9.1 Generating sequences · Unit 9 Sequences and functions

1 · Teaching slidesuse ← → keys

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2 · Key words

sequenceA list of numbers in a definite order.

termOne of the numbers in a sequence.

term-to-term ruleHow to get from one term to the next.

first termThe number the sequence starts at.

common differenceThe constant gap in a linear sequence.

linear sequenceOne whose terms go up or down by the same amount.

square numbers1, 4, 9, 16, … — the results of squaring.

triangular numbers1, 3, 6, 10, … — the gaps grow by 1 each time.

3 · Summary of the sectionrevise from this

A sequence is an ordered list; each number in it is a term.
A term-to-term rule says how to get from one term to the next.
To generate a sequence you need the rule and the first term — one without the other is not enough.
A sequence is linear when the gap between terms is always the same. That gap is the common difference.
To find the common difference, subtract any term from the one after it — and check the gap really is constant.
To reach the kth term from the first, take k − 1 steps, not k. That off-by-one is the commonest slip.
Not every sequence is linear: 2, 6, 18, 54 multiplies by 3; 1, 4, 9, 16 squares the position.
Learn the square, cube and triangular numbers by sight — they come up all year.

PDFPrintable worksheet All 64 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons1 videos

Sequences: Patterns

British corbettmaths

Spotting the rule in a growing pattern, and continuing it.

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Generating sequences