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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 794 · 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 9 terms of the AP 7, 9, 11, …? (a) 144 (b) 135 (c) 270 (d) 23
  2. 2.What is the 32nd term of the AP 19, 27, 35, 43, …? (a) 267 (b) 256 (c) 275 (d) 248
  3. 3.What is the sum of all the whole numbers from 1 to 20? (a) 200 (b) 210 (c) 420 (d) 190
  4. 4.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 4970 (c) 2450 (d) 2485
  5. 5.What is the 12th term of the AP 5, 14, 23, 32, …? (a) 99 (b) 108 (c) 104 (d) 113
  6. 6.What is the 17th term of the AP 8, 16, 24, 32, …? (a) 144 (b) 128 (c) 137 (d) 136
  7. 7.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 189 (b) 378 (c) 41 (d) 194
  8. 8.Which term of the AP 7, 11, 15, 19, … is 47? (a) 12th (b) 10th (c) 11th (d) 13th
  9. 9.What is the sum of all the whole numbers from 1 to 85? (a) 3570 (b) 7310 (c) 3656 (d) 3655
  10. 10.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 45 (d) 17
  11. 11.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 342 (c) 171 (d) 153
  12. 12.What is the missing term in the AP 4, 10, ?, 22, 28? (a) 17 (b) 16 (c) 15 (d) 22
  13. 13.What is the 13th term of the AP 5, 14, 23, 32, …? (a) 113 (b) 122 (c) 108 (d) 117
  14. 14.What is the 22nd term of the AP 6, 12, 18, 24, …? (a) 138 (b) 133 (c) 132 (d) 126
  15. 15.What is the sum of all the whole numbers from 1 to 82? (a) 3362 (b) 3321 (c) 3403 (d) 6806
  16. 16.Which term of the AP 7, 10, 13, 16, … is 112? (a) 35th (b) 36th (c) 37th (d) 38th
  17. 17.What is the 19th term of the AP 9, 15, 21, 27, …? (a) 114 (b) 108 (c) 117 (d) 123
  18. 18.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1326 (c) 1378 (d) 1352
  19. 19.What is the sum of the first 11 terms of the AP 7, 11, 15, …? (a) 47 (b) 594 (c) 319 (d) 297
  20. 20.What is the sum of all the whole numbers from 1 to 25? (a) 325 (b) 326 (c) 300 (d) 650
  21. 21.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 130 (b) 19 (c) 65 (d) 68
  22. 22.What is the 12th term of the AP 11, 19, 27, 35, …? (a) 88 (b) 99 (c) 96 (d) 107
  23. 23.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 36 (b) 66 (c) 8 (d) 33
  24. 24.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 36 (b) 11 (c) 72 (d) 42
  25. 25.What is the sum of the first 7 terms of the AP 10, 15, 20, …? (a) 175 (b) 350 (c) 40 (d) 180
  26. 26.What is the sum of the first 12 terms of the AP 9, 14, 19, …? (a) 876 (b) 64 (c) 468 (d) 438
  27. 27.What is the 40th term of the AP 17, 26, 35, 44, …? (a) 360 (b) 377 (c) 351 (d) 368
  28. 28.What is the 22nd term of the AP 15, 17, 19, 21, …? (a) 59 (b) 44 (c) 42 (d) 57
  29. 29.What is the sum of the first 8 terms of the AP 6, 12, 18, …? (a) 240 (b) 432 (c) 216 (d) 48
  30. 30.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 71 (b) 70 (c) 13 (d) 140
  31. 31.What is the 29th term of the AP 9, 18, 27, 36, …? (a) 252 (b) 262 (c) 270 (d) 261
  32. 32.Which term of the AP 17, 20, 23, 26, … is 50? (a) 11th (b) 13th (c) 12th (d) 14th
  33. 33.What is the 14th term of the AP 4, 7, 10, 13, …? (a) 46 (b) 39 (c) 42 (d) 43
  34. 34.What is the 34th term of the AP 2, 4, 6, 8, …? (a) 68 (b) 69 (c) 70 (d) 66
  35. 35.Which term of the AP 15, 23, 31, 39, … is 311? (a) 38th (b) 40th (c) 39th (d) 37th
  36. 36.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 19 (b) 84 (c) 90 (d) 168
  37. 37.What is the missing term in the AP 5, 10, 15, ?, 25? (a) 19 (b) 25 (c) 20 (d) 21
  38. 38.What is the 33rd term of the AP 14, 21, 28, 35, …? (a) 245 (b) 224 (c) 238 (d) 231
  39. 39.What is the 36th term of the AP 9, 13, 17, 21, …? (a) 153 (b) 140 (c) 144 (d) 149
  40. 40.What is the 28th term of the AP 9, 16, 23, 30, …? (a) 196 (b) 189 (c) 205 (d) 198

Answer key

  1. 135
  2. 267
  3. 210
  4. 2485
  5. 104
  6. 136
  7. 189
  8. 11th
  9. 3655
  10. 81
  11. 171
  12. 16
  13. 113
  14. 132
  15. 3403
  16. 36th
  17. 117
  18. 1378
  19. 297
  20. 325
  21. 65
  22. 99
  23. 33
  24. 36
  25. 175
  26. 438
  27. 368
  28. 57
  29. 216
  30. 70
  31. 261
  32. 12th
  33. 43
  34. 68
  35. 38th
  36. 84
  37. 20
  38. 238
  39. 149
  40. 198

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