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Year 11 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.Find the sum of the first 10 terms of 2, 4, 6, 8, ...

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

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

  4. 4.In the AP 20, 17, 14, ... what is the common difference?

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

  6. 6.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
    • -4
    • 3
    • 2
    • 1
    • 10

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

    Groups: Is an AP · Is not an AP

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

  8. 8.In the AP 20, 17, 14, ... what is the 8th term?

Answer key — Year 11 Maths — Arithmetic progressions

  1. 1. 110
  2. 2. 4
  3. 3. 225
  4. 4. -3
  5. 5. 62
  6. 6. 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
  7. 7. 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
  8. 8. -1