substitute n = 1, 2, 3 to confirm the formula gives back the original terms.

Exam Tips for Geometric Sequences

• Common ratio r = T₂ ÷ T₁, not T₂ − T₁ — always divide, never subtract, for geometric sequences.
• The sum formula Sₙ = a(rⁿ−1)/(r−1) is on the formula sheet — but identify a and r correctly first.
• For r between −1 and 1 (e.g. r = 1/2), a sum to infinity exists: S∞ = a/(1−r).
• Compound interest is a geometric sequence: P(1+r/100)ⁿ — recognise this connection in application questions.

Practice Questions

Frequently Asked Questions