Sequences and the nth term
Linear (arithmetic) sequences and the formula for the nth term: an + b.
A linear sequence has a constant difference. The nth term formula is a×n + b where a is the common difference and b is chosen so n=1 gives the first term.
Worked examples
3, 5, 7, 9, ... has nth term 2n + 1. Difference = 2; first term = 3 means b = 1.
−1, 3, 7, 11, ... has nth term 4n − 5.
The 50th term of 3, 5, 7, ... is 2×50 + 1 = 101.
Frequently asked questions
How do I find the formula?
Step 1: common difference a. Step 2: b = first term − a.
Quadratic sequences?
Year 9 sees quadratic (second difference constant). Full quadratic nth term comes in GCSE.