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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 631 · 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 12 terms of the AP 9, 14, 19, …? (a) 438 (b) 64 (c) 876 (d) 468
  2. 2.What is the sum of all the whole numbers from 1 to 45? (a) 1035 (b) 990 (c) 2070 (d) 1036
  3. 3.What is the 38th term of the AP 12, 19, 26, 33, …? (a) 278 (b) 266 (c) 259 (d) 271
  4. 4.What is the sum of all the whole numbers from 1 to 85? (a) 7310 (b) 3655 (c) 3570 (d) 3656
  5. 5.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 10 (b) 15 (c) 12 (d) 11
  6. 6.What is the 40th term of the AP 4, 12, 20, 28, …? (a) 324 (b) 312 (c) 320 (d) 316
  7. 7.What is the sum of all the whole numbers from 1 to 94? (a) 8930 (b) 4418 (c) 4371 (d) 4465
  8. 8.What is the missing term in the AP 7, 16, 25, ?, 43? (a) 33 (b) 43 (c) 35 (d) 34
  9. 9.What is the 10th term of the AP 19, 28, 37, 46, …? (a) 90 (b) 81 (c) 109 (d) 100
  10. 10.What is the 24th term of the AP 3, 9, 15, 21, …? (a) 147 (b) 141 (c) 138 (d) 144
  11. 11.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 12 (b) 48 (c) 84 (d) 42
  12. 12.What is the sum of all the whole numbers from 1 to 78? (a) 3081 (b) 6162 (c) 3042 (d) 3003
  13. 13.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 27 (b) 180 (c) 190 (d) 360
  14. 14.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 123 (b) 246 (c) 138 (d) 33
  15. 15.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 192 (b) 114 (c) 31 (d) 96
  16. 16.What is the missing term in the AP 12, 19, 26, ?, 40? (a) 34 (b) 40 (c) 32 (d) 33
  17. 17.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 396 (b) 66 (c) 429 (d) 792
  18. 18.Which term of the AP 18, 25, 32, 39, … is 186? (a) 27th (b) 26th (c) 24th (d) 25th
  19. 19.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 132 (d) 66
  20. 20.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 16 (b) 140 (c) 70 (d) 77
  21. 21.What is the missing term in the AP 19, 25, 31, ?, 43? (a) 43 (b) 37 (c) 36 (d) 38
  22. 22.What is the missing term in the AP 1, 5, 9, ?, 17? (a) 12 (b) 14 (c) 13 (d) 17
  23. 23.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 140 (b) 270 (c) 135 (d) 18
  24. 24.What is the 32nd term of the AP 13, 16, 19, 22, …? (a) 93 (b) 96 (c) 106 (d) 109
  25. 25.What is the missing term in the AP 14, 16, 18, ?, 22? (a) 19 (b) 21 (c) 22 (d) 20
  26. 26.What is the missing term in the AP 19, ?, 37, 46, 55? (a) 28 (b) 27 (c) 37 (d) 29
  27. 27.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 110 (b) 220 (c) 111 (d) 15
  28. 28.What is the missing term in the AP 17, ?, 23, 26, 29? (a) 21 (b) 20 (c) 23 (d) 19
  29. 29.Which term of the AP 14, 22, 30, 38, … is 270? (a) 35th (b) 34th (c) 32nd (d) 33rd
  30. 30.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 200 (b) 176 (c) 352 (d) 43
  31. 31.What is the sum of all the whole numbers from 1 to 60? (a) 1800 (b) 1770 (c) 1830 (d) 3660
  32. 32.What is the 25th term of the AP 8, 17, 26, 35, …? (a) 225 (b) 233 (c) 224 (d) 216
  33. 33.What is the 21st term of the AP 15, 23, 31, 39, …? (a) 168 (b) 183 (c) 160 (d) 175
  34. 34.What is the sum of the first 9 terms of the AP 1, 4, 7, …? (a) 117 (b) 25 (c) 234 (d) 120
  35. 35.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 600 (c) 47 (d) 300
  36. 36.What is the 20th term of the AP 7, 9, 11, 13, …? (a) 47 (b) 40 (c) 45 (d) 38
  37. 37.What is the missing term in the AP 14, ?, 24, 29, 34? (a) 24 (b) 20 (c) 18 (d) 19
  38. 38.What is the sum of all the whole numbers from 1 to 55? (a) 1540 (b) 1541 (c) 3080 (d) 1485
  39. 39.Which term of the AP 13, 22, 31, 40, … is 166? (a) 17th (b) 19th (c) 20th (d) 18th
  40. 40.What is the 18th term of the AP 11, 16, 21, 26, …? (a) 85 (b) 90 (c) 96 (d) 101

Answer key

  1. 438
  2. 1035
  3. 271
  4. 3655
  5. 11
  6. 316
  7. 4465
  8. 34
  9. 100
  10. 141
  11. 42
  12. 3081
  13. 180
  14. 123
  15. 96
  16. 33
  17. 396
  18. 25th
  19. 121
  20. 70
  21. 37
  22. 13
  23. 135
  24. 106
  25. 20
  26. 28
  27. 110
  28. 20
  29. 33rd
  30. 176
  31. 1830
  32. 224
  33. 175
  34. 117
  35. 576
  36. 45
  37. 19
  38. 1540
  39. 18th
  40. 96

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