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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 673 · 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 21st term of the AP 10, 18, 26, 34, …? (a) 178 (b) 160 (c) 168 (d) 170
  2. 2.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 2 (b) 4 (c) 5 (d) 3
  3. 3.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 28 (c) 49 (d) 56
  4. 4.What is the 27th term of the AP 4, 6, 8, 10, …? (a) 52 (b) 58 (c) 56 (d) 54
  5. 5.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 230 (b) 35 (c) 215 (d) 430
  6. 6.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 84 (b) 72 (c) 144 (d) 22
  7. 7.What is the 26th term of the AP 1, 8, 15, 22, …? (a) 175 (b) 183 (c) 176 (d) 182
  8. 8.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 69 (b) 429 (c) 462 (d) 858
  9. 9.What is the 14th term of the AP 13, 19, 25, 31, …? (a) 84 (b) 91 (c) 78 (d) 97
  10. 10.What is the 12th term of the AP 8, 17, 26, 35, …? (a) 99 (b) 116 (c) 107 (d) 108
  11. 11.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 100 (b) 51 (c) 12 (d) 50
  12. 12.What is the missing term in the AP 7, 16, 25, ?, 43? (a) 33 (b) 43 (c) 34 (d) 35
  13. 13.What is the 10th term of the AP 20, 25, 30, 35, …? (a) 50 (b) 45 (c) 65 (d) 70
  14. 14.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 1122 (c) 562 (d) 528
  15. 15.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 66 (b) 429 (c) 792 (d) 396
  16. 16.What is the 38th term of the AP 19, 22, 25, 28, …? (a) 133 (b) 130 (c) 114 (d) 111
  17. 17.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 112 (b) 57 (c) 56 (d) 11
  18. 18.What is the 16th term of the AP 8, 13, 18, 23, …? (a) 75 (b) 80 (c) 83 (d) 88
  19. 19.What is the 14th term of the AP 19, 21, 23, 25, …? (a) 28 (b) 47 (c) 45 (d) 26
  20. 20.What is the 40th term of the AP 8, 13, 18, 23, …? (a) 208 (b) 200 (c) 203 (d) 195
  21. 21.What is the 15th term of the AP 5, 13, 21, 29, …? (a) 112 (b) 125 (c) 120 (d) 117
  22. 22.Which term of the AP 5, 10, 15, 20, … is 190? (a) 39th (b) 38th (c) 37th (d) 40th
  23. 23.What is the missing term in the AP 11, 20, 29, ?, 47? (a) 38 (b) 39 (c) 47 (d) 37
  24. 24.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 100 (c) 55 (d) 110
  25. 25.What is the missing term in the AP 12, 15, 18, ?, 24? (a) 20 (b) 21 (c) 24 (d) 22
  26. 26.What is the sum of the first 12 terms of the AP 10, 13, 16, …? (a) 43 (b) 318 (c) 636 (d) 336
  27. 27.What is the missing term in the AP 9, 17, 25, ?, 41? (a) 32 (b) 33 (c) 41 (d) 34
  28. 28.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 350 (b) 31 (c) 190 (d) 175
  29. 29.What is the missing term in the AP 20, 25, ?, 35, 40? (a) 31 (b) 30 (c) 35 (d) 29
  30. 30.What is the sum of all the whole numbers from 1 to 94? (a) 4418 (b) 4371 (c) 8930 (d) 4465
  31. 31.What is the sum of all the whole numbers from 1 to 27? (a) 378 (b) 379 (c) 756 (d) 351
  32. 32.What is the 20th term of the AP 15, 20, 25, 30, …? (a) 100 (b) 115 (c) 110 (d) 95
  33. 33.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 35 (b) 240 (c) 120 (d) 138
  34. 34.What is the sum of the first 9 terms of the AP 5, 10, 15, …? (a) 230 (b) 225 (c) 450 (d) 45
  35. 35.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 10 (b) 35 (c) 60 (d) 30
  36. 36.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 36 (b) 252 (c) 126 (d) 144
  37. 37.Which term of the AP 1, 8, 15, 22, … is 99? (a) 16th (b) 17th (c) 14th (d) 15th
  38. 38.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 190 (b) 27 (c) 360 (d) 180
  39. 39.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 105 (b) 210 (c) 119 (d) 27
  40. 40.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 41 (c) 462 (d) 441

Answer key

  1. 170
  2. 3
  3. 49
  4. 56
  5. 215
  6. 72
  7. 176
  8. 429
  9. 91
  10. 107
  11. 50
  12. 34
  13. 65
  14. 561
  15. 396
  16. 130
  17. 56
  18. 83
  19. 45
  20. 203
  21. 117
  22. 38th
  23. 38
  24. 100
  25. 21
  26. 318
  27. 33
  28. 175
  29. 30
  30. 4465
  31. 378
  32. 110
  33. 120
  34. 225
  35. 30
  36. 126
  37. 15th
  38. 180
  39. 105
  40. 441

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