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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 811 · 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 missing term in the AP 1, 10, 19, ?, 37? (a) 27 (b) 37 (c) 28 (d) 29
  2. 2.What is the 14th term of the AP 5, 7, 9, 11, …? (a) 31 (b) 28 (c) 33 (d) 26
  3. 3.What is the 24th term of the AP 12, 17, 22, 27, …? (a) 120 (b) 127 (c) 132 (d) 115
  4. 4.What is the 11th term of the AP 6, 11, 16, 21, …? (a) 61 (b) 55 (c) 56 (d) 50
  5. 5.What is the sum of all the whole numbers from 1 to 42? (a) 861 (b) 1806 (c) 882 (d) 903
  6. 6.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 272 (b) 24 (c) 136 (d) 144
  7. 7.What is the missing term in the AP 20, ?, 28, 32, 36? (a) 28 (b) 25 (c) 23 (d) 24
  8. 8.What is the missing term in the AP 5, 11, 17, ?, 29? (a) 29 (b) 23 (c) 22 (d) 24
  9. 9.What is the missing term in the AP 18, 25, 32, ?, 46? (a) 40 (b) 38 (c) 46 (d) 39
  10. 10.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 35 (b) 189 (c) 342 (d) 171
  11. 11.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 289 (c) 306 (d) 33
  12. 12.What is the missing term in the AP 10, 13, ?, 19, 22? (a) 16 (b) 19 (c) 17 (d) 15
  13. 13.What is the 18th term of the AP 9, 14, 19, 24, …? (a) 99 (b) 90 (c) 85 (d) 94
  14. 14.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 21 (d) 121
  15. 15.What is the sum of the first 5 terms of the AP 1, 6, 11, …? (a) 60 (b) 110 (c) 55 (d) 21
  16. 16.What is the sum of all the whole numbers from 1 to 85? (a) 3570 (b) 3655 (c) 7310 (d) 3656
  17. 17.What is the 17th term of the AP 9, 16, 23, 30, …? (a) 112 (b) 119 (c) 128 (d) 121
  18. 18.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 172 (b) 192 (c) 344 (d) 39
  19. 19.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 325 (c) 650 (d) 300
  20. 20.What is the sum of the first 5 terms of the AP 9, 15, 21, …? (a) 210 (b) 120 (c) 105 (d) 33
  21. 21.What is the 33rd term of the AP 20, 23, 26, 29, …? (a) 99 (b) 119 (c) 116 (d) 96
  22. 22.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 528 (c) 562 (d) 561
  23. 23.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 36 (b) 72 (c) 11 (d) 42
  24. 24.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 100 (c) 110 (d) 55
  25. 25.What is the missing term in the AP 17, 20, 23, ?, 29? (a) 29 (b) 27 (c) 25 (d) 26
  26. 26.What is the 18th term of the AP 17, 21, 25, 29, …? (a) 72 (b) 89 (c) 85 (d) 68
  27. 27.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 24 (b) 108 (c) 210 (d) 105
  28. 28.What is the missing term in the AP 11, ?, 19, 23, 27? (a) 14 (b) 16 (c) 15 (d) 19
  29. 29.What is the 32nd term of the AP 20, 27, 34, 41, …? (a) 237 (b) 244 (c) 217 (d) 224
  30. 30.What is the sum of all the whole numbers from 1 to 58? (a) 1711 (b) 1653 (c) 3422 (d) 1682
  31. 31.What is the missing term in the AP 3, 5, 7, ?, 11? (a) 10 (b) 8 (c) 11 (d) 9
  32. 32.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 900 (d) 930
  33. 33.What is the sum of all the whole numbers from 1 to 35? (a) 1260 (b) 630 (c) 631 (d) 595
  34. 34.What is the 20th term of the AP 2, 9, 16, 23, …? (a) 142 (b) 140 (c) 135 (d) 133
  35. 35.What is the 14th term of the AP 2, 4, 6, 8, …? (a) 26 (b) 30 (c) 28 (d) 29
  36. 36.What is the 18th term of the AP 4, 13, 22, 31, …? (a) 153 (b) 166 (c) 162 (d) 157
  37. 37.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 115 (b) 200 (c) 32 (d) 100
  38. 38.What is the sum of all the whole numbers from 1 to 98? (a) 4851 (b) 9702 (c) 4802 (d) 4753
  39. 39.What is the missing term in the AP 4, ?, 14, 19, 24? (a) 9 (b) 14 (c) 8 (d) 10
  40. 40.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 25 (d) 9

Answer key

  1. 28
  2. 31
  3. 127
  4. 56
  5. 903
  6. 136
  7. 24
  8. 23
  9. 39
  10. 171
  11. 289
  12. 16
  13. 94
  14. 121
  15. 55
  16. 3655
  17. 121
  18. 172
  19. 325
  20. 105
  21. 116
  22. 561
  23. 36
  24. 100
  25. 26
  26. 85
  27. 105
  28. 15
  29. 237
  30. 1711
  31. 9
  32. 900
  33. 630
  34. 135
  35. 28
  36. 157
  37. 100
  38. 4851
  39. 9
  40. 25

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