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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 662 · 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 7 terms of the AP 7, 10, 13, …? (a) 112 (b) 25 (c) 115 (d) 224
  2. 2.Which term of the AP 18, 21, 24, 27, … is 51? (a) 11th (b) 12th (c) 17th (d) 13th
  3. 3.Which term of the AP 15, 21, 27, 33, … is 75? (a) 12th (b) 10th (c) 11th (d) 13th
  4. 4.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 66 (d) 132
  5. 5.What is the sum of all the whole numbers from 1 to 61? (a) 1830 (b) 1892 (c) 1891 (d) 3782
  6. 6.What is the sum of all the whole numbers from 1 to 78? (a) 3003 (b) 3042 (c) 3081 (d) 6162
  7. 7.What is the missing term in the AP 12, ?, 28, 36, 44? (a) 21 (b) 20 (c) 19 (d) 28
  8. 8.What is the 34th term of the AP 19, 25, 31, 37, …? (a) 217 (b) 223 (c) 204 (d) 198
  9. 9.What is the 17th term of the AP 15, 19, 23, 27, …? (a) 79 (b) 68 (c) 83 (d) 64
  10. 10.What is the 14th term of the AP 6, 10, 14, 18, …? (a) 56 (b) 62 (c) 52 (d) 58
  11. 11.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 320 (b) 290 (c) 580 (d) 56
  12. 12.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 18 (b) 144 (c) 143 (d) 286
  13. 13.What is the missing term in the AP 10, 17, 24, ?, 38? (a) 31 (b) 32 (c) 38 (d) 30
  14. 14.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 420 (c) 200 (d) 190
  15. 15.What is the missing term in the AP 8, 15, ?, 29, 36? (a) 22 (b) 23 (c) 29 (d) 21
  16. 16.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 45 (c) 17 (d) 81
  17. 17.What is the 21st term of the AP 17, 22, 27, 32, …? (a) 117 (b) 100 (c) 105 (d) 122
  18. 18.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 120 (b) 65 (c) 16 (d) 60
  19. 19.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 78 (c) 66 (d) 156
  20. 20.What is the missing term in the AP 17, ?, 27, 32, 37? (a) 23 (b) 27 (c) 21 (d) 22
  21. 21.What is the 37th term of the AP 10, 19, 28, 37, …? (a) 343 (b) 333 (c) 334 (d) 324
  22. 22.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 21 (b) 372 (c) 186 (d) 192
  23. 23.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 132 (b) 16 (c) 66 (d) 72
  24. 24.What is the missing term in the AP 18, ?, 24, 27, 30? (a) 22 (b) 21 (c) 20 (d) 24
  25. 25.Which term of the AP 14, 17, 20, 23, … is 74? (a) 22nd (b) 20th (c) 21st (d) 23rd
  26. 26.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 390 (b) 195 (c) 33 (d) 210
  27. 27.What is the 14th term of the AP 8, 14, 20, 26, …? (a) 78 (b) 86 (c) 84 (d) 92
  28. 28.What is the 35th term of the AP 13, 17, 21, 25, …? (a) 153 (b) 140 (c) 136 (d) 149
  29. 29.What is the 11th term of the AP 9, 14, 19, 24, …? (a) 50 (b) 64 (c) 55 (d) 59
  30. 30.What is the missing term in the AP 4, 6, 8, ?, 12? (a) 10 (b) 12 (c) 9 (d) 11
  31. 31.What is the 12th term of the AP 5, 8, 11, 14, …? (a) 41 (b) 33 (c) 36 (d) 38
  32. 32.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 650 (d) 625
  33. 33.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 496 (c) 528 (d) 512
  34. 34.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 161 (b) 33 (c) 147 (d) 294
  35. 35.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 120 (c) 240 (d) 105
  36. 36.What is the 18th term of the AP 7, 10, 13, 16, …? (a) 58 (b) 51 (c) 54 (d) 61
  37. 37.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 111 (b) 15 (c) 220 (d) 110
  38. 38.What is the 33rd term of the AP 18, 27, 36, 45, …? (a) 288 (b) 306 (c) 315 (d) 297
  39. 39.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 242 (c) 506 (d) 253
  40. 40.What is the 34th term of the AP 8, 10, 12, 14, …? (a) 68 (b) 74 (c) 76 (d) 66

Answer key

  1. 112
  2. 12th
  3. 11th
  4. 121
  5. 1891
  6. 3081
  7. 20
  8. 217
  9. 79
  10. 58
  11. 290
  12. 143
  13. 31
  14. 210
  15. 22
  16. 81
  17. 117
  18. 60
  19. 78
  20. 22
  21. 334
  22. 186
  23. 66
  24. 21
  25. 21st
  26. 195
  27. 86
  28. 149
  29. 59
  30. 10
  31. 38
  32. 625
  33. 528
  34. 147
  35. 120
  36. 58
  37. 110
  38. 306
  39. 253
  40. 74

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