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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.

5 … 8
Illustrated card showing 5 … 8
  1. 1Common difference is 3, so start with 3n.
  2. 23 × 1 = 3 but the first term is 5, so add 2.
  3. 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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