Quadratic sequence

Definition

A quadratic sequence has first differences that change but second differences that are constant. Its general term is Tₙ = an² + bn + c, where 2a equals the second difference, 3a + b equals the first first-difference, and a + b + c equals T₁.

Worked example

2; 5; 10; 17; … has first differences 3; 5; 7 and second difference 2, so a = 1, b = 0, c = 1 and Tₙ = n² + 1.

3; 6; 11; 18; … gives Tₙ = n² + 2, so T₂₀ = 402 and the 25th term is 627.

Where it appears in the exam

Quadratic sequence is part of the number patterns section of CAPS Grade 11 Mathematics and is examined in Paper 1 of the November exam.

Step-by-step method

1. Find the first and second differences.
2. 2a = second difference.
3. 3a + b = T₂ − T₁.
4. a + b + c = T₁; then check with T₃.

Common mistake

Setting a equal to the second difference instead of 2a.

Related number patterns terms

• General term

Frequently asked questions

What does quadratic sequence mean in Grade 11 Maths?

A quadratic sequence has first differences that change but second differences that are constant. Its general term is Tₙ = an² + bn + c, where 2a equals the second difference, 3a + b equals the first first-difference, and a + b + c equals T₁.

Which paper tests quadratic sequence in Grade 11?

Quadratic sequence belongs to the Number patterns section of CAPS Grade 11 Mathematics, which is examined in Paper 1 of the November exam.

How do I practise questions involving quadratic sequence?

Snap a question that uses quadratic sequence into Snap&Learn with your grade set to Grade 11, or work through the Grade 11 topic guide and practice papers.