Geometric sequence formula: aₙ = arⁿ⁻¹
The geometric sequence formula is aₙ = arⁿ⁻¹.
What each letter means
- \(a_n\) the nth term of the GP
- \(a\) the first term
- \(r\) the common ratio
- \(n\) the position of the term
When to use it
When each term is the previous one multiplied by the same number: compound growth, depreciation, bouncing balls, populations.
Worked example
Find the 10th term of the GP \(5,\ 10,\ 20,\ \dots\)
- \(a=5,\ r=\tfrac{10}{5}=2\)
- \(a_{10}=5\times2^{9}=5\times512\)
Answer: \(a_{10}=2560\)
Common mistake
Using rⁿ instead of rⁿ⁻¹. The first term has not been multiplied by r at all, so the 8th term has r⁷.
On your course
| Course | In the exam |
|---|---|
| Class 11 | Learn it: CBSE gives no formula booklet |
From our own CBSE Maths formula sheets, in our words.
Practise and revise
Questions
What is the geometric sequence formula?
The geometric sequence formula is aₙ = arⁿ⁻¹. aₙ: the nth term of the GP; a: the first term; r: the common ratio; n: the position of the term.
Is the geometric sequence (nth term) given in the exam?
Class 11: learn it: CBSE gives no formula booklet. This comes from our own CBSE Maths formula sheets; your teacher has the official booklet.
How do I find the common ratio?
Divide any term by the one before it: r = u₂ ÷ u₁. If you know two terms that are not next to each other, divide them to get a power of r and take the root.
Our own wording, examples and card, checked by CBSE Math Revision. Not produced or endorsed by CBSE or NCERT.