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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 372 · 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 16th term of the AP 20, 23, 26, 29, …? (a) 45 (b) 65 (c) 68 (d) 48
  2. 2.What is the 12th term of the AP 3, 6, 9, 12, …? (a) 39 (b) 36 (c) 37 (d) 33
  3. 3.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 2485 (c) 5112 (d) 2557
  4. 4.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 78 (b) 77 (c) 12 (d) 154
  5. 5.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 14 (b) 40 (c) 80 (d) 43
  6. 6.What is the sum of the first 11 terms of the AP 9, 12, 15, …? (a) 267 (b) 264 (c) 528 (d) 39
  7. 7.Which term of the AP 2, 5, 8, 11, … is 32? (a) 13th (b) 12th (c) 10th (d) 11th
  8. 8.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 21 (b) 120 (c) 224 (d) 112
  9. 9.What is the 16th term of the AP 15, 20, 25, 30, …? (a) 80 (b) 95 (c) 75 (d) 90
  10. 10.What is the 28th term of the AP 5, 7, 9, 11, …? (a) 56 (b) 61 (c) 54 (d) 59
  11. 11.Which term of the AP 1, 9, 17, 25, … is 273? (a) 37th (b) 36th (c) 34th (d) 35th
  12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 756 (d) 729
  13. 13.What is the sum of all the whole numbers from 1 to 11? (a) 55 (b) 66 (c) 67 (d) 132
  14. 14.What is the 24th term of the AP 10, 13, 16, 19, …? (a) 72 (b) 82 (c) 69 (d) 79
  15. 15.What is the 27th term of the AP 4, 9, 14, 19, …? (a) 130 (b) 139 (c) 135 (d) 134
  16. 16.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 5 (b) 6 (c) 7 (d) 8
  17. 17.What is the missing term in the AP 8, 13, 18, ?, 28? (a) 24 (b) 23 (c) 22 (d) 28
  18. 18.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 45 (b) 50 (c) 90 (d) 13
  19. 19.Which term of the AP 8, 11, 14, 17, … is 44? (a) 14th (b) 13th (c) 15th (d) 12th
  20. 20.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 330 (b) 166 (c) 165 (d) 20
  21. 21.Which term of the AP 1, 3, 5, 7, … is 15? (a) 9th (b) 10th (c) 8th (d) 7th
  22. 22.Which term of the AP 16, 24, 32, 40, … is 88? (a) 9th (b) 11th (c) 12th (d) 10th
  23. 23.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 325 (c) 650 (d) 49
  24. 24.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 289 (c) 33 (d) 306
  25. 25.What is the missing term in the AP 1, 5, 9, ?, 17? (a) 12 (b) 14 (c) 13 (d) 17
  26. 26.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 136 (b) 240 (c) 29 (d) 120
  27. 27.Which term of the AP 3, 10, 17, 24, … is 59? (a) 11th (b) 8th (c) 9th (d) 10th
  28. 28.What is the 19th term of the AP 13, 22, 31, 40, …? (a) 175 (b) 184 (c) 162 (d) 171
  29. 29.What is the 17th term of the AP 2, 10, 18, 26, …? (a) 136 (b) 128 (c) 130 (d) 138
  30. 30.Which term of the AP 1, 4, 7, 10, … is 34? (a) 12th (b) 14th (c) 13th (d) 11th
  31. 31.What is the 10th term of the AP 8, 13, 18, 23, …? (a) 53 (b) 58 (c) 45 (d) 50
  32. 32.What is the sum of the first 6 terms of the AP 8, 11, 14, …? (a) 23 (b) 93 (c) 186 (d) 102
  33. 33.What is the 32nd term of the AP 16, 24, 32, 40, …? (a) 256 (b) 264 (c) 272 (d) 248
  34. 34.What is the 40th term of the AP 16, 21, 26, 31, …? (a) 216 (b) 211 (c) 200 (d) 195
  35. 35.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 379 (c) 378 (d) 756
  36. 36.What is the 19th term of the AP 17, 20, 23, 26, …? (a) 71 (b) 54 (c) 74 (d) 57
  37. 37.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 156 (c) 23 (d) 78
  38. 38.What is the 18th term of the AP 10, 15, 20, 25, …? (a) 90 (b) 95 (c) 85 (d) 100
  39. 39.What is the sum of all the whole numbers from 1 to 84? (a) 3486 (b) 7140 (c) 3570 (d) 3528
  40. 40.What is the 14th term of the AP 7, 11, 15, 19, …? (a) 56 (b) 52 (c) 59 (d) 63

Answer key

  1. 65
  2. 36
  3. 2556
  4. 77
  5. 40
  6. 264
  7. 11th
  8. 112
  9. 90
  10. 59
  11. 35th
  12. 729
  13. 66
  14. 79
  15. 134
  16. 6
  17. 23
  18. 45
  19. 13th
  20. 165
  21. 8th
  22. 10th
  23. 625
  24. 289
  25. 13
  26. 120
  27. 9th
  28. 175
  29. 130
  30. 12th
  31. 53
  32. 93
  33. 264
  34. 211
  35. 378
  36. 71
  37. 144
  38. 95
  39. 3570
  40. 59

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