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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 316 · 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 6 terms of the AP 7, 13, 19, …? (a) 132 (b) 37 (c) 264 (d) 150
  2. 2.What is the missing term in the AP 16, ?, 28, 34, 40? (a) 28 (b) 23 (c) 22 (d) 21
  3. 3.Which term of the AP 18, 25, 32, 39, … is 235? (a) 33rd (b) 34th (c) 31st (d) 32nd
  4. 4.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 182 (b) 94 (c) 22 (d) 91
  5. 5.What is the 37th term of the AP 18, 21, 24, 27, …? (a) 129 (b) 108 (c) 126 (d) 111
  6. 6.What is the 34th term of the AP 16, 25, 34, 43, …? (a) 322 (b) 313 (c) 306 (d) 297
  7. 7.What is the sum of the first 10 terms of the AP 10, 13, 16, …? (a) 250 (b) 37 (c) 470 (d) 235
  8. 8.What is the missing term in the AP 19, ?, 29, 34, 39? (a) 23 (b) 24 (c) 25 (d) 29
  9. 9.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 217 (b) 46 (c) 392 (d) 196
  10. 10.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 484 (c) 506 (d) 43
  11. 11.What is the 14th term of the AP 12, 21, 30, 39, …? (a) 129 (b) 138 (c) 126 (d) 117
  12. 12.What is the 10th term of the AP 7, 13, 19, 25, …? (a) 67 (b) 60 (c) 61 (d) 54
  13. 13.What is the 39th term of the AP 17, 22, 27, 32, …? (a) 195 (b) 207 (c) 190 (d) 212
  14. 14.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 17 (b) 154 (c) 84 (d) 77
  15. 15.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 180 (b) 102 (c) 25 (d) 90
  16. 16.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 132 (d) 121
  17. 17.What is the 13th term of the AP 7, 14, 21, 28, …? (a) 98 (b) 92 (c) 84 (d) 91
  18. 18.What is the 18th term of the AP 10, 17, 24, 31, …? (a) 129 (b) 126 (c) 136 (d) 119
  19. 19.What is the 17th term of the AP 9, 18, 27, 36, …? (a) 162 (b) 153 (c) 144 (d) 154
  20. 20.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 43 (b) 506 (c) 275 (d) 253
  21. 21.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 4160 (c) 2080 (d) 2016
  22. 22.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 216 (b) 28 (c) 120 (d) 108
  23. 23.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 90 (b) 85 (c) 170 (d) 13
  24. 24.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 198 (b) 24 (c) 99 (d) 108
  25. 25.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 324 (b) 162 (c) 165 (d) 30
  26. 26.What is the 19th term of the AP 1, 3, 5, 7, …? (a) 36 (b) 39 (c) 38 (d) 37
  27. 27.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 112 (b) 14 (c) 63 (d) 56
  28. 28.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 300 (c) 650 (d) 325
  29. 29.What is the 18th term of the AP 8, 10, 12, 14, …? (a) 42 (b) 34 (c) 36 (d) 44
  30. 30.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 56 (c) 13 (d) 28
  31. 31.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 45 (d) 81
  32. 32.What is the 27th term of the AP 15, 19, 23, 27, …? (a) 108 (b) 119 (c) 104 (d) 123
  33. 33.What is the 12th term of the AP 12, 18, 24, 30, …? (a) 78 (b) 84 (c) 66 (d) 72
  34. 34.What is the 14th term of the AP 9, 15, 21, 27, …? (a) 78 (b) 84 (c) 93 (d) 87
  35. 35.What is the sum of the first 8 terms of the AP 5, 6, 7, …? (a) 12 (b) 72 (c) 136 (d) 68
  36. 36.What is the sum of all the whole numbers from 1 to 16? (a) 272 (b) 120 (c) 136 (d) 128
  37. 37.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 127 (b) 252 (c) 126 (d) 18
  38. 38.What is the sum of the first 11 terms of the AP 10, 14, 18, …? (a) 660 (b) 352 (c) 50 (d) 330
  39. 39.What is the 26th term of the AP 12, 20, 28, 36, …? (a) 212 (b) 200 (c) 208 (d) 220
  40. 40.What is the 12th term of the AP 1, 10, 19, 28, …? (a) 108 (b) 109 (c) 100 (d) 99

Answer key

  1. 132
  2. 22
  3. 32nd
  4. 91
  5. 126
  6. 313
  7. 235
  8. 24
  9. 196
  10. 484
  11. 129
  12. 61
  13. 207
  14. 77
  15. 90
  16. 121
  17. 91
  18. 129
  19. 153
  20. 253
  21. 2080
  22. 108
  23. 85
  24. 99
  25. 162
  26. 37
  27. 56
  28. 325
  29. 42
  30. 49
  31. 81
  32. 119
  33. 78
  34. 87
  35. 68
  36. 136
  37. 126
  38. 330
  39. 212
  40. 100

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