What is covered in Grade 11 Mathematics Number Patterns?

Quadratic sequences: find the general term and verify. Introduction to arithmetic and geometric sequences.

Is Grade 11 Number Patterns tested in Paper 1 or Paper 2?

Grade 11 Mathematics Number Patterns is assessed in Paper 1 of the end-of-year examinations, as per the CAPS Mathematics curriculum guidelines.

When is Number Patterns taught in Grade 11 Mathematics?

Number Patterns is taught in Term 1 of Grade 11 according to the CAPS Annual Teaching Plan (ATP) for Mathematics in South Africa.

Is Grade 11 Mathematics Number Patterns on the CAPS curriculum?

Yes. Number Patterns is part of the official CAPS Mathematics curriculum for Grade 11, Term 1 in South Africa. The content on MathSciBuddy follows the Annual Teaching Plan (ATP) set by the Department of Basic Education.

Is this Grade 11 Mathematics study material free?

Yes. All chapter notes, definitions, formulas, and worked examples on MathSciBuddy are completely free to read. No account or subscription is needed to access CAPS-aligned study notes.

Grade 11 Mathematics

Grade 11 · Term 1Mathematics

Number Patterns

We extend Grade 10 quadratic patterns and introduce arithmetic and geometric sequences, laying the groundwork for Grade 12 series.

Week 5

3.1 Arithmetic & Geometric Sequences

Recognise arithmetic sequences and find the general term $T_n=a+(n-1)d$
Recognise geometric sequences and find the general term $T_n=ar^{n-1}$
Apply to real-world contexts

🌍

Real-World Connection

An arithmetic sequence is a constant salary raise each year. A geometric sequence is a percentage raise — which sounds smaller initially but compounds to overtake the arithmetic raise. That is the power of geometric (exponential) growth.

Definition

Arithmetic Sequence

A sequence with a CONSTANT difference $d$ between consecutive terms. The general term formula counts $n-1$ steps of $d$ from the first term $a$ .

T_n = a + (n-1)d \quad d = T_{n+1}-T_n = \text{const}

Definition

Geometric Sequence

A sequence with a CONSTANT ratio $r$ between consecutive terms. Each term is found by multiplying the previous term by $r$ .

T_n = ar^{n-1} \quad r = \frac{T_{n+1}}{T_n} = \text{const}

🚨 Common Mistake

The common difference $d$ can be negative (decreasing sequence). The common ratio $r$ can be a fraction (between 0 and 1 → decreasing geometric sequence). Neither $d$ nor $r$ can be zero in a valid sequence.

Worked Examples

Worked Example

Arithmetic sequence — find a term

Problem

T_{50}

Worked Example

Geometric sequence — general term

Problem

T_n

Activity — 8 Questions

CAPS Cognitive Level Distribution

L1 · Knowledge2 Q

L2 · Routine Procedures2 Q

L3 · Complex Procedures2 Q

L4 · Problem Solving2 Q

L1 · Knowledge1 mark

State the common difference of

14, 9, 4, -1, \ldots

L1 · Knowledge1 mark

State the common ratio of

2, 6, 18, 54, \ldots

L2 · Routine Procedures3 marks

Find the 20th term of the arithmetic sequence

-3, 2, 7, 12, \ldots

L2 · Routine Procedures3 marks

A geometric sequence has

T_1=4

and

r=\frac{1}{2}

. Find

T_5

L3 · Complex Procedures4 marks

In an arithmetic sequence

T_3=7

and

T_9=25

. Find

a

and

d

L3 · Complex Procedures4 marks

In a geometric sequence

T_2=6

and

T_5=48

. Find

r

and

T_1

L4 · Problem Solving4 marks

How many terms of the arithmetic sequence

5, 9, 13, \ldots

are less than 100?

L4 · Problem Solving5 marks

A geometric sequence has

T_3+T_4=3

and

T_3\cdot T_4=2

. Find the common ratio.

Equations & Inequalities