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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 804 · 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.Which term of the AP 12, 20, 28, 36, … is 92? (a) 10th (b) 13th (c) 12th (d) 11th
  2. 2.What is the 15th term of the AP 9, 15, 21, 27, …? (a) 90 (b) 93 (c) 99 (d) 84
  3. 3.What is the 40th term of the AP 14, 19, 24, 29, …? (a) 195 (b) 209 (c) 200 (d) 214
  4. 4.What is the sum of all the whole numbers from 1 to 85? (a) 3570 (b) 3656 (c) 7310 (d) 3655
  5. 5.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 33 (b) 26 (c) 27 (d) 25
  6. 6.What is the sum of all the whole numbers from 1 to 82? (a) 3321 (b) 3403 (c) 3362 (d) 6806
  7. 7.What is the 31st term of the AP 17, 26, 35, 44, …? (a) 270 (b) 296 (c) 279 (d) 287
  8. 8.What is the 36th term of the AP 14, 16, 18, 20, …? (a) 86 (b) 70 (c) 84 (d) 72
  9. 9.What is the missing term in the AP 18, 25, ?, 39, 46? (a) 33 (b) 32 (c) 31 (d) 39
  10. 10.What is the 15th term of the AP 6, 10, 14, 18, …? (a) 62 (b) 66 (c) 60 (d) 56
  11. 11.What is the 22nd term of the AP 4, 10, 16, 22, …? (a) 132 (b) 130 (c) 136 (d) 126
  12. 12.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 21 (b) 75 (c) 150 (d) 78
  13. 13.What is the 40th term of the AP 11, 13, 15, 17, …? (a) 89 (b) 80 (c) 91 (d) 78
  14. 14.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 676 (c) 351 (d) 51
  15. 15.What is the sum of all the whole numbers from 1 to 63? (a) 2016 (b) 2017 (c) 4032 (d) 1953
  16. 16.What is the 33rd term of the AP 14, 19, 24, 29, …? (a) 160 (b) 179 (c) 165 (d) 174
  17. 17.What is the 17th term of the AP 7, 9, 11, 13, …? (a) 39 (b) 34 (c) 41 (d) 32
  18. 18.What is the sum of the first 9 terms of the AP 5, 10, 15, …? (a) 225 (b) 45 (c) 450 (d) 230
  19. 19.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 190 (b) 32 (c) 187 (d) 374
  20. 20.What is the missing term in the AP 18, 24, 30, ?, 42? (a) 42 (b) 37 (c) 35 (d) 36
  21. 21.What is the missing term in the AP 4, ?, 18, 25, 32? (a) 12 (b) 10 (c) 11 (d) 18
  22. 22.Which term of the AP 3, 5, 7, 9, … is 23? (a) 13th (b) 11th (c) 12th (d) 10th
  23. 23.What is the 30th term of the AP 18, 20, 22, 24, …? (a) 78 (b) 58 (c) 76 (d) 60
  24. 24.What is the 26th term of the AP 14, 16, 18, 20, …? (a) 64 (b) 50 (c) 66 (d) 52
  25. 25.What is the sum of the first 10 terms of the AP 7, 10, 13, …? (a) 220 (b) 410 (c) 34 (d) 205
  26. 26.What is the sum of the first 5 terms of the AP 5, 10, 15, …? (a) 25 (b) 150 (c) 75 (d) 80
  27. 27.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 420 (b) 39 (c) 210 (d) 230
  28. 28.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 132 (d) 21
  29. 29.Which term of the AP 4, 8, 12, 16, … is 72? (a) 20th (b) 18th (c) 19th (d) 17th
  30. 30.What is the missing term in the AP 8, 14, ?, 26, 32? (a) 26 (b) 19 (c) 21 (d) 20
  31. 31.What is the 36th term of the AP 3, 11, 19, 27, …? (a) 283 (b) 280 (c) 291 (d) 288
  32. 32.What is the sum of the first 10 terms of the AP 6, 7, 8, …? (a) 105 (b) 110 (c) 210 (d) 15
  33. 33.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 23 (d) 144
  34. 34.What is the 18th term of the AP 6, 14, 22, 30, …? (a) 150 (b) 136 (c) 144 (d) 142
  35. 35.What is the 11th term of the AP 2, 5, 8, 11, …? (a) 33 (b) 32 (c) 35 (d) 30
  36. 36.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 264 (b) 42 (c) 484 (d) 242
  37. 37.What is the missing term in the AP 12, ?, 24, 30, 36? (a) 17 (b) 24 (c) 19 (d) 18
  38. 38.What is the 22nd term of the AP 9, 14, 19, 24, …? (a) 105 (b) 119 (c) 110 (d) 114
  39. 39.What is the 30th term of the AP 4, 12, 20, 28, …? (a) 244 (b) 236 (c) 232 (d) 240
  40. 40.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 40 (b) 70 (c) 11 (d) 35

Answer key

  1. 11th
  2. 93
  3. 209
  4. 3655
  5. 26
  6. 3403
  7. 287
  8. 84
  9. 32
  10. 62
  11. 130
  12. 75
  13. 89
  14. 676
  15. 2016
  16. 174
  17. 39
  18. 225
  19. 187
  20. 36
  21. 11
  22. 11th
  23. 76
  24. 64
  25. 205
  26. 75
  27. 210
  28. 121
  29. 18th
  30. 20
  31. 283
  32. 105
  33. 144
  34. 142
  35. 32
  36. 242
  37. 18
  38. 114
  39. 236
  40. 35

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