① Spot the sequence
A mix of sequence types — linear, geometric and Fibonacci-type. Work out how the terms are changing, then continue the pattern.
② Linear sequences — next terms
Focusing on linear (arithmetic) sequences: find the next terms, or continue the pattern to a later term.
③ Visual growing patterns (linear)
Tables and chairs pushed together in a row — see how the pattern grows, then find the rule connecting the two.
④ Finding the nth-term rule
Work out the rule \(dn+c\) that generates a sequence, from a list of terms or a table of two related variables.
⑤ Using the rule — substitution
Substitute into a given rule to find a term, then work backwards to find which term number a value has.
⑥ Decreasing linear sequences — finding the rule
Sequences that go down each time give a negative coefficient in the rule (e.g. \(16-4n\)) — focused practice on getting the sign right.
⑦ Using the rule — from two given terms
Given two terms of a sequence, find the common difference and use it to work out another term.
Key reminders
Linear (arithmetic): add the same number each time. nth term = \(dn+c\) where \(d\) = common difference.
Geometric: multiply by the same ratio each time.
Fibonacci-type: each term = sum of the two before it.
Finding the rule: work out how much the sequence changes by each step to get \(d\), then use the 1st term to find \(c\).