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Auralith Learning

Year 7 · Maths · Sequences · Lesson 3

Using a given nth term

Use a given nth term formula to generate terms, find any term, find which term has a given value, and decide if a number is in a sequence.

Whiteboard video lesson: Using a given nth term

28-minute video lesson

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

Watch free for a month

What your child will learn

  • Understand position and term
  • Generate a sequence from an nth term
  • Find any term from the nth term
  • Find which term has a given value
  • Decide whether a number is a term

The method

  1. n is the position: 1, 2, 3, ...
  2. Replace n with the position number.
  3. Multiply first, then add or subtract.
  4. To find which term has a value, solve an equation.

Key words: nth term, position, term, substitute, sequence.

Worked examples

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

Question 1

Write the first 5 terms of the sequence with nth term 3n + 1.

  1. Step 1: n = 1: 3 × 1 + 1 = 4
  2. Step 2: n = 2: 3 × 2 + 1 = 7
  3. Step 3: n = 3: 3 × 3 + 1 = 10
  4. Step 4: n = 4: 3 × 4 + 1 = 13
  5. Step 5: n = 5: 3 × 5 + 1 = 16

Answer: 4, 7, 10, 13, 16

Question 2

Write the first 5 terms of the sequence with nth term 5n.

  1. Step 1: n = 1: 5 × 1 = 5
  2. Step 2: n = 2: 5 × 2 = 10
  3. Step 3: n = 3: 5 × 3 = 15
  4. Step 4: n = 4: 5 × 4 = 20
  5. Step 5: n = 5: 5 × 5 = 25

Answer: 5, 10, 15, 20, 25

Question 3

Write the first 5 terms of the sequence with nth term 2n + 7.

  1. Step 1: n = 1: 2 × 1 + 7 = 9
  2. Step 2: n = 2: 2 × 2 + 7 = 11
  3. Step 3: n = 3: 2 × 3 + 7 = 13
  4. Step 4: n = 4: 2 × 4 + 7 = 15
  5. Step 5: n = 5: 2 × 5 + 7 = 17

Answer: 9, 11, 13, 15, 17