9.2 Using the nth term · Unit 9 Sequences and functions

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2 · Key words

nth termA rule giving any term directly from its position n.

positionWhere a term sits: n = 1 for the first term.

coefficientThe number multiplying n; it is the common difference.

substitutePut a number in place of the letter.

position-to-term ruleAnother name for the nth term rule.

3 · Summary of the sectionrevise from this

The nth term rule gives any term straight from its position, with no stepping.
n = 1 for the first term, n = 2 for the second, and so on.
The coefficient of n is the common difference. A gap of 4 means the rule starts 4n.
Find the constant by comparing 4n with the sequence: what must be added to reach it?
For a decreasing sequence the coefficient is negative: 20, 17, 14 has rule −3n + 23.
Always check by substituting n = 1, 2, 3. It takes seconds and catches almost everything.
To find a term's position, set the rule equal to it and solve.
If solving gives a fraction, that number is not in the sequence — positions must be whole numbers.

PDFPrintable worksheet All 61 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons2 videos

The nth Term

British corbettmaths

Finding the nth-term rule of a linear sequence, then using it to reach any term.

The nth Term — worked answers

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Full solutions to a practice set. Try the questions yourself first.

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Using the nth term