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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 487 · 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 77? (a) 3004 (b) 6006 (c) 2926 (d) 3003
  2. 2.What is the 28th term of the AP 5, 8, 11, 14, …? (a) 81 (b) 86 (c) 84 (d) 89
  3. 3.What is the sum of all the whole numbers from 1 to 97? (a) 9506 (b) 4753 (c) 4656 (d) 4754
  4. 4.What is the sum of the first 5 terms of the AP 10, 13, 16, …? (a) 160 (b) 83 (c) 80 (d) 22
  5. 5.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 171 (c) 190 (d) 380
  6. 6.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 75 (b) 23 (c) 85 (d) 150
  7. 7.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 650 (d) 625
  8. 8.What is the 16th term of the AP 9, 18, 27, 36, …? (a) 135 (b) 144 (c) 153 (d) 145
  9. 9.What is the missing term in the AP 5, 7, ?, 11, 13? (a) 10 (b) 11 (c) 9 (d) 8
  10. 10.What is the 18th term of the AP 7, 9, 11, 13, …? (a) 36 (b) 43 (c) 41 (d) 34
  11. 11.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 53 (c) 756 (d) 378
  12. 12.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 169 (c) 91 (d) 182
  13. 13.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 68 (b) 65 (c) 130 (d) 19
  14. 14.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 64 (d) 72
  15. 15.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 324 (d) 35
  16. 16.What is the 15th term of the AP 14, 19, 24, 29, …? (a) 75 (b) 84 (c) 89 (d) 70
  17. 17.What is the 37th term of the AP 17, 22, 27, 32, …? (a) 197 (b) 185 (c) 202 (d) 180
  18. 18.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 506 (b) 38 (c) 256 (d) 253
  19. 19.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 13 (b) 63 (c) 126 (d) 66
  20. 20.What is the 37th term of the AP 3, 7, 11, 15, …? (a) 148 (b) 147 (c) 151 (d) 144
  21. 21.What is the 10th term of the AP 2, 5, 8, 11, …? (a) 29 (b) 30 (c) 32 (d) 27
  22. 22.What is the sum of all the whole numbers from 1 to 36? (a) 648 (b) 1332 (c) 666 (d) 630
  23. 23.What is the missing term in the AP 18, 24, 30, ?, 42? (a) 35 (b) 36 (c) 37 (d) 42
  24. 24.What is the 36th term of the AP 6, 8, 10, 12, …? (a) 70 (b) 76 (c) 72 (d) 78
  25. 25.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 14 (b) 91 (c) 90 (d) 180
  26. 26.What is the missing term in the AP 13, 18, 23, ?, 33? (a) 29 (b) 28 (c) 33 (d) 27
  27. 27.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 435 (c) 436 (d) 406
  28. 28.What is the 35th term of the AP 3, 12, 21, 30, …? (a) 306 (b) 315 (c) 318 (d) 309
  29. 29.What is the 18th term of the AP 7, 13, 19, 25, …? (a) 102 (b) 115 (c) 109 (d) 108
  30. 30.What is the 31st term of the AP 13, 19, 25, 31, …? (a) 180 (b) 193 (c) 199 (d) 186
  31. 31.What is the 12th term of the AP 11, 15, 19, 23, …? (a) 59 (b) 55 (c) 48 (d) 44
  32. 32.Which term of the AP 4, 7, 10, 13, … is 100? (a) 33rd (b) 34th (c) 35th (d) 32nd
  33. 33.What is the missing term in the AP 10, 16, ?, 28, 34? (a) 21 (b) 22 (c) 28 (d) 23
  34. 34.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 136 (b) 120 (c) 29 (d) 240
  35. 35.What is the missing term in the AP 5, 14, ?, 32, 41? (a) 24 (b) 22 (c) 32 (d) 23
  36. 36.What is the sum of all the whole numbers from 1 to 60? (a) 1770 (b) 1830 (c) 3660 (d) 1800
  37. 37.Which term of the AP 12, 18, 24, 30, … is 168? (a) 28th (b) 27th (c) 26th (d) 29th
  38. 38.What is the 30th term of the AP 12, 17, 22, 27, …? (a) 145 (b) 162 (c) 150 (d) 157
  39. 39.What is the missing term in the AP 18, ?, 36, 45, 54? (a) 26 (b) 28 (c) 36 (d) 27
  40. 40.What is the 39th term of the AP 9, 15, 21, 27, …? (a) 243 (b) 228 (c) 237 (d) 234

Answer key

  1. 3003
  2. 86
  3. 4753
  4. 80
  5. 190
  6. 75
  7. 625
  8. 144
  9. 9
  10. 41
  11. 729
  12. 169
  13. 65
  14. 64
  15. 324
  16. 84
  17. 197
  18. 253
  19. 63
  20. 147
  21. 29
  22. 666
  23. 36
  24. 76
  25. 90
  26. 28
  27. 435
  28. 309
  29. 109
  30. 193
  31. 55
  32. 33rd
  33. 22
  34. 120
  35. 23
  36. 1830
  37. 27th
  38. 157
  39. 27
  40. 237

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