← Back to the activity

Year 10 Maths — Arithmetic progressions

Find the common difference, the nth term and the sum of an arithmetic progression.

Name: ________________________

Before you start

This line is the progression 5, 10, 15, 20 and onwards. Move from one term to the next and count the steps you have taken.

510152025303540

The first term takes no steps at all, so the 8th term is 5 with seven steps of 5 added on: 5 + 7 × 5 = 40. That is a + (n - 1)d, read straight off the line.

  1. 1.In the AP 3, 7, 11, 15, ... what is the common difference?

  2. 2.Sort each list by whether it is an arithmetic progression.

    Groups: Is an AP · Is not an AP

    • 9, 6, 3, 0
    • 10, 20, 30, 40
    • 2, 3, 5, 7
    • 1, 2, 4, 8
    • 1, 4, 9, 16
    • 1, 3, 5, 7

  3. 3.Find the sum of the first 10 terms of 2, 4, 6, 8, ...

  4. 4.Match each progression to its common difference.

    • 2, 5, 8, 11
    • 1, 3, 5, 7
    • 10, 6, 2, -2
    • 7, 8, 9, 10
    • 0, 10, 20, 30
    • 3
    • 10
    • 2
    • -4
    • 1

  5. 5.Find the sum 1 + 2 + 3 + ... + 100.

  6. 6.In the AP 5, 8, 11, ... what is the 20th term?

  7. 7.In the AP 3, 7, 11, 15, ... what is the 10th term?

  8. 8.Find the sum of the first 15 terms of 1, 3, 5, 7, ...

Answer key — Year 10 Maths — Arithmetic progressions

  1. 1. 4
  2. 2. 1, 3, 5, 7 → Is an AP; 10, 20, 30, 40 → Is an AP; 9, 6, 3, 0 → Is an AP; 1, 2, 4, 8 → Is not an AP; 2, 3, 5, 7 → Is not an AP; 1, 4, 9, 16 → Is not an AP
  3. 3. 110
  4. 4. 2, 5, 8, 11 → 3; 1, 3, 5, 7 → 2; 10, 6, 2, -2 → -4; 7, 8, 9, 10 → 1; 0, 10, 20, 30 → 10
  5. 5. 5050
  6. 6. 62
  7. 7. 39
  8. 8. 225