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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 140 · 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 6 terms of the AP 10, 15, 20, …? (a) 150 (b) 35 (c) 270 (d) 135
  2. 2.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 20 (b) 154 (c) 80 (d) 77
  3. 3.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 528 (c) 1056 (d) 496
  4. 4.What is the 36th term of the AP 2, 11, 20, 29, …? (a) 326 (b) 317 (c) 315 (d) 324
  5. 5.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 55 (c) 110 (d) 19
  6. 6.What is the missing term in the AP 5, 13, ?, 29, 37? (a) 20 (b) 29 (c) 21 (d) 22
  7. 7.Which term of the AP 5, 12, 19, 26, … is 194? (a) 29th (b) 30th (c) 28th (d) 27th
  8. 8.What is the 13th term of the AP 14, 21, 28, 35, …? (a) 105 (b) 91 (c) 84 (d) 98
  9. 9.What is the sum of all the whole numbers from 1 to 94? (a) 4371 (b) 4465 (c) 4418 (d) 8930
  10. 10.What is the missing term in the AP 12, 15, ?, 21, 24? (a) 18 (b) 19 (c) 21 (d) 17
  11. 11.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 650 (d) 625
  12. 12.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 25 (b) 9 (c) 50 (d) 30
  13. 13.What is the sum of all the whole numbers from 1 to 34? (a) 578 (b) 561 (c) 595 (d) 1190
  14. 14.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 700 (b) 350 (c) 380 (d) 62
  15. 15.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 57 (d) 435
  16. 16.Which term of the AP 2, 5, 8, 11, … is 65? (a) 22nd (b) 23rd (c) 24th (d) 21st
  17. 17.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 136 (b) 256 (c) 23 (d) 128
  18. 18.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 29 (c) 120 (d) 225
  19. 19.What is the sum of the first 9 terms of the AP 9, 12, 15, …? (a) 33 (b) 192 (c) 378 (d) 189
  20. 20.What is the missing term in the AP 7, ?, 13, 16, 19? (a) 11 (b) 10 (c) 9 (d) 13
  21. 21.Which term of the AP 5, 8, 11, 14, … is 44? (a) 14th (b) 15th (c) 13th (d) 16th
  22. 22.What is the sum of all the whole numbers from 1 to 13? (a) 78 (b) 91 (c) 92 (d) 182
  23. 23.What is the 14th term of the AP 14, 23, 32, 41, …? (a) 131 (b) 140 (c) 117 (d) 126
  24. 24.What is the 17th term of the AP 20, 27, 34, 41, …? (a) 132 (b) 139 (c) 112 (d) 119
  25. 25.What is the 38th term of the AP 11, 14, 17, 20, …? (a) 111 (b) 114 (c) 125 (d) 122
  26. 26.What is the 39th term of the AP 1, 4, 7, 10, …? (a) 114 (b) 118 (c) 117 (d) 115
  27. 27.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 72 (b) 15 (c) 64 (d) 128
  28. 28.What is the sum of the first 12 terms of the AP 2, 4, 6, …? (a) 168 (b) 312 (c) 24 (d) 156
  29. 29.What is the 39th term of the AP 19, 21, 23, 25, …? (a) 76 (b) 97 (c) 95 (d) 78
  30. 30.What is the missing term in the AP 3, 5, 7, ?, 11? (a) 8 (b) 10 (c) 9 (d) 11
  31. 31.What is the missing term in the AP 8, 15, ?, 29, 36? (a) 21 (b) 22 (c) 29 (d) 23
  32. 32.What is the 36th term of the AP 14, 16, 18, 20, …? (a) 72 (b) 86 (c) 70 (d) 84
  33. 33.Which term of the AP 19, 26, 33, 40, … is 292? (a) 40th (b) 41st (c) 42nd (d) 39th
  34. 34.Which term of the AP 3, 10, 17, 24, … is 94? (a) 13th (b) 15th (c) 14th (d) 16th
  35. 35.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 71 (b) 13 (c) 140 (d) 70
  36. 36.What is the 20th term of the AP 18, 23, 28, 33, …? (a) 113 (b) 118 (c) 100 (d) 95
  37. 37.What is the sum of the first 8 terms of the AP 9, 10, 11, …? (a) 100 (b) 104 (c) 200 (d) 16
  38. 38.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 186 (b) 28 (c) 93 (d) 108
  39. 39.What is the sum of the first 6 terms of the AP 6, 9, 12, …? (a) 90 (b) 21 (c) 162 (d) 81
  40. 40.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 2415 (c) 4970 (d) 2485

Answer key

  1. 135
  2. 77
  3. 528
  4. 317
  5. 100
  6. 21
  7. 28th
  8. 98
  9. 4465
  10. 18
  11. 625
  12. 25
  13. 595
  14. 350
  15. 841
  16. 22nd
  17. 128
  18. 225
  19. 189
  20. 10
  21. 14th
  22. 91
  23. 131
  24. 132
  25. 122
  26. 115
  27. 64
  28. 156
  29. 95
  30. 9
  31. 22
  32. 84
  33. 40th
  34. 14th
  35. 70
  36. 113
  37. 100
  38. 93
  39. 81
  40. 2485

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