Grade 10 Number Patterns — How to Identify the Question Type

Grade 10 number patterns focus on linear sequences (constant first difference). Before answering, check whether you are asked to find a term, find the general term, or find which term has a specific value.

Type 1: Finding the next term or missing term

Trigger words: "Write down the next two terms", "Find the missing term"

Trigger structure: A sequence is given with one or more blanks, or you are asked to continue the pattern.

Do not confuse with: Finding the general term — if the question asks for a 'formula' or 'Tn =', that is a different type.

Method (no numbers — just the steps)

Calculate the first difference (subtract consecutive terms)
Confirm the difference is constant — if yes, it is a linear sequence
Add the constant difference to find the next term

Grade 10Paper 1Level 1 — Knowledge

The sequence is: 4 ; 7 ; 10 ; 13 ; ... Write down the next TWO terms.

Practice question — not sourced from a past paper.

See the progression — same type, increasing difficulty

Easy

5 ; 9 ; 13 ; 17 ; ... Write down the next term.

Practice question — not sourced from a past paper.

Medium

3 ; ___ ; 11 ; 15 ; ... Find the missing term.

Practice question — not sourced from a past paper.

Hard

The sequence −1 ; ___ ; ___ ; 14 ; 19 ; ... has a constant first difference. Find the two missing terms.

Practice question — not sourced from a past paper.

Type 2: Finding the general term (Tn formula)

Trigger words: "Determine a formula", "Write down the general term", "Tn ="

Trigger structure: The question asks for a rule or formula in terms of n, not a specific term value.

Do not confuse with: Finding a specific term — once you have Tn, substitute n to find a term value.

Method (no numbers — just the steps)

Calculate the first difference (d)
Use the formula: Tn = a + (n − 1)d, where a is the first term
Simplify to the form Tn = dn + c

Grade 10Paper 1Level 2 — Routine Procedures

2.1 Consider the sequence: 2 ; 5 ; 8 ; 11 ; ... Determine the general term Tn.

Source: DBE Mathematics Paper 1, November 2018, Question 2.1

Common mistake

Writing Tn = a + nd instead of a + (n − 1)d — the off-by-one error shifts every term value.

See the progression — same type, increasing difficulty

Easy

Write down the general term of the sequence: 6 ; 11 ; 16 ; 21 ; ...

Practice question — not sourced from a past paper.

Medium

The general term of a sequence is Tn = 4n − 3. Write down the first FOUR terms.

Practice question — not sourced from a past paper.

Hard

A sequence has a constant difference. The 3rd term is 11 and the 7th term is 27. Determine the general term.

Practice question — not sourced from a past paper.

Type 3: Finding which term has a given value

Trigger words: "Which term", "For which value of n", "Determine n if Tn = ..."

Trigger structure: The question gives you a value and asks which position (n) it occupies in the sequence.

Do not confuse with: Finding a term value — here the value is given and n is unknown.

Method (no numbers — just the steps)

Write out the general term formula (find it first if not given)
Set Tn equal to the given value
Solve for n
Check that n is a positive whole number — if not, that value is not in the sequence

Grade 10Paper 1Level 2 — Routine Procedures

The general term of a sequence is Tn = 3n + 2. Determine which term of the sequence is equal to 41.

Practice question — not sourced from a past paper.

See the progression — same type, increasing difficulty

Easy

Tn = 5n − 2. For which value of n is Tn = 48?

Practice question — not sourced from a past paper.

Medium

The sequence 4 ; 7 ; 10 ; 13 ; ... continues. Is 100 a term in this sequence? Show how you determined your answer.

Practice question — not sourced from a past paper.

Hard

The sequence 7 ; 11 ; 15 ; ... continues. Is 200 a term of the sequence? Justify your answer.

Practice question — not sourced from a past paper.

Words like determine and hence appear throughout this topic — see the instruction word glossary for full definitions.