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Grade 9 Math — 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 1 + 2 + 3 + ... + 100.

  2. 2.The first term of an AP is 7 and the common difference is 5. What is the 4th term?

  3. 3.Which of these lists is an arithmetic progression?

    • a) 2, 5, 8, 11
    • b) 1, 2, 4, 8
    • c) 1, 4, 9, 16
    • d) 3, 3, 4, 6

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

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

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

  7. 7.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
    • 1
    • 2
    • 10
    • -4
    • 3

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

Answer key — Grade 9 Math — Arithmetic progressions

  1. 1. 5050
  2. 2. 22
  3. 3. a) 2, 5, 8, 11
  4. 4. 62
  5. 5. 39
  6. 6. 225
  7. 7. 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
  8. 8. -3