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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 355 · 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 sum of the first 9 terms of the AP 1, 5, 9, …? (a) 171 (b) 306 (c) 153 (d) 33
  2. 2.What is the 31st term of the AP 16, 21, 26, 31, …? (a) 171 (b) 150 (c) 155 (d) 166
  3. 3.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 2557 (c) 2485 (d) 5112
  4. 4.What is the 26th term of the AP 19, 22, 25, 28, …? (a) 97 (b) 75 (c) 78 (d) 94
  5. 5.What is the 22nd term of the AP 3, 9, 15, 21, …? (a) 126 (b) 129 (c) 135 (d) 132
  6. 6.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 496 (c) 497 (d) 465
  7. 7.What is the 38th term of the AP 15, 19, 23, 27, …? (a) 152 (b) 148 (c) 163 (d) 167
  8. 8.Which term of the AP 11, 20, 29, 38, … is 128? (a) 14th (b) 13th (c) 16th (d) 15th
  9. 9.What is the 10th term of the AP 4, 7, 10, 13, …? (a) 27 (b) 30 (c) 34 (d) 31
  10. 10.What is the 36th term of the AP 9, 11, 13, 15, …? (a) 79 (b) 81 (c) 70 (d) 72
  11. 11.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 435 (c) 841 (d) 870
  12. 12.What is the 35th term of the AP 13, 15, 17, 19, …? (a) 83 (b) 81 (c) 68 (d) 70
  13. 13.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 168 (b) 184 (c) 35 (d) 336
  14. 14.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 150 (b) 84 (c) 20 (d) 75
  15. 15.What is the sum of all the whole numbers from 1 to 29? (a) 435 (b) 406 (c) 870 (d) 436
  16. 16.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 21 (b) 130 (c) 120 (d) 240
  17. 17.What is the 16th term of the AP 8, 12, 16, 20, …? (a) 60 (b) 64 (c) 72 (d) 68
  18. 18.Which term of the AP 20, 28, 36, 44, … is 284? (a) 34th (b) 36th (c) 33rd (d) 35th
  19. 19.Which term of the AP 14, 19, 24, 29, … is 194? (a) 36th (b) 38th (c) 37th (d) 39th
  20. 20.What is the 15th term of the AP 5, 9, 13, 17, …? (a) 56 (b) 65 (c) 61 (d) 60
  21. 21.Which term of the AP 15, 22, 29, 36, … is 176? (a) 25th (b) 26th (c) 24th (d) 23rd
  22. 22.What is the sum of all the whole numbers from 1 to 23? (a) 276 (b) 253 (c) 552 (d) 277
  23. 23.What is the 31st term of the AP 20, 23, 26, 29, …? (a) 93 (b) 110 (c) 90 (d) 113
  24. 24.What is the missing term in the AP 8, 11, ?, 17, 20? (a) 17 (b) 13 (c) 15 (d) 14
  25. 25.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 144 (c) 156 (d) 23
  26. 26.What is the sum of all the whole numbers from 1 to 77? (a) 6006 (b) 3003 (c) 2926 (d) 3004
  27. 27.What is the sum of all the whole numbers from 1 to 55? (a) 1540 (b) 1541 (c) 1485 (d) 3080
  28. 28.What is the 14th term of the AP 8, 10, 12, 14, …? (a) 28 (b) 26 (c) 36 (d) 34
  29. 29.What is the 29th term of the AP 18, 23, 28, 33, …? (a) 140 (b) 163 (c) 145 (d) 158
  30. 30.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 45 (b) 13 (c) 50 (d) 90
  31. 31.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3828 (c) 7832 (d) 3916
  32. 32.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 650 (d) 625
  33. 33.What is the 26th term of the AP 5, 8, 11, 14, …? (a) 78 (b) 83 (c) 80 (d) 75
  34. 34.What is the sum of all the whole numbers from 1 to 50? (a) 1275 (b) 1250 (c) 2550 (d) 1225
  35. 35.Which term of the AP 12, 17, 22, 27, … is 62? (a) 11th (b) 10th (c) 13th (d) 12th
  36. 36.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 136 (b) 144 (c) 272 (d) 24
  37. 37.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 171 (b) 162 (c) 26 (d) 324
  38. 38.What is the 18th term of the AP 16, 18, 20, 22, …? (a) 36 (b) 52 (c) 34 (d) 50
  39. 39.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 220 (b) 125 (c) 34 (d) 110
  40. 40.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 231 (c) 441 (d) 41

Answer key

  1. 153
  2. 166
  3. 2556
  4. 94
  5. 129
  6. 496
  7. 163
  8. 14th
  9. 31
  10. 79
  11. 841
  12. 81
  13. 168
  14. 75
  15. 435
  16. 120
  17. 68
  18. 34th
  19. 37th
  20. 61
  21. 24th
  22. 276
  23. 110
  24. 14
  25. 144
  26. 3003
  27. 1540
  28. 34
  29. 158
  30. 45
  31. 3916
  32. 625
  33. 80
  34. 1275
  35. 11th
  36. 136
  37. 162
  38. 50
  39. 110
  40. 441

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