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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 833 · 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 17th term of the AP 17, 24, 31, 38, …? (a) 112 (b) 129 (c) 136 (d) 119
  2. 2.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 36 (d) 11
  3. 3.What is the sum of all the whole numbers from 1 to 29? (a) 435 (b) 870 (c) 436 (d) 406
  4. 4.What is the missing term in the AP 15, 21, ?, 33, 39? (a) 33 (b) 28 (c) 26 (d) 27
  5. 5.Which term of the AP 14, 23, 32, 41, … is 122? (a) 14th (b) 13th (c) 15th (d) 12th
  6. 6.What is the sum of the first 11 terms of the AP 1, 7, 13, …? (a) 61 (b) 341 (c) 682 (d) 374
  7. 7.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 171 (c) 324 (d) 342
  8. 8.What is the missing term in the AP 18, 26, ?, 42, 50? (a) 34 (b) 35 (c) 33 (d) 42
  9. 9.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 120 (c) 225 (d) 240
  10. 10.What is the 11th term of the AP 1, 10, 19, 28, …? (a) 90 (b) 99 (c) 100 (d) 91
  11. 11.What is the sum of all the whole numbers from 1 to 93? (a) 4278 (b) 4371 (c) 4372 (d) 8742
  12. 12.Which term of the AP 12, 19, 26, 33, … is 271? (a) 39th (b) 37th (c) 38th (d) 40th
  13. 13.What is the 21st term of the AP 9, 12, 15, 18, …? (a) 72 (b) 60 (c) 69 (d) 63
  14. 14.What is the 19th term of the AP 17, 22, 27, 32, …? (a) 95 (b) 90 (c) 112 (d) 107
  15. 15.What is the 27th term of the AP 10, 15, 20, 25, …? (a) 145 (b) 135 (c) 130 (d) 140
  16. 16.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 203 (b) 182 (c) 364 (d) 44
  17. 17.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 81 (d) 45
  18. 18.What is the 20th term of the AP 2, 4, 6, 8, …? (a) 38 (b) 40 (c) 42 (d) 41
  19. 19.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 30 (c) 15 (d) 9
  20. 20.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 66 (b) 126 (c) 63 (d) 13
  21. 21.What is the sum of all the whole numbers from 1 to 21? (a) 231 (b) 210 (c) 232 (d) 462
  22. 22.What is the missing term in the AP 15, 19, ?, 27, 31? (a) 27 (b) 22 (c) 24 (d) 23
  23. 23.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 119 (b) 22 (c) 112 (d) 224
  24. 24.What is the 13th term of the AP 20, 24, 28, 32, …? (a) 72 (b) 52 (c) 48 (d) 68
  25. 25.What is the sum of all the whole numbers from 1 to 19? (a) 380 (b) 171 (c) 190 (d) 191
  26. 26.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 110 (b) 19 (c) 100 (d) 200
  27. 27.What is the 14th term of the AP 2, 5, 8, 11, …? (a) 44 (b) 39 (c) 41 (d) 42
  28. 28.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 15 (c) 64 (d) 36
  29. 29.What is the sum of the first 7 terms of the AP 7, 12, 17, …? (a) 308 (b) 159 (c) 37 (d) 154
  30. 30.What is the 35th term of the AP 19, 21, 23, 25, …? (a) 89 (b) 87 (c) 70 (d) 68
  31. 31.What is the 15th term of the AP 16, 25, 34, 43, …? (a) 151 (b) 142 (c) 126 (d) 135
  32. 32.What is the 18th term of the AP 15, 22, 29, 36, …? (a) 141 (b) 126 (c) 119 (d) 134
  33. 33.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 400 (c) 210 (d) 420
  34. 34.Which term of the AP 12, 20, 28, 36, … is 196? (a) 26th (b) 24th (c) 25th (d) 23rd
  35. 35.What is the sum of all the whole numbers from 1 to 86? (a) 7482 (b) 3655 (c) 3741 (d) 3698
  36. 36.What is the sum of all the whole numbers from 1 to 57? (a) 1596 (b) 1654 (c) 3306 (d) 1653
  37. 37.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 528 (c) 496 (d) 512
  38. 38.What is the 27th term of the AP 5, 13, 21, 29, …? (a) 216 (b) 221 (c) 213 (d) 208
  39. 39.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 42 (b) 84 (c) 48 (d) 12
  40. 40.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 31 (b) 190 (c) 95 (d) 110

Answer key

  1. 129
  2. 36
  3. 435
  4. 27
  5. 13th
  6. 341
  7. 324
  8. 34
  9. 225
  10. 91
  11. 4371
  12. 38th
  13. 69
  14. 107
  15. 140
  16. 182
  17. 81
  18. 40
  19. 25
  20. 63
  21. 231
  22. 23
  23. 112
  24. 68
  25. 190
  26. 100
  27. 41
  28. 64
  29. 154
  30. 87
  31. 142
  32. 134
  33. 400
  34. 24th
  35. 3741
  36. 1653
  37. 528
  38. 213
  39. 42
  40. 95

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