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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 485 · 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 22nd term of the AP 15, 22, 29, 36, …? (a) 169 (b) 162 (c) 154 (d) 147
  2. 2.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 48 (b) 45 (c) 15 (d) 90
  3. 3.What is the 27th term of the AP 9, 11, 13, 15, …? (a) 54 (b) 52 (c) 63 (d) 61
  4. 4.What is the 17th term of the AP 17, 20, 23, 26, …? (a) 51 (b) 48 (c) 65 (d) 68
  5. 5.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 51 (c) 351 (d) 702
  6. 6.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 496 (c) 465 (d) 497
  7. 7.What is the sum of the first 11 terms of the AP 7, 8, 9, …? (a) 132 (b) 17 (c) 133 (d) 264
  8. 8.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 900 (c) 465 (d) 59
  9. 9.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 682 (b) 341 (c) 346 (d) 56
  10. 10.What is the missing term in the AP 7, 9, ?, 13, 15? (a) 10 (b) 12 (c) 11 (d) 13
  11. 11.What is the missing term in the AP 5, 13, 21, ?, 37? (a) 30 (b) 28 (c) 29 (d) 37
  12. 12.What is the missing term in the AP 4, ?, 12, 16, 20? (a) 12 (b) 7 (c) 9 (d) 8
  13. 13.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 15 (c) 30 (d) 25
  14. 14.Which term of the AP 7, 9, 11, 13, … is 75? (a) 37th (b) 35th (c) 34th (d) 36th
  15. 15.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 252 (b) 126 (c) 129 (d) 27
  16. 16.What is the sum of all the whole numbers from 1 to 61? (a) 3782 (b) 1830 (c) 1891 (d) 1892
  17. 17.What is the 32nd term of the AP 19, 27, 35, 43, …? (a) 256 (b) 267 (c) 248 (d) 275
  18. 18.What is the 39th term of the AP 3, 5, 7, 9, …? (a) 78 (b) 79 (c) 76 (d) 81
  19. 19.What is the 21st term of the AP 6, 14, 22, 30, …? (a) 160 (b) 174 (c) 168 (d) 166
  20. 20.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 35 (b) 11 (c) 40 (d) 70
  21. 21.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 132 (d) 121
  22. 22.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 66 (b) 21 (c) 132 (d) 78
  23. 23.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 28 (b) 144 (c) 147 (d) 288
  24. 24.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 108 (b) 210 (c) 24 (d) 105
  25. 25.Which term of the AP 15, 23, 31, 39, … is 327? (a) 42nd (b) 39th (c) 41st (d) 40th
  26. 26.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 53 (b) 305 (c) 330 (d) 610
  27. 27.What is the sum of all the whole numbers from 1 to 54? (a) 1458 (b) 1485 (c) 1431 (d) 2970
  28. 28.What is the 28th term of the AP 15, 17, 19, 21, …? (a) 71 (b) 54 (c) 56 (d) 69
  29. 29.What is the 18th term of the AP 20, 23, 26, 29, …? (a) 71 (b) 51 (c) 54 (d) 74
  30. 30.What is the 24th term of the AP 7, 9, 11, 13, …? (a) 55 (b) 53 (c) 46 (d) 48
  31. 31.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 280 (b) 140 (c) 152 (d) 28
  32. 32.What is the 11th term of the AP 19, 25, 31, 37, …? (a) 66 (b) 79 (c) 85 (d) 60
  33. 33.What is the 15th term of the AP 4, 13, 22, 31, …? (a) 126 (b) 135 (c) 139 (d) 130
  34. 34.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 156 (b) 176 (c) 312 (d) 37
  35. 35.What is the sum of all the whole numbers from 1 to 91? (a) 4095 (b) 4186 (c) 4187 (d) 8372
  36. 36.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 210 (c) 27 (d) 196
  37. 37.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 26 (b) 140 (c) 70 (d) 85
  38. 38.What is the 21st term of the AP 5, 13, 21, 29, …? (a) 173 (b) 168 (c) 165 (d) 160
  39. 39.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 80 (b) 43 (c) 14 (d) 40
  40. 40.Which term of the AP 13, 20, 27, 34, … is 97? (a) 12th (b) 13th (c) 14th (d) 15th

Answer key

  1. 162
  2. 45
  3. 61
  4. 65
  5. 676
  6. 496
  7. 132
  8. 900
  9. 341
  10. 11
  11. 29
  12. 8
  13. 25
  14. 35th
  15. 126
  16. 1891
  17. 267
  18. 79
  19. 166
  20. 35
  21. 121
  22. 66
  23. 144
  24. 105
  25. 40th
  26. 305
  27. 1485
  28. 69
  29. 71
  30. 53
  31. 140
  32. 79
  33. 130
  34. 156
  35. 4186
  36. 196
  37. 70
  38. 165
  39. 40
  40. 13th

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