An arithmetic sequence adds the same amount each time. Its nth term is dn + (first term − d), where d is the common difference. For 24, 32, 40, 48 the difference is 8, so the nth term is 8n + 16.
Use the rule to answer questions. To find which term is 134 in 26, 30, 34, 38, use the nth term 4n + 22 and solve 4n + 22 = 134: n = 28. If n is not a whole number, the value is not in the sequence.
Worked example
Find the nth term of 9, 6, 3, 0, …
- The difference is −3, so start with −3n: −3, −6, −9.
- Each term is 12 more than −3n.
Answer:−3n + 12 (or 12 − 3n)
Key words
- arithmetic sequence
- goes up or down by the same amount
- common difference
- the amount added each time
- nth term
- a formula for any term
Practise this
New questions every time.
Common Core-referenced: HSF-BF.A.2