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🔢 Finding the Nth Term

Crack the formula behind any arithmetic sequence. Once you can write rules like 4n − 1, you can name the 100th term without listing the 99 before it.

lessons

~15 min

to learn

🔢 Math

subject

Teens

level

Start the course →

What you’ll learn

Spotting the PatternRecognise arithmetic sequences and find the common difference.A sequence is an ordered list of numbers. It is arithmetic when every term changes by the same amount — the common difference. Spotting that steady jump is the first step to writing a rule for the whole sequence.
Building the RuleWrite the nth-term rule using the common difference and the zero term.The nth-term rule is d·n plus the zero term (the value one step before the first term). For 3, 7, 11, 15 the jump is 4 and the zero term is −1, giving 4n − 1. Feeding a position n into the rule returns that term.
Using the RuleUse an nth-term rule to find distant terms and test whether a number belongs.Substituting n into the rule gives any term instantly, so 4n − 1 hands you the 100th term as 399. To test membership, set the rule equal to the number and solve for n; a whole-number answer means it belongs.

Questions this course answers

What is the nth-term rule for 5, 8, 11, 14?

Jump 3 gives 3n; zero term 5 − 3 = 2 gives 3n + 2.

Is 30 a term of the sequence 4n − 1?

4n − 1 = 30 gives n = 7.75, which is not whole.

Grounded in trusted sources

Khan Academy — Algebra
OpenStax — Elementary Algebra 2e
BBC Bitesize — Maths
Cuemath — Algebra

Every Wunder lesson is built from real, reputable sources — never invented.

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