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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)

  1. Calculate the first difference (subtract consecutive terms)
  2. Confirm the difference is constant, if yes, it is a linear sequence
  3. Add the constant difference to find the next term
Grade 10Paper 1Level 1, Knowledge
Consider the finite linear pattern: 20 ; 17 ; 14 ; ... ; −103 3.1 Write down the 4th term of the pattern.

Source: DBE Mathematics Paper 1, Grade 10, November 2018, Question 3.1

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)

  1. Calculate the first difference (d)
  2. Use the formula: Tn = a + (n − 1)d, where a is the first term
  3. Simplify to the form Tn = dn + c
Grade 10Paper 1Level 2, Routine Procedures
Consider the finite linear pattern: 20 ; 17 ; 14 ; ... ; −103 3.2 Determine the expression for the nth term.

Source: DBE Mathematics Paper 1, Grade 10, November 2018, Question 3.2

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)

  1. Write out the general term formula (find it first if not given)
  2. Set Tn equal to the given value
  3. Solve for n
  4. Check that n is a positive whole number, if not, that value is not in the sequence
Grade 10Paper 1Level 2, Routine Procedures
Consider the finite linear pattern: 20 ; 17 ; 14 ; ... ; −103 3.4 Which term is the first to have a negative value?

Source: DBE Mathematics Paper 1, Grade 10, November 2018, Question 3.4

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.