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Auralith Learning

Year 8 · Maths · Sequences and the nth term · Lesson 2

Finding the nth term

Find the nth term of increasing and decreasing linear sequences, use it to find any term, and solve pattern problems.

Whiteboard video lesson: Finding the nth term

40-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

Watch free for a month

What your child will learn

  • Find the nth term of an increasing linear sequence
  • Find the nth term of a decreasing linear sequence
  • Use the zero term
  • Use the nth term to find any term
  • Solve pattern problems

The method

  1. Find the difference. Difference 3 means the nth term starts with 3n.
  2. Write out the 3n sequence underneath.
  3. Compare: what do you add or subtract?
  4. Check with one of the terms.

Key words: nth term, linear sequence, difference, zero term, position.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

Find the nth term of the sequence 7, 9, 11, 13, 15, ...

  1. Step 1: Find the difference
  2. Step 2: Difference 2: write out 2n
  3. Step 3: Terms − 2n: 7 − 2 = 5 every time
  4. Step 4: nth term = 2n + 5 (check n = 3: 2 × 3 + 5 = 11)

Answer: 2n + 5

Question 2

Find the nth term of the sequence 4, 7, 10, 13, 16, ...

  1. Step 1: Find the difference
  2. Step 2: Difference 3: write out 3n
  3. Step 3: Terms − 3n: 4 − 3 = 1 every time
  4. Step 4: nth term = 3n + 1 (check n = 3: 3 × 3 + 1 = 10)

Answer: 3n + 1

Question 3

Find the nth term of the sequence 9, 13, 17, 21, 25, ...

  1. Step 1: Find the difference
  2. Step 2: Difference 4: write out 4n
  3. Step 3: Terms − 4n: 9 − 4 = 5 every time
  4. Step 4: nth term = 4n + 5 (check n = 3: 4 × 3 + 5 = 17)

Answer: 4n + 5