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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 713 · 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 11? (a) 55 (b) 67 (c) 66 (d) 132
  2. 2.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 324 (d) 342
  3. 3.What is the 26th term of the AP 12, 18, 24, 30, …? (a) 156 (b) 168 (c) 150 (d) 162
  4. 4.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 11 (d) 36
  5. 5.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 55 (c) 812 (d) 406
  6. 6.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 126 (b) 131 (c) 252 (d) 33
  7. 7.What is the 20th term of the AP 1, 9, 17, 25, …? (a) 152 (b) 160 (c) 161 (d) 153
  8. 8.What is the missing term in the AP 5, 9, ?, 17, 21? (a) 13 (b) 12 (c) 14 (d) 17
  9. 9.What is the 30th term of the AP 2, 8, 14, 20, …? (a) 182 (b) 174 (c) 180 (d) 176
  10. 10.What is the 22nd term of the AP 6, 10, 14, 18, …? (a) 88 (b) 90 (c) 84 (d) 94
  11. 11.What is the 27th term of the AP 6, 14, 22, 30, …? (a) 222 (b) 216 (c) 214 (d) 208
  12. 12.What is the missing term in the AP 4, ?, 14, 19, 24? (a) 9 (b) 8 (c) 14 (d) 10
  13. 13.What is the 22nd term of the AP 8, 12, 16, 20, …? (a) 96 (b) 92 (c) 84 (d) 88
  14. 14.What is the 38th term of the AP 4, 9, 14, 19, …? (a) 185 (b) 190 (c) 194 (d) 189
  15. 15.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 228 (b) 15 (c) 120 (d) 114
  16. 16.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 31 (b) 480 (c) 252 (d) 240
  17. 17.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 26 (b) 324 (c) 171 (d) 162
  18. 18.What is the 35th term of the AP 14, 19, 24, 29, …? (a) 175 (b) 170 (c) 189 (d) 184
  19. 19.What is the sum of all the whole numbers from 1 to 30? (a) 435 (b) 465 (c) 930 (d) 450
  20. 20.What is the 15th term of the AP 11, 16, 21, 26, …? (a) 81 (b) 75 (c) 86 (d) 70
  21. 21.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 484 (c) 506 (d) 253
  22. 22.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 65 (b) 120 (c) 22 (d) 60
  23. 23.What is the 15th term of the AP 2, 9, 16, 23, …? (a) 98 (b) 105 (c) 107 (d) 100
  24. 24.What is the missing term in the AP 6, 13, ?, 27, 34? (a) 21 (b) 19 (c) 20 (d) 27
  25. 25.Which term of the AP 5, 11, 17, 23, … is 155? (a) 27th (b) 25th (c) 28th (d) 26th
  26. 26.What is the 13th term of the AP 17, 23, 29, 35, …? (a) 78 (b) 95 (c) 89 (d) 72
  27. 27.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 726 (b) 396 (c) 363 (d) 63
  28. 28.What is the 14th term of the AP 12, 15, 18, 21, …? (a) 54 (b) 39 (c) 51 (d) 42
  29. 29.Which term of the AP 20, 26, 32, 38, … is 110? (a) 15th (b) 17th (c) 18th (d) 16th
  30. 30.What is the 21st term of the AP 4, 6, 8, 10, …? (a) 42 (b) 40 (c) 46 (d) 44
  31. 31.What is the missing term in the AP 2, 9, 16, ?, 30? (a) 24 (b) 30 (c) 23 (d) 22
  32. 32.What is the 32nd term of the AP 5, 14, 23, 32, …? (a) 284 (b) 293 (c) 279 (d) 288
  33. 33.What is the sum of the first 7 terms of the AP 6, 11, 16, …? (a) 147 (b) 152 (c) 294 (d) 36
  34. 34.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 55 (c) 19 (d) 110
  35. 35.What is the missing term in the AP 9, 11, ?, 15, 17? (a) 13 (b) 15 (c) 12 (d) 14
  36. 36.What is the 25th term of the AP 19, 24, 29, 34, …? (a) 125 (b) 144 (c) 139 (d) 120
  37. 37.What is the 13th term of the AP 12, 18, 24, 30, …? (a) 90 (b) 78 (c) 84 (d) 72
  38. 38.What is the 14th term of the AP 6, 12, 18, 24, …? (a) 85 (b) 90 (c) 84 (d) 78
  39. 39.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 15 (b) 78 (c) 150 (d) 75
  40. 40.What is the 36th term of the AP 12, 17, 22, 27, …? (a) 180 (b) 187 (c) 175 (d) 192

Answer key

  1. 66
  2. 324
  3. 162
  4. 36
  5. 784
  6. 126
  7. 153
  8. 13
  9. 176
  10. 90
  11. 214
  12. 9
  13. 92
  14. 189
  15. 114
  16. 240
  17. 162
  18. 184
  19. 465
  20. 81
  21. 484
  22. 60
  23. 100
  24. 20
  25. 26th
  26. 89
  27. 363
  28. 51
  29. 16th
  30. 44
  31. 23
  32. 284
  33. 147
  34. 100
  35. 13
  36. 139
  37. 84
  38. 84
  39. 75
  40. 187

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