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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 821 · 40 questions
TalentJR

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

NameDateTime takenScore ___ / 40
  1. 1.What is the sum of the first 9 terms of the AP 1, 4, 7, …? (a) 25 (b) 234 (c) 117 (d) 120
  2. 2.What is the 40th term of the AP 12, 19, 26, 33, …? (a) 292 (b) 280 (c) 285 (d) 273
  3. 3.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 351 (c) 51 (d) 676
  4. 4.What is the sum of all the whole numbers from 1 to 12? (a) 78 (b) 72 (c) 66 (d) 156
  5. 5.What is the missing term in the AP 10, 17, 24, ?, 38? (a) 30 (b) 38 (c) 31 (d) 32
  6. 6.What is the 23rd term of the AP 14, 17, 20, 23, …? (a) 69 (b) 80 (c) 83 (d) 66
  7. 7.What is the sum of all the whole numbers from 1 to 40? (a) 780 (b) 1640 (c) 820 (d) 800
  8. 8.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 156 (d) 144
  9. 9.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 9 (d) 25
  10. 10.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 81 (d) 17
  11. 11.What is the 26th term of the AP 8, 12, 16, 20, …? (a) 100 (b) 112 (c) 104 (d) 108
  12. 12.What is the missing term in the AP 10, 13, 16, ?, 22? (a) 22 (b) 19 (c) 20 (d) 18
  13. 13.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 529 (d) 276
  14. 14.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 4753 (c) 4656 (d) 9506
  15. 15.What is the 34th term of the AP 15, 20, 25, 30, …? (a) 180 (b) 185 (c) 170 (d) 165
  16. 16.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 102 (b) 204 (c) 32 (d) 120
  17. 17.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 37 (c) 190 (d) 361
  18. 18.What is the sum of the first 5 terms of the AP 10, 13, 16, …? (a) 83 (b) 160 (c) 80 (d) 22
  19. 19.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 39 (c) 210 (d) 420
  20. 20.What is the 23rd term of the AP 8, 14, 20, 26, …? (a) 140 (b) 132 (c) 138 (d) 146
  21. 21.What is the sum of all the whole numbers from 1 to 88? (a) 3828 (b) 3916 (c) 7832 (d) 3872
  22. 22.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 150 (b) 264 (c) 132 (d) 37
  23. 23.What is the 24th term of the AP 2, 5, 8, 11, …? (a) 71 (b) 69 (c) 74 (d) 72
  24. 24.What is the 28th term of the AP 1, 3, 5, 7, …? (a) 57 (b) 54 (c) 55 (d) 56
  25. 25.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 225 (b) 450 (c) 243 (d) 41
  26. 26.What is the missing term in the AP 7, 14, 21, ?, 35? (a) 27 (b) 29 (c) 35 (d) 28
  27. 27.Which term of the AP 6, 14, 22, 30, … is 286? (a) 36th (b) 37th (c) 38th (d) 35th
  28. 28.What is the sum of all the whole numbers from 1 to 98? (a) 9702 (b) 4753 (c) 4851 (d) 4802
  29. 29.What is the missing term in the AP 10, 18, 26, ?, 42? (a) 34 (b) 35 (c) 42 (d) 33
  30. 30.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 27 (c) 210 (d) 105
  31. 31.Which term of the AP 17, 19, 21, 23, … is 47? (a) 16th (b) 18th (c) 17th (d) 15th
  32. 32.What is the 17th term of the AP 5, 8, 11, 14, …? (a) 48 (b) 51 (c) 53 (d) 56
  33. 33.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 55 (b) 10 (c) 54 (d) 108
  34. 34.What is the sum of all the whole numbers from 1 to 54? (a) 2970 (b) 1431 (c) 1458 (d) 1485
  35. 35.What is the sum of all the whole numbers from 1 to 29? (a) 436 (b) 435 (c) 406 (d) 870
  36. 36.What is the 28th term of the AP 3, 9, 15, 21, …? (a) 165 (b) 168 (c) 171 (d) 162
  37. 37.What is the missing term in the AP 20, 25, 30, ?, 40? (a) 36 (b) 34 (c) 40 (d) 35
  38. 38.What is the 33rd term of the AP 3, 5, 7, 9, …? (a) 64 (b) 69 (c) 66 (d) 67
  39. 39.What is the sum of all the whole numbers from 1 to 43? (a) 946 (b) 1892 (c) 903 (d) 947
  40. 40.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 26 (b) 122 (c) 238 (d) 119

Answer key

  1. 117
  2. 285
  3. 676
  4. 78
  5. 31
  6. 80
  7. 820
  8. 144
  9. 25
  10. 81
  11. 108
  12. 19
  13. 529
  14. 4753
  15. 180
  16. 102
  17. 361
  18. 80
  19. 400
  20. 140
  21. 3916
  22. 132
  23. 71
  24. 55
  25. 225
  26. 28
  27. 36th
  28. 4851
  29. 34
  30. 196
  31. 16th
  32. 53
  33. 54
  34. 1485
  35. 435
  36. 165
  37. 35
  38. 67
  39. 946
  40. 119

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