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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 62 · 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 40th term of the AP 18, 22, 26, 30, …? (a) 178 (b) 174 (c) 156 (d) 160
  2. 2.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 15 (b) 228 (c) 114 (d) 120
  3. 3.What is the 19th term of the AP 3, 12, 21, 30, …? (a) 171 (b) 162 (c) 174 (d) 165
  4. 4.What is the sum of the first 5 terms of the AP 9, 15, 21, …? (a) 105 (b) 120 (c) 33 (d) 210
  5. 5.What is the sum of the first 6 terms of the AP 9, 14, 19, …? (a) 144 (b) 34 (c) 129 (d) 258
  6. 6.What is the 39th term of the AP 18, 23, 28, 33, …? (a) 190 (b) 195 (c) 208 (d) 213
  7. 7.What is the 20th term of the AP 7, 11, 15, 19, …? (a) 80 (b) 76 (c) 83 (d) 87
  8. 8.What is the missing term in the AP 2, ?, 18, 26, 34? (a) 11 (b) 9 (c) 18 (d) 10
  9. 9.What is the 40th term of the AP 6, 8, 10, 12, …? (a) 84 (b) 78 (c) 80 (d) 86
  10. 10.What is the 18th term of the AP 2, 7, 12, 17, …? (a) 85 (b) 90 (c) 87 (d) 92
  11. 11.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 363 (b) 63 (c) 726 (d) 396
  12. 12.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 15 (d) 30
  13. 13.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 812 (c) 406 (d) 378
  14. 14.What is the 38th term of the AP 20, 29, 38, 47, …? (a) 333 (b) 362 (c) 353 (d) 342
  15. 15.What is the 14th term of the AP 7, 9, 11, 13, …? (a) 28 (b) 35 (c) 33 (d) 26
  16. 16.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 342 (c) 153 (d) 171
  17. 17.What is the 36th term of the AP 9, 11, 13, 15, …? (a) 72 (b) 79 (c) 81 (d) 70
  18. 18.What is the 25th term of the AP 18, 22, 26, 30, …? (a) 118 (b) 100 (c) 96 (d) 114
  19. 19.What is the sum of all the whole numbers from 1 to 75? (a) 2851 (b) 2775 (c) 5700 (d) 2850
  20. 20.Which term of the AP 4, 11, 18, 25, … is 81? (a) 14th (b) 11th (c) 13th (d) 12th
  21. 21.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 7 (b) 25 (c) 50 (d) 26
  22. 22.What is the 13th term of the AP 1, 9, 17, 25, …? (a) 97 (b) 96 (c) 105 (d) 104
  23. 23.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 210 (c) 91 (d) 105
  24. 24.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 380 (d) 361
  25. 25.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 9 (b) 8 (c) 10 (d) 7
  26. 26.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 45 (c) 552 (d) 276
  27. 27.What is the missing term in the AP 7, ?, 15, 19, 23? (a) 10 (b) 15 (c) 12 (d) 11
  28. 28.What is the 10th term of the AP 13, 22, 31, 40, …? (a) 94 (b) 81 (c) 103 (d) 90
  29. 29.What is the 15th term of the AP 10, 12, 14, 16, …? (a) 30 (b) 40 (c) 28 (d) 38
  30. 30.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 32 (b) 200 (c) 100 (d) 115
  31. 31.What is the 25th term of the AP 3, 9, 15, 21, …? (a) 147 (b) 153 (c) 150 (d) 144
  32. 32.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 580 (b) 56 (c) 320 (d) 290
  33. 33.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 780 (c) 781 (d) 1560
  34. 34.What is the sum of all the whole numbers from 1 to 11? (a) 67 (b) 132 (c) 55 (d) 66
  35. 35.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 72 (c) 156 (d) 78
  36. 36.What is the 11th term of the AP 3, 5, 7, 9, …? (a) 22 (b) 25 (c) 23 (d) 20
  37. 37.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 300 (c) 576 (d) 600
  38. 38.What is the missing term in the AP 5, ?, 17, 23, 29? (a) 11 (b) 12 (c) 10 (d) 17
  39. 39.What is the 22nd term of the AP 2, 7, 12, 17, …? (a) 112 (b) 105 (c) 110 (d) 107
  40. 40.Which term of the AP 6, 8, 10, 12, … is 20? (a) 8th (b) 10th (c) 7th (d) 9th

Answer key

  1. 174
  2. 114
  3. 165
  4. 105
  5. 129
  6. 208
  7. 83
  8. 10
  9. 84
  10. 87
  11. 363
  12. 25
  13. 406
  14. 353
  15. 33
  16. 171
  17. 79
  18. 114
  19. 2850
  20. 12th
  21. 25
  22. 97
  23. 105
  24. 361
  25. 8
  26. 529
  27. 11
  28. 94
  29. 38
  30. 100
  31. 147
  32. 290
  33. 780
  34. 66
  35. 78
  36. 23
  37. 576
  38. 11
  39. 107
  40. 8th

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