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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 406 · 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 17th term of the AP 3, 9, 15, 21, …? (a) 102 (b) 99 (c) 96 (d) 105
  2. 2.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 153 (c) 289 (d) 33
  3. 3.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 351 (c) 756 (d) 378
  4. 4.What is the sum of all the whole numbers from 1 to 88? (a) 3828 (b) 7832 (c) 3872 (d) 3916
  5. 5.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 198 (b) 187 (c) 374 (d) 27
  6. 6.Which term of the AP 10, 15, 20, 25, … is 190? (a) 37th (b) 38th (c) 39th (d) 36th
  7. 7.Which term of the AP 7, 15, 23, 31, … is 207? (a) 26th (b) 28th (c) 25th (d) 27th
  8. 8.What is the missing term in the AP 2, ?, 18, 26, 34? (a) 9 (b) 10 (c) 18 (d) 11
  9. 9.What is the 40th term of the AP 11, 13, 15, 17, …? (a) 89 (b) 91 (c) 78 (d) 80
  10. 10.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 9 (b) 90 (c) 45 (d) 46
  11. 11.What is the missing term in the AP 20, ?, 36, 44, 52? (a) 28 (b) 27 (c) 29 (d) 36
  12. 12.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 73 (b) 144 (c) 72 (d) 12
  13. 13.What is the missing term in the AP 13, ?, 23, 28, 33? (a) 18 (b) 23 (c) 17 (d) 19
  14. 14.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 3741 (c) 7482 (d) 3655
  15. 15.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 870 (c) 57 (d) 435
  16. 16.What is the 24th term of the AP 2, 9, 16, 23, …? (a) 170 (b) 168 (c) 161 (d) 163
  17. 17.What is the sum of all the whole numbers from 1 to 80? (a) 3240 (b) 3200 (c) 6480 (d) 3160
  18. 18.What is the 30th term of the AP 8, 13, 18, 23, …? (a) 145 (b) 158 (c) 150 (d) 153
  19. 19.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 198 (b) 99 (c) 100 (d) 14
  20. 20.What is the sum of the first 9 terms of the AP 9, 15, 21, …? (a) 57 (b) 324 (c) 297 (d) 594
  21. 21.What is the 11th term of the AP 9, 16, 23, 30, …? (a) 79 (b) 86 (c) 77 (d) 70
  22. 22.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 420 (b) 210 (c) 34 (d) 228
  23. 23.What is the sum of all the whole numbers from 1 to 12? (a) 156 (b) 66 (c) 78 (d) 72
  24. 24.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 162 (b) 82 (c) 81 (d) 13
  25. 25.What is the 13th term of the AP 13, 21, 29, 37, …? (a) 96 (b) 104 (c) 117 (d) 109
  26. 26.What is the missing term in the AP 4, 6, ?, 10, 12? (a) 8 (b) 9 (c) 7 (d) 10
  27. 27.What is the missing term in the AP 16, 23, 30, ?, 44? (a) 38 (b) 36 (c) 44 (d) 37
  28. 28.Which term of the AP 4, 11, 18, 25, … is 95? (a) 16th (b) 14th (c) 13th (d) 15th
  29. 29.What is the 36th term of the AP 3, 12, 21, 30, …? (a) 315 (b) 324 (c) 327 (d) 318
  30. 30.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 12 (b) 13 (c) 14 (d) 16
  31. 31.What is the sum of the first 8 terms of the AP 3, 7, 11, …? (a) 272 (b) 31 (c) 136 (d) 152
  32. 32.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 1770 (c) 3540 (d) 1711
  33. 33.What is the sum of the first 7 terms of the AP 2, 8, 14, …? (a) 140 (b) 38 (c) 161 (d) 280
  34. 34.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 9 (b) 35 (c) 36 (d) 70
  35. 35.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 105 (d) 196
  36. 36.What is the 36th term of the AP 15, 19, 23, 27, …? (a) 155 (b) 140 (c) 144 (d) 159
  37. 37.What is the 25th term of the AP 17, 22, 27, 32, …? (a) 142 (b) 125 (c) 120 (d) 137
  38. 38.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 12 (b) 15 (c) 14 (d) 13
  39. 39.What is the 26th term of the AP 11, 15, 19, 23, …? (a) 111 (b) 100 (c) 115 (d) 104
  40. 40.What is the sum of all the whole numbers from 1 to 51? (a) 1275 (b) 1326 (c) 2652 (d) 1327

Answer key

  1. 99
  2. 289
  3. 378
  4. 3916
  5. 187
  6. 37th
  7. 26th
  8. 10
  9. 89
  10. 45
  11. 28
  12. 72
  13. 18
  14. 3741
  15. 841
  16. 163
  17. 3240
  18. 153
  19. 99
  20. 297
  21. 79
  22. 210
  23. 78
  24. 81
  25. 109
  26. 8
  27. 37
  28. 14th
  29. 318
  30. 13
  31. 136
  32. 1770
  33. 140
  34. 35
  35. 196
  36. 155
  37. 137
  38. 13
  39. 111
  40. 1326

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