Visual sequences
Objective. Generalise growing patterns from diagrams and tables.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
A visual sequence presents a pattern through diagrams, such as growing arrangements of dots or matchsticks, where each new diagram adds a consistent number of extra elements. To generalise the pattern, count how many elements are in each diagram and find the difference between consecutive counts, which reveals the coefficient of n. For example, if a pattern of squares has 4, 7, 10, 13 matchsticks, the difference of 3 each time means the rule is 3n plus some constant, found by checking the first diagram. Drawing or sketching the next diagram in the pattern helps confirm the rule before writing it algebraically.
Worked example
A visual pattern of L-shapes uses 3, 5, 7, 9 tiles for pattern numbers 1, 2, 3, 4. Find the nth-term rule for the number of tiles.
- 1Find the common difference between consecutive tile counts: 5−3=2.
- 2Start the rule with 2n.
- 3Compare 2×1=2 to the first term 3: the constant is 3−2=1.
- 4Check with n=4: 2×4+1=9, which matches the fourth pattern.
Answer: 2n + 1
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils sometimes count only the newly added elements in each diagram rather than the total elements shown, leading to an incorrect sequence of numbers. Always count the whole diagram's total each time.
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