Sequences

After studying this section, you will be able to:

generate sequences given a rule and understand some of the vocabulary used in algebra
construct an algebraic expression for the nth term of a sequence

Generating terms of a sequence

NOTE: u₁is shorthand for the first term; t₁ is also used.

NOTE: Sequence rules stated in this way are sometimes called ‘term to term’ rules − one term is expressed in terms of another.

Finding the nth term

NOTE: When looking for patterns in sequences look for factors, square and cube numbers and terms going up or down by the same amount.

NOTE: In the expression 3x² − 2x + 4 the coefficient of x² is 3 and the coefficient of x is −2.

NOTE:

Differences between terms are 3, 5, 7 and 9, so the nth term probably involves a quadratic.

When asked questions like this it is helpful to look at how the pattern is built up.

Always check that your expression for the nth term agreeswith the terms you are given

PROGRESS TEST

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