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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 405 · 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 all the whole numbers from 1 to 56? (a) 1568 (b) 1540 (c) 1596 (d) 3192
  2. 2.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 28 (c) 13 (d) 49
  3. 3.What is the sum of the first 12 terms of the AP 3, 5, 7, …? (a) 25 (b) 168 (c) 180 (d) 336
  4. 4.What is the missing term in the AP 1, 7, ?, 19, 25? (a) 19 (b) 14 (c) 13 (d) 12
  5. 5.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 50 (b) 12 (c) 51 (d) 100
  6. 6.What is the 14th term of the AP 2, 4, 6, 8, …? (a) 26 (b) 29 (c) 30 (d) 28
  7. 7.What is the 32nd term of the AP 13, 16, 19, 22, …? (a) 93 (b) 109 (c) 96 (d) 106
  8. 8.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 435 (c) 930 (d) 465
  9. 9.What is the 18th term of the AP 6, 12, 18, 24, …? (a) 109 (b) 114 (c) 102 (d) 108
  10. 10.What is the 21st term of the AP 10, 14, 18, 22, …? (a) 84 (b) 94 (c) 80 (d) 90
  11. 11.What is the 34th term of the AP 13, 21, 29, 37, …? (a) 264 (b) 277 (c) 272 (d) 285
  12. 12.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 55 (c) 19 (d) 100
  13. 13.What is the 17th term of the AP 1, 9, 17, 25, …? (a) 128 (b) 136 (c) 129 (d) 137
  14. 14.What is the 37th term of the AP 15, 19, 23, 27, …? (a) 144 (b) 163 (c) 148 (d) 159
  15. 15.What is the 16th term of the AP 17, 23, 29, 35, …? (a) 96 (b) 90 (c) 107 (d) 113
  16. 16.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 153 (c) 154 (d) 136
  17. 17.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 12 (b) 72 (c) 73 (d) 144
  18. 18.What is the missing term in the AP 12, 14, 16, ?, 20? (a) 20 (b) 18 (c) 17 (d) 19
  19. 19.What is the sum of all the whole numbers from 1 to 45? (a) 1035 (b) 990 (c) 1036 (d) 2070
  20. 20.Which term of the AP 19, 21, 23, 25, … is 59? (a) 23rd (b) 22nd (c) 21st (d) 20th
  21. 21.What is the 11th term of the AP 7, 14, 21, 28, …? (a) 77 (b) 84 (c) 78 (d) 70
  22. 22.What is the 14th term of the AP 2, 5, 8, 11, …? (a) 44 (b) 42 (c) 41 (d) 39
  23. 23.What is the sum of all the whole numbers from 1 to 14? (a) 210 (b) 98 (c) 105 (d) 91
  24. 24.What is the missing term in the AP 9, 18, 27, ?, 45? (a) 45 (b) 36 (c) 35 (d) 37
  25. 25.What is the sum of the first 12 terms of the AP 6, 11, 16, …? (a) 61 (b) 402 (c) 432 (d) 804
  26. 26.What is the 40th term of the AP 1, 6, 11, 16, …? (a) 196 (b) 201 (c) 200 (d) 195
  27. 27.What is the missing term in the AP 5, 12, ?, 26, 33? (a) 20 (b) 26 (c) 18 (d) 19
  28. 28.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 27 (c) 105 (d) 210
  29. 29.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 40 (b) 36 (c) 72 (d) 8
  30. 30.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 96 (b) 13 (c) 54 (d) 48
  31. 31.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 31 (c) 136 (d) 256
  32. 32.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 41 (b) 312 (c) 294 (d) 588
  33. 33.What is the 11th term of the AP 14, 23, 32, 41, …? (a) 99 (b) 90 (c) 113 (d) 104
  34. 34.What is the 29th term of the AP 16, 21, 26, 31, …? (a) 161 (b) 156 (c) 145 (d) 140
  35. 35.Which term of the AP 17, 23, 29, 35, … is 179? (a) 27th (b) 30th (c) 29th (d) 28th
  36. 36.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 45 (c) 17 (d) 90
  37. 37.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 39 (b) 168 (c) 294 (d) 147
  38. 38.Which term of the AP 7, 14, 21, 28, … is 84? (a) 13th (b) 11th (c) 12th (d) 14th
  39. 39.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 456 (b) 840 (c) 68 (d) 420
  40. 40.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 144 (b) 72 (c) 22 (d) 84

Answer key

  1. 1596
  2. 49
  3. 168
  4. 13
  5. 50
  6. 28
  7. 106
  8. 465
  9. 108
  10. 90
  11. 277
  12. 100
  13. 129
  14. 159
  15. 107
  16. 153
  17. 72
  18. 18
  19. 1035
  20. 21st
  21. 77
  22. 41
  23. 105
  24. 36
  25. 402
  26. 196
  27. 19
  28. 196
  29. 36
  30. 48
  31. 256
  32. 294
  33. 104
  34. 156
  35. 28th
  36. 81
  37. 147
  38. 12th
  39. 420
  40. 72

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