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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 321 · 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 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 144 (d) 156
  2. 2.What is the missing term in the AP 8, 17, ?, 35, 44? (a) 25 (b) 35 (c) 26 (d) 27
  3. 3.What is the 36th term of the AP 19, 21, 23, 25, …? (a) 91 (b) 72 (c) 89 (d) 70
  4. 4.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 305 (b) 610 (c) 53 (d) 330
  5. 5.What is the 39th term of the AP 2, 6, 10, 14, …? (a) 158 (b) 152 (c) 156 (d) 154
  6. 6.What is the 19th term of the AP 6, 12, 18, 24, …? (a) 120 (b) 114 (c) 115 (d) 108
  7. 7.What is the 32nd term of the AP 19, 25, 31, 37, …? (a) 186 (b) 205 (c) 192 (d) 211
  8. 8.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 7 (b) 8 (c) 9 (d) 10
  9. 9.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 702 (d) 676
  10. 10.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 168 (b) 84 (c) 85 (d) 15
  11. 11.What is the sum of all the whole numbers from 1 to 59? (a) 1770 (b) 3540 (c) 1771 (d) 1711
  12. 12.What is the missing term in the AP 11, ?, 25, 32, 39? (a) 25 (b) 19 (c) 18 (d) 17
  13. 13.Which term of the AP 16, 20, 24, 28, … is 172? (a) 39th (b) 41st (c) 40th (d) 43rd
  14. 14.What is the 39th term of the AP 7, 9, 11, 13, …? (a) 85 (b) 76 (c) 83 (d) 78
  15. 15.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 870 (d) 841
  16. 16.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 756 (c) 379 (d) 378
  17. 17.What is the 13th term of the AP 2, 6, 10, 14, …? (a) 52 (b) 54 (c) 50 (d) 48
  18. 18.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 78 (b) 66 (c) 21 (d) 132
  19. 19.What is the 24th term of the AP 6, 12, 18, 24, …? (a) 145 (b) 144 (c) 150 (d) 138
  20. 20.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 82 (b) 162 (c) 13 (d) 81
  21. 21.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 240 (c) 105 (d) 120
  22. 22.What is the 17th term of the AP 12, 21, 30, 39, …? (a) 156 (b) 153 (c) 144 (d) 165
  23. 23.What is the 28th term of the AP 14, 22, 30, 38, …? (a) 216 (b) 224 (c) 230 (d) 238
  24. 24.What is the missing term in the AP 8, ?, 18, 23, 28? (a) 14 (b) 18 (c) 13 (d) 12
  25. 25.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 66 (c) 132 (d) 121
  26. 26.What is the 18th term of the AP 2, 9, 16, 23, …? (a) 126 (b) 119 (c) 121 (d) 128
  27. 27.What is the 18th term of the AP 10, 13, 16, 19, …? (a) 54 (b) 51 (c) 61 (d) 64
  28. 28.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 1122 (c) 561 (d) 528
  29. 29.Which term of the AP 4, 9, 14, 19, … is 109? (a) 22nd (b) 23rd (c) 21st (d) 24th
  30. 30.What is the 17th term of the AP 2, 5, 8, 11, …? (a) 50 (b) 51 (c) 53 (d) 48
  31. 31.What is the 36th term of the AP 8, 12, 16, 20, …? (a) 140 (b) 152 (c) 148 (d) 144
  32. 32.What is the sum of all the whole numbers from 1 to 67? (a) 2279 (b) 4556 (c) 2211 (d) 2278
  33. 33.What is the 37th term of the AP 15, 18, 21, 24, …? (a) 108 (b) 123 (c) 126 (d) 111
  34. 34.What is the 16th term of the AP 17, 19, 21, 23, …? (a) 32 (b) 30 (c) 49 (d) 47
  35. 35.What is the 32nd term of the AP 14, 21, 28, 35, …? (a) 224 (b) 231 (c) 217 (d) 238
  36. 36.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 289 (c) 153 (d) 33
  37. 37.What is the sum of all the whole numbers from 1 to 85? (a) 3656 (b) 7310 (c) 3570 (d) 3655
  38. 38.What is the sum of all the whole numbers from 1 to 60? (a) 3660 (b) 1830 (c) 1800 (d) 1770
  39. 39.What is the sum of the first 7 terms of the AP 7, 9, 11, …? (a) 182 (b) 98 (c) 19 (d) 91
  40. 40.What is the sum of all the whole numbers from 1 to 65? (a) 2080 (b) 4290 (c) 2146 (d) 2145

Answer key

  1. 144
  2. 26
  3. 89
  4. 305
  5. 154
  6. 114
  7. 205
  8. 8
  9. 676
  10. 84
  11. 1770
  12. 18
  13. 40th
  14. 83
  15. 841
  16. 378
  17. 50
  18. 66
  19. 144
  20. 81
  21. 120
  22. 156
  23. 230
  24. 13
  25. 121
  26. 121
  27. 61
  28. 561
  29. 22nd
  30. 50
  31. 148
  32. 2278
  33. 123
  34. 47
  35. 231
  36. 289
  37. 3655
  38. 1830
  39. 91
  40. 2145

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