The nth term of a linear sequence
Objective. Find an expression for the nth term of an arithmetic sequence.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: 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
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Start practisingCommon mistake. Using the first term as the constant instead of the zeroth term.
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