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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 29 · 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 all the whole numbers from 1 to 88? (a) 3916 (b) 3872 (c) 3828 (d) 7832
  2. 2.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 132 (b) 34 (c) 114 (d) 228
  3. 3.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 650 (d) 625
  4. 4.What is the 14th term of the AP 7, 12, 17, 22, …? (a) 77 (b) 72 (c) 65 (d) 70
  5. 5.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 153 (c) 33 (d) 289
  6. 6.What is the 14th term of the AP 18, 23, 28, 33, …? (a) 70 (b) 88 (c) 65 (d) 83
  7. 7.What is the missing term in the AP 1, 5, 9, ?, 17? (a) 17 (b) 12 (c) 14 (d) 13
  8. 8.Which term of the AP 1, 8, 15, 22, … is 162? (a) 26th (b) 24th (c) 23rd (d) 25th
  9. 9.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 37 (c) 380 (d) 190
  10. 10.What is the missing term in the AP 20, ?, 34, 41, 48? (a) 27 (b) 28 (c) 26 (d) 34
  11. 11.What is the 14th term of the AP 2, 8, 14, 20, …? (a) 86 (b) 80 (c) 84 (d) 78
  12. 12.What is the sum of all the whole numbers from 1 to 87? (a) 3829 (b) 7656 (c) 3828 (d) 3741
  13. 13.Which term of the AP 3, 10, 17, 24, … is 269? (a) 41st (b) 39th (c) 40th (d) 38th
  14. 14.What is the 31st term of the AP 20, 24, 28, 32, …? (a) 120 (b) 140 (c) 144 (d) 124
  15. 15.What is the 37th term of the AP 19, 23, 27, 31, …? (a) 144 (b) 163 (c) 148 (d) 167
  16. 16.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 45 (c) 110 (d) 55
  17. 17.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 72 (c) 78 (d) 156
  18. 18.What is the sum of the first 9 terms of the AP 8, 12, 16, …? (a) 40 (b) 432 (c) 234 (d) 216
  19. 19.What is the sum of all the whole numbers from 1 to 75? (a) 2850 (b) 5700 (c) 2851 (d) 2775
  20. 20.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 600 (c) 576 (d) 300
  21. 21.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 169 (c) 25 (d) 182
  22. 22.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 28 (b) 380 (c) 200 (d) 190
  23. 23.Which term of the AP 5, 13, 21, 29, … is 61? (a) 10th (b) 9th (c) 8th (d) 7th
  24. 24.What is the missing term in the AP 8, 11, 14, ?, 20? (a) 16 (b) 17 (c) 18 (d) 20
  25. 25.What is the 27th term of the AP 20, 26, 32, 38, …? (a) 162 (b) 182 (c) 176 (d) 156
  26. 26.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 272 (d) 31
  27. 27.What is the 22nd term of the AP 14, 17, 20, 23, …? (a) 63 (b) 80 (c) 66 (d) 77
  28. 28.What is the 13th term of the AP 12, 16, 20, 24, …? (a) 60 (b) 52 (c) 64 (d) 48
  29. 29.What is the 14th term of the AP 2, 5, 8, 11, …? (a) 44 (b) 42 (c) 41 (d) 39
  30. 30.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 180 (b) 170 (c) 26 (d) 340
  31. 31.What is the 34th term of the AP 4, 6, 8, 10, …? (a) 72 (b) 68 (c) 70 (d) 66
  32. 32.What is the sum of all the whole numbers from 1 to 48? (a) 1128 (b) 1176 (c) 1152 (d) 2352
  33. 33.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 29 (d) 120
  34. 34.What is the sum of all the whole numbers from 1 to 85? (a) 3656 (b) 7310 (c) 3655 (d) 3570
  35. 35.What is the 29th term of the AP 19, 24, 29, 34, …? (a) 164 (b) 140 (c) 159 (d) 145
  36. 36.What is the sum of the first 5 terms of the AP 9, 15, 21, …? (a) 33 (b) 105 (c) 210 (d) 120
  37. 37.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 22 (b) 120 (c) 65 (d) 60
  38. 38.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 238 (b) 32 (c) 119 (d) 124
  39. 39.What is the missing term in the AP 9, 15, 21, ?, 33? (a) 27 (b) 28 (c) 26 (d) 33
  40. 40.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 190 (b) 29 (c) 100 (d) 95

Answer key

  1. 3916
  2. 114
  3. 625
  4. 72
  5. 289
  6. 83
  7. 13
  8. 24th
  9. 361
  10. 27
  11. 80
  12. 3828
  13. 39th
  14. 140
  15. 163
  16. 55
  17. 78
  18. 216
  19. 2850
  20. 576
  21. 169
  22. 190
  23. 8th
  24. 17
  25. 176
  26. 256
  27. 77
  28. 60
  29. 41
  30. 170
  31. 70
  32. 1176
  33. 225
  34. 3655
  35. 159
  36. 105
  37. 60
  38. 119
  39. 27
  40. 95

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