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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 48 · 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 10 terms of the AP 3, 9, 15, …? (a) 300 (b) 600 (c) 330 (d) 57
  2. 2.What is the missing term in the AP 19, ?, 31, 37, 43? (a) 26 (b) 24 (c) 25 (d) 31
  3. 3.Which term of the AP 15, 22, 29, 36, … is 85? (a) 10th (b) 11th (c) 12th (d) 13th
  4. 4.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 120 (c) 29 (d) 225
  5. 5.What is the sum of the first 11 terms of the AP 8, 12, 16, …? (a) 308 (b) 616 (c) 48 (d) 330
  6. 6.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 2145 (c) 4422 (d) 2211
  7. 7.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 119 (b) 124 (c) 238 (d) 32
  8. 8.What is the missing term in the AP 5, 10, 15, ?, 25? (a) 20 (b) 25 (c) 19 (d) 21
  9. 9.What is the 33rd term of the AP 18, 22, 26, 30, …? (a) 128 (b) 146 (c) 132 (d) 150
  10. 10.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 41 (b) 450 (c) 225 (d) 243
  11. 11.Which term of the AP 3, 6, 9, 12, … is 48? (a) 17th (b) 18th (c) 15th (d) 16th
  12. 12.What is the missing term in the AP 13, 20, 27, ?, 41? (a) 34 (b) 41 (c) 35 (d) 33
  13. 13.What is the 18th term of the AP 18, 23, 28, 33, …? (a) 85 (b) 108 (c) 103 (d) 90
  14. 14.What is the 23rd term of the AP 14, 22, 30, 38, …? (a) 184 (b) 198 (c) 190 (d) 176
  15. 15.Which term of the AP 5, 7, 9, 11, … is 67? (a) 32nd (b) 31st (c) 33rd (d) 34th
  16. 16.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 650 (c) 49 (d) 625
  17. 17.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 32 (b) 120 (c) 102 (d) 204
  18. 18.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 49 (b) 450 (c) 252 (d) 225
  19. 19.What is the sum of all the whole numbers from 1 to 29? (a) 406 (b) 436 (c) 870 (d) 435
  20. 20.What is the sum of all the whole numbers from 1 to 80? (a) 3240 (b) 6480 (c) 3160 (d) 3200
  21. 21.What is the 28th term of the AP 5, 10, 15, 20, …? (a) 145 (b) 135 (c) 140 (d) 141
  22. 22.What is the 24th term of the AP 6, 9, 12, 15, …? (a) 72 (b) 69 (c) 78 (d) 75
  23. 23.What is the missing term in the AP 20, 26, ?, 38, 44? (a) 31 (b) 32 (c) 33 (d) 38
  24. 24.What is the 19th term of the AP 16, 23, 30, 37, …? (a) 133 (b) 126 (c) 149 (d) 142
  25. 25.What is the missing term in the AP 5, 12, ?, 26, 33? (a) 20 (b) 19 (c) 18 (d) 26
  26. 26.What is the sum of all the whole numbers from 1 to 86? (a) 7482 (b) 3741 (c) 3698 (d) 3655
  27. 27.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 490 (b) 47 (c) 270 (d) 245
  28. 28.Which term of the AP 2, 4, 6, 8, … is 20? (a) 11th (b) 12th (c) 10th (d) 9th
  29. 29.Which term of the AP 9, 11, 13, 15, … is 31? (a) 13th (b) 12th (c) 11th (d) 14th
  30. 30.What is the 37th term of the AP 4, 7, 10, 13, …? (a) 108 (b) 112 (c) 111 (d) 115
  31. 31.What is the 39th term of the AP 15, 23, 31, 39, …? (a) 304 (b) 327 (c) 312 (d) 319
  32. 32.What is the sum of all the whole numbers from 1 to 99? (a) 4851 (b) 4951 (c) 9900 (d) 4950
  33. 33.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 15 (c) 9 (d) 30
  34. 34.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 841 (c) 435 (d) 870
  35. 35.Which term of the AP 14, 17, 20, 23, … is 116? (a) 37th (b) 34th (c) 35th (d) 36th
  36. 36.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 216 (b) 109 (c) 16 (d) 108
  37. 37.What is the 13th term of the AP 4, 6, 8, 10, …? (a) 26 (b) 28 (c) 24 (d) 30
  38. 38.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 82 (b) 162 (c) 81 (d) 13
  39. 39.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 92 (c) 78 (d) 91
  40. 40.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 42 (b) 24 (c) 6 (d) 21

Answer key

  1. 300
  2. 25
  3. 11th
  4. 225
  5. 308
  6. 2211
  7. 119
  8. 20
  9. 146
  10. 225
  11. 16th
  12. 34
  13. 103
  14. 190
  15. 32nd
  16. 625
  17. 102
  18. 225
  19. 435
  20. 3240
  21. 140
  22. 75
  23. 32
  24. 142
  25. 19
  26. 3741
  27. 245
  28. 10th
  29. 12th
  30. 112
  31. 319
  32. 4950
  33. 25
  34. 841
  35. 35th
  36. 108
  37. 28
  38. 81
  39. 91
  40. 21

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