lesson
A rule describes more than one term
1 · Learn
A linear sequence changes by a constant amount. In 5, 8, 11, 14, the step is 3. If n starts at 1 for the first term, 3n + 2 gives each listed value.
A few terms can fit more than one possible rule, so state the intended pattern. Distinguish the term's position from its value: the fourth term here is 14, not 4.
2 · Worked example
For n = 6, 3n + 2 = 20. Checking n = 1 gives 5, confirming that the starting position matches the rule.
3 · Your turn
Using the stated rule 4n - 1 with n starting at 1, find the first three terms and the tenth term.
Check your answer
3, 7, 11; the tenth term is 39.
4 · Apply your learning
Make a position-value table and explain the difference between the step size and the first value.
Adult guidance and safety
Ask the learner to explain the method and check it using a different representation. Supply place-value grids, fraction strips, accurate diagrams and measuring tools where needed. These examples need varied practice; a short correct answer alone does not establish fluency.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
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