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Problem Solving - Identifying patterns and sequences

Grade 4IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Definition of a Sequence: An ordered list of numbers or shapes that follow a specific rule.

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Term: Each individual number or object in a pattern or sequence.

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The Rule: The mathematical instruction used to find the next term (e.g., 'add 5' or 'subtract 3').

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Ascending Sequences: Patterns where the numbers increase (usually through addition or multiplication).

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Descending Sequences: Patterns where the numbers decrease (usually through subtraction or division).

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Linear Patterns: Sequences where the difference between terms is always the same.

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Spatial Patterns: Using shapes or dots to represent numerical sequences.

📐Formulae

Next Term=Previous Term+Common Difference\text{Next Term} = \text{Previous Term} + \text{Common Difference}

Next Term=Previous Term−Common Difference\text{Next Term} = \text{Previous Term} - \text{Common Difference}

Difference=Term2−Term1\text{Difference} = \text{Term}_2 - \text{Term}_1

💡Examples

Problem 1:

Find the next two numbers in the sequence: 4, 11, 18, 25, __, __

Solution:

32, 39

Explanation:

First, find the difference between consecutive terms: 11−4=711 - 4 = 7 and 18−11=718 - 11 = 7. The rule is to add 7. Therefore, 25+7=3225 + 7 = 32 and 32+7=3932 + 7 = 39.

Problem 2:

Identify the missing number in this descending sequence: 100, 92, 84, __, 68

Solution:

76

Explanation:

Determine the rule by subtracting the second term from the first: 100−92=8100 - 92 = 8. The sequence is decreasing by 8 each time. 84−8=7684 - 8 = 76. To check: 76−8=6876 - 8 = 68, which matches the final term.

Problem 3:

A pattern uses triangles. Shape 1 has 3 sides, Shape 2 has 6 sides, Shape 3 has 9 sides. How many sides will Shape 5 have?

Solution:

15 sides

Explanation:

The sequence of sides is 3, 6, 9... This is the 3 times table. The rule is Shape Number×3Shape \, Number \times 3. For Shape 5, the calculation is 5×3=155 \times 3 = 15.