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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 689 · 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 69? (a) 4830 (b) 2415 (c) 2346 (d) 2416
  2. 2.What is the 15th term of the AP 19, 27, 35, 43, …? (a) 139 (b) 131 (c) 120 (d) 112
  3. 3.Which term of the AP 9, 15, 21, 27, … is 147? (a) 23rd (b) 25th (c) 24th (d) 26th
  4. 4.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 100 (b) 51 (c) 50 (d) 12
  5. 5.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 436 (c) 406 (d) 435
  6. 6.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 330 (b) 176 (c) 165 (d) 25
  7. 7.What is the sum of all the whole numbers from 1 to 75? (a) 2775 (b) 5700 (c) 2851 (d) 2850
  8. 8.What is the 19th term of the AP 20, 28, 36, 44, …? (a) 172 (b) 164 (c) 144 (d) 152
  9. 9.What is the missing term in the AP 19, ?, 37, 46, 55? (a) 27 (b) 37 (c) 29 (d) 28
  10. 10.What is the 25th term of the AP 14, 23, 32, 41, …? (a) 216 (b) 239 (c) 230 (d) 225
  11. 11.What is the 25th term of the AP 4, 6, 8, 10, …? (a) 48 (b) 50 (c) 52 (d) 54
  12. 12.What is the sum of all the whole numbers from 1 to 90? (a) 4005 (b) 8190 (c) 4050 (d) 4095
  13. 13.What is the 27th term of the AP 16, 22, 28, 34, …? (a) 178 (b) 156 (c) 162 (d) 172
  14. 14.What is the 24th term of the AP 2, 11, 20, 29, …? (a) 209 (b) 216 (c) 207 (d) 218
  15. 15.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 200 (b) 368 (c) 184 (d) 37
  16. 16.What is the 36th term of the AP 20, 24, 28, 32, …? (a) 144 (b) 160 (c) 140 (d) 164
  17. 17.What is the sum of the first 12 terms of the AP 5, 6, 7, …? (a) 132 (b) 126 (c) 252 (d) 16
  18. 18.What is the 14th term of the AP 15, 21, 27, 33, …? (a) 78 (b) 99 (c) 84 (d) 93
  19. 19.What is the 31st term of the AP 6, 10, 14, 18, …? (a) 130 (b) 126 (c) 124 (d) 120
  20. 20.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 420 (c) 210 (d) 400
  21. 21.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3828 (c) 3916 (d) 7832
  22. 22.Which term of the AP 17, 21, 25, 29, … is 141? (a) 31st (b) 33rd (c) 32nd (d) 34th
  23. 23.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 378 (c) 392 (d) 406
  24. 24.What is the sum of the first 9 terms of the AP 5, 8, 11, …? (a) 306 (b) 29 (c) 153 (d) 156
  25. 25.Which term of the AP 11, 19, 27, 35, … is 131? (a) 18th (b) 17th (c) 16th (d) 15th
  26. 26.What is the 15th term of the AP 2, 9, 16, 23, …? (a) 105 (b) 107 (c) 98 (d) 100
  27. 27.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 528 (c) 496 (d) 512
  28. 28.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 6 (b) 7 (c) 4 (d) 5
  29. 29.Which term of the AP 1, 6, 11, 16, … is 71? (a) 16th (b) 15th (c) 14th (d) 17th
  30. 30.What is the 16th term of the AP 5, 12, 19, 26, …? (a) 117 (b) 110 (c) 112 (d) 105
  31. 31.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 182 (c) 91 (d) 25
  32. 32.What is the 30th term of the AP 2, 4, 6, 8, …? (a) 60 (b) 61 (c) 58 (d) 62
  33. 33.What is the missing term in the AP 5, ?, 17, 23, 29? (a) 11 (b) 12 (c) 17 (d) 10
  34. 34.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 12 (b) 13 (c) 14 (d) 16
  35. 35.What is the 27th term of the AP 6, 14, 22, 30, …? (a) 216 (b) 214 (c) 208 (d) 222
  36. 36.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 2450 (c) 1226 (d) 1225
  37. 37.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 702 (d) 676
  38. 38.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 121 (c) 105 (d) 120
  39. 39.What is the missing term in the AP 17, 26, 35, ?, 53? (a) 44 (b) 43 (c) 45 (d) 53
  40. 40.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 352 (b) 179 (c) 31 (d) 176

Answer key

  1. 2415
  2. 131
  3. 24th
  4. 50
  5. 435
  6. 165
  7. 2850
  8. 164
  9. 28
  10. 230
  11. 52
  12. 4095
  13. 172
  14. 209
  15. 184
  16. 160
  17. 126
  18. 93
  19. 126
  20. 400
  21. 3916
  22. 32nd
  23. 406
  24. 153
  25. 16th
  26. 100
  27. 528
  28. 5
  29. 15th
  30. 110
  31. 169
  32. 60
  33. 11
  34. 13
  35. 214
  36. 1225
  37. 676
  38. 120
  39. 44
  40. 176

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