Nth-Term Rules — Jump to Any Term (Grades 6–7)
An nth-term rule lets you find any term without listing them all.
Understanding nth-term rules
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.
A common mistake, and the fix
Adding the position instead of multiplying it.
With 3n + 1, the 10th term is 3 × 10 + 1 = 31; 3 + 10 + 1 = 14 treats 3n as 3 + n. Check the rule against a term you know: the 1st term is 3 × 1 + 1 = 4.
Try a few
Rule 2n: the 8th term?
Rule 5n − 2: the 4th term?
5 × 4 = 20, then 20 − 2.
Rule n + 10: the 7th term?
Number Current
A calm number-line game for placing whole numbers and extending patterns.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
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