Continue a sequence, describe its rule, fill gaps, and generate terms from a rule or an nth term.
What you will learn
- Continue a sequence and describe its rule
- Find missing terms
- Generate terms from a rule or from an nth term
The rule from one term to the next
A term-to-term rule says how to get the next term from the one before: 5, 9, 13, 17, ...
is "add 4"; 3, 6, 12, 24, ... is "multiply by 2".
A rule can have two steps: start at 2, then "multiply by 3 and subtract 1" gives 2, 5, 14, 41, ...
A sequence that goes down keeps going past zero: 14, 9, 4, ... subtracts 5, so the next terms are −1, −6, ...: the first negative term is −1.
If the terms go up or down by the same amount each time, a missing term sits halfway between its neighbours: in 7, □, 19, the gap of 12 covers two steps, so each step is 6 and the missing term is 13.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- The rule from one term to the next
- Using the position: the nth term
7 practice questions, marked as you go; about 20 minutes in all.
Key terms
Term-to-term rule, Nth term
In this unit: Sequences
Term-to-term rules, the nth term of linear sequences, special sequences, geometric sequences and (Higher) the nth term of quadratic sequences.