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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 381 · 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 32nd term of the AP 7, 10, 13, 16, …? (a) 100 (b) 96 (c) 103 (d) 93
  2. 2.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 46 (b) 470 (c) 235 (d) 260
  3. 3.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1682 (c) 1653 (d) 1711
  4. 4.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 276 (c) 45 (d) 552
  5. 5.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 595 (c) 631 (d) 1260
  6. 6.What is the sum of all the whole numbers from 1 to 14? (a) 210 (b) 98 (c) 105 (d) 91
  7. 7.What is the sum of all the whole numbers from 1 to 52? (a) 1326 (b) 2756 (c) 1352 (d) 1378
  8. 8.What is the 38th term of the AP 17, 21, 25, 29, …? (a) 169 (b) 165 (c) 152 (d) 148
  9. 9.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 26 (b) 140 (c) 85 (d) 70
  10. 10.What is the 17th term of the AP 5, 13, 21, 29, …? (a) 128 (b) 141 (c) 133 (d) 136
  11. 11.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 384 (b) 708 (c) 354 (d) 57
  12. 12.What is the sum of all the whole numbers from 1 to 96? (a) 4560 (b) 4608 (c) 4656 (d) 9312
  13. 13.What is the sum of the first 8 terms of the AP 7, 13, 19, …? (a) 224 (b) 448 (c) 248 (d) 49
  14. 14.Which term of the AP 2, 4, 6, 8, … is 58? (a) 30th (b) 31st (c) 28th (d) 29th
  15. 15.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 66 (b) 120 (c) 60 (d) 15
  16. 16.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 72 (b) 11 (c) 36 (d) 42
  17. 17.What is the sum of the first 11 terms of the AP 9, 11, 13, …? (a) 29 (b) 220 (c) 209 (d) 418
  18. 18.What is the 28th term of the AP 20, 26, 32, 38, …? (a) 162 (b) 168 (c) 188 (d) 182
  19. 19.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 10 (b) 60 (c) 30 (d) 35
  20. 20.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 23 (b) 26 (c) 24 (d) 22
  21. 21.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 56 (d) 28
  22. 22.What is the sum of the first 12 terms of the AP 3, 8, 13, …? (a) 366 (b) 732 (c) 396 (d) 58
  23. 23.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 51 (b) 264 (c) 480 (d) 240
  24. 24.What is the missing term in the AP 15, ?, 31, 39, 47? (a) 22 (b) 24 (c) 31 (d) 23
  25. 25.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 45 (d) 81
  26. 26.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 308 (b) 46 (c) 572 (d) 286
  27. 27.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 144 (d) 156
  28. 28.What is the 10th term of the AP 1, 3, 5, 7, …? (a) 18 (b) 21 (c) 20 (d) 19
  29. 29.What is the 14th term of the AP 14, 23, 32, 41, …? (a) 117 (b) 140 (c) 131 (d) 126
  30. 30.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 121 (c) 21 (d) 66
  31. 31.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 27 (c) 210 (d) 196
  32. 32.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 36 (c) 11 (d) 42
  33. 33.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 253 (c) 506 (d) 484
  34. 34.What is the missing term in the AP 5, 11, 17, ?, 29? (a) 29 (b) 24 (c) 22 (d) 23
  35. 35.What is the sum of the first 6 terms of the AP 5, 6, 7, …? (a) 45 (b) 90 (c) 48 (d) 10
  36. 36.Which term of the AP 12, 15, 18, 21, … is 45? (a) 12th (b) 11th (c) 15th (d) 13th
  37. 37.What is the missing term in the AP 14, 23, 32, ?, 50? (a) 50 (b) 41 (c) 40 (d) 42
  38. 38.What is the sum of the first 7 terms of the AP 6, 11, 16, …? (a) 294 (b) 152 (c) 147 (d) 36
  39. 39.What is the sum of all the whole numbers from 1 to 64? (a) 2080 (b) 2016 (c) 4160 (d) 2048
  40. 40.What is the sum of the first 8 terms of the AP 2, 5, 8, …? (a) 112 (b) 200 (c) 23 (d) 100

Answer key

  1. 100
  2. 235
  3. 1711
  4. 529
  5. 630
  6. 105
  7. 1378
  8. 165
  9. 70
  10. 133
  11. 354
  12. 4656
  13. 224
  14. 29th
  15. 60
  16. 36
  17. 209
  18. 182
  19. 30
  20. 23
  21. 49
  22. 366
  23. 240
  24. 23
  25. 81
  26. 286
  27. 144
  28. 19
  29. 131
  30. 121
  31. 196
  32. 36
  33. 484
  34. 23
  35. 45
  36. 12th
  37. 41
  38. 147
  39. 2080
  40. 100

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