Sequences
Lesson 9 of 13
The nth term of a linear sequence
Objective. Find an expression for the nth term of an arithmetic sequence.
The key idea
For a common difference d, the nth term is dn + c, where c is the value you would need before the first term (the 'zeroth' term).
Worked example
Find the nth term of 5, 8, 11, 14.
- 1Common difference is 3, so start with 3n.
- 23 × 1 = 3 but the first term is 5, so add 2.
- 3nth term is 3n + 2.
Answer: 3n + 2
Practice
Each question comes with a picture and a listen button. Try it first, then reveal the answer.
Common mistake. Using the first term as the constant instead of the zeroth term.
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