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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 123 · 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 40th term of the AP 10, 13, 16, 19, …? (a) 130 (b) 127 (c) 117 (d) 120
  2. 2.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 270 (b) 18 (c) 140 (d) 135
  3. 3.What is the sum of all the whole numbers from 1 to 81? (a) 6642 (b) 3240 (c) 3322 (d) 3321
  4. 4.What is the 11th term of the AP 13, 22, 31, 40, …? (a) 112 (b) 99 (c) 90 (d) 103
  5. 5.What is the missing term in the AP 5, ?, 23, 32, 41? (a) 14 (b) 23 (c) 15 (d) 13
  6. 6.What is the 15th term of the AP 1, 9, 17, 25, …? (a) 121 (b) 112 (c) 120 (d) 113
  7. 7.What is the missing term in the AP 12, 15, ?, 21, 24? (a) 19 (b) 17 (c) 21 (d) 18
  8. 8.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 9 (d) 25
  9. 9.What is the sum of all the whole numbers from 1 to 92? (a) 8556 (b) 4232 (c) 4278 (d) 4186
  10. 10.What is the 30th term of the AP 6, 9, 12, 15, …? (a) 90 (b) 96 (c) 87 (d) 93
  11. 11.What is the missing term in the AP 8, ?, 12, 14, 16? (a) 12 (b) 11 (c) 10 (d) 9
  12. 12.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 43 (c) 484 (d) 506
  13. 13.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 5 (b) 30 (c) 16 (d) 15
  14. 14.What is the 20th term of the AP 10, 17, 24, 31, …? (a) 140 (b) 133 (c) 143 (d) 150
  15. 15.Which term of the AP 1, 6, 11, 16, … is 196? (a) 42nd (b) 41st (c) 39th (d) 40th
  16. 16.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 132 (d) 121
  17. 17.Which term of the AP 18, 22, 26, 30, … is 138? (a) 30th (b) 32nd (c) 31st (d) 33rd
  18. 18.What is the 17th term of the AP 4, 7, 10, 13, …? (a) 55 (b) 51 (c) 52 (d) 48
  19. 19.What is the sum of the first 9 terms of the AP 7, 10, 13, …? (a) 342 (b) 174 (c) 171 (d) 31
  20. 20.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 600 (c) 47 (d) 576
  21. 21.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 180 (b) 348 (c) 20 (d) 174
  22. 22.What is the 14th term of the AP 3, 8, 13, 18, …? (a) 68 (b) 70 (c) 65 (d) 73
  23. 23.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 9900 (c) 4950 (d) 4851
  24. 24.What is the sum of the first 5 terms of the AP 5, 10, 15, …? (a) 80 (b) 25 (c) 150 (d) 75
  25. 25.What is the sum of all the whole numbers from 1 to 46? (a) 1081 (b) 1058 (c) 1035 (d) 2162
  26. 26.What is the 40th term of the AP 7, 15, 23, 31, …? (a) 320 (b) 327 (c) 319 (d) 312
  27. 27.What is the missing term in the AP 13, ?, 27, 34, 41? (a) 27 (b) 20 (c) 19 (d) 21
  28. 28.What is the 17th term of the AP 3, 11, 19, 27, …? (a) 136 (b) 131 (c) 139 (d) 128
  29. 29.Which term of the AP 18, 25, 32, 39, … is 67? (a) 7th (b) 10th (c) 9th (d) 8th
  30. 30.What is the 27th term of the AP 8, 11, 14, 17, …? (a) 86 (b) 81 (c) 89 (d) 78
  31. 31.What is the 10th term of the AP 1, 6, 11, 16, …? (a) 45 (b) 50 (c) 46 (d) 51
  32. 32.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 150 (b) 75 (c) 27 (d) 90
  33. 33.What is the missing term in the AP 1, ?, 17, 25, 33? (a) 9 (b) 8 (c) 17 (d) 10
  34. 34.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 198 (b) 108 (c) 99 (d) 19
  35. 35.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 195 (b) 33 (c) 210 (d) 390
  36. 36.What is the missing term in the AP 1, 6, 11, ?, 21? (a) 17 (b) 16 (c) 15 (d) 21
  37. 37.What is the missing term in the AP 11, ?, 27, 35, 43? (a) 20 (b) 27 (c) 19 (d) 18
  38. 38.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 17 (b) 162 (c) 81 (d) 90
  39. 39.What is the missing term in the AP 13, ?, 25, 31, 37? (a) 20 (b) 25 (c) 19 (d) 18
  40. 40.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 105 (d) 210

Answer key

  1. 127
  2. 135
  3. 3321
  4. 103
  5. 14
  6. 113
  7. 18
  8. 25
  9. 4278
  10. 93
  11. 10
  12. 484
  13. 15
  14. 143
  15. 40th
  16. 121
  17. 31st
  18. 52
  19. 171
  20. 576
  21. 174
  22. 68
  23. 4950
  24. 75
  25. 1081
  26. 319
  27. 20
  28. 131
  29. 8th
  30. 86
  31. 46
  32. 75
  33. 9
  34. 99
  35. 195
  36. 16
  37. 19
  38. 81
  39. 19
  40. 196

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