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Grades 8–11 · CAPS · Gr 11 Term 1 - Number patterns

Grade 11 Number patterns

Patterns with a constant second difference, and the quadratic general term that fits them.

Gr 11 Term 1 - Number patternsTerm 1 - 2 weeks (CAPS)

Practise Number patterns in the app →

What gets asked

Show that a pattern has a constant second difference.
Find the general term $T_{n}$ of a quadratic pattern.
Use $T_{n}$ to find a term, or to find which position holds a given value.

You must be able to

Difference the terms twice; a quadratic pattern goes constant on the second pass.
The coefficient of $n^{2}$ is half the constant second difference.
Fit the remaining linear part against the first two terms.
When solving for a position, keep only the positive whole-number root.

Traps that cost marks

Using the second difference itself as the coefficient of $n^{2}$ . Halve it: a second difference of 4 means $2 n^{2}$ , not $4 n^{2}$ .
Accepting $n = - 3$ as the position of a term. Positions count 1, 2, 3, ... - reject roots that are negative or not whole.

Worked example

Find the general term of

3; 8; 15; 24; \dots

First differences: $5; 7; 9$ . Second difference: constant $2$ , so $a = 1$ .
Subtract $n^{2}$ : $3 - 1 = 2$ , $8 - 4 = 4$ , $15 - 9 = 6$ - the remainder is $2 n$ .
$T_{n} = n^{2} + 2 n$ . Check: $T_{4} = 16 + 8 = 24$ .

About this material

This platform provides original CAPS-aligned practice material and study tools. Content is machine-verified and has not been reviewed by subject specialists. It is not affiliated with or endorsed by the Department of Basic Education. Learners should also use official past papers and consult their teachers where uncertain.