Nth-Term Rules — Jump to Any Term (Grades 6–7)
An nth-term rule lets you find any term without listing them all. If the rule is value = 3n + 1, the 10th term is 3·10 + 1 = 31 — no need to write the first nine. Build the rule (use the common difference for the coefficient, then adjust the constant), then plug in the position you want.
Understanding nth-term rules
An nth-term rule lets you find any term without listing them all. If the rule is value = 3n + 1, the 10th term is 3·10 + 1 = 31 — no need to write the first nine. Build the rule (use the common difference for the coefficient, then adjust the constant), then plug in the position you want.
Key Idea
An nth-term rule lets you find any term without listing them all. If the rule is value = 3n + 1, the 10th term is 3·10 + 1 = 31 — no need to write the first nine. Build the rule (use the common difference for the coefficient, then adjust the constant), then plug in the position you want.
Seeing it in action
Worked example
The rule is 3n + 1. Find the 10th term.
3·10 + 1 = 31.
Plug the position into the rule.
Try a few
Rule 2n: the 8th term?
Rule 5n − 2: the 4th term?
Rule n + 10: the 7th term?
Number Current
A calm number-line game for placing whole numbers and extending patterns.
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Practice nth-term rules in Numeris with instant feedback.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
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