Sequences

Identify arithmetic patterns, calculate missing terms and form or use a linear nth-term rule.

Curriculum rangeYears 7–11

Each term is found by adding the common difference to the term before it.

First term (a)

Common difference (d)

37111519…

Add 4 each time. Term 1 is 3, so the difference from n to the constant is a − d = 3 − 4 = -1.

n^th term = $4n - 1$

Check: when n = 1, $4n - 1 = 3$ . When n = 5, $4n - 1 = 19$ .