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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 201 · 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 15th term of the AP 8, 13, 18, 23, …? (a) 75 (b) 70 (c) 78 (d) 83
  2. 2.What is the 23rd term of the AP 5, 12, 19, 26, …? (a) 159 (b) 154 (c) 166 (d) 161
  3. 3.What is the 37th term of the AP 18, 21, 24, 27, …? (a) 111 (b) 126 (c) 129 (d) 108
  4. 4.What is the missing term in the AP 16, 22, 28, ?, 40? (a) 35 (b) 34 (c) 33 (d) 40
  5. 5.Which term of the AP 12, 21, 30, 39, … is 138? (a) 15th (b) 16th (c) 14th (d) 17th
  6. 6.What is the sum of the first 9 terms of the AP 9, 12, 15, …? (a) 33 (b) 378 (c) 192 (d) 189
  7. 7.What is the 25th term of the AP 7, 12, 17, 22, …? (a) 120 (b) 132 (c) 127 (d) 125
  8. 8.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 650 (c) 49 (d) 325
  9. 9.What is the sum of the first 9 terms of the AP 8, 14, 20, …? (a) 576 (b) 288 (c) 315 (d) 56
  10. 10.What is the 29th term of the AP 9, 14, 19, 24, …? (a) 145 (b) 154 (c) 140 (d) 149
  11. 11.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 63 (b) 18 (c) 120 (d) 60
  12. 12.What is the 30th term of the AP 3, 5, 7, 9, …? (a) 60 (b) 58 (c) 63 (d) 61
  13. 13.What is the sum of all the whole numbers from 1 to 27? (a) 378 (b) 756 (c) 379 (d) 351
  14. 14.What is the 39th term of the AP 8, 11, 14, 17, …? (a) 122 (b) 114 (c) 117 (d) 125
  15. 15.What is the 38th term of the AP 10, 15, 20, 25, …? (a) 185 (b) 190 (c) 195 (d) 200
  16. 16.What is the missing term in the AP 3, 8, 13, ?, 23? (a) 17 (b) 23 (c) 19 (d) 18
  17. 17.What is the sum of the first 11 terms of the AP 7, 13, 19, …? (a) 67 (b) 814 (c) 407 (d) 440
  18. 18.What is the 32nd term of the AP 4, 10, 16, 22, …? (a) 186 (b) 190 (c) 196 (d) 192
  19. 19.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 91 (c) 25 (d) 182
  20. 20.What is the 30th term of the AP 16, 25, 34, 43, …? (a) 277 (b) 286 (c) 261 (d) 270
  21. 21.What is the 14th term of the AP 1, 9, 17, 25, …? (a) 112 (b) 104 (c) 105 (d) 113
  22. 22.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 36 (d) 11
  23. 23.What is the 19th term of the AP 2, 5, 8, 11, …? (a) 59 (b) 57 (c) 54 (d) 56
  24. 24.What is the missing term in the AP 2, 10, ?, 26, 34? (a) 19 (b) 18 (c) 17 (d) 26
  25. 25.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 31 (c) 136 (d) 256
  26. 26.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 8 (b) 33 (c) 36 (d) 66
  27. 27.What is the sum of the first 8 terms of the AP 4, 10, 16, …? (a) 224 (b) 400 (c) 200 (d) 46
  28. 28.What is the missing term in the AP 13, ?, 29, 37, 45? (a) 22 (b) 21 (c) 20 (d) 29
  29. 29.What is the 25th term of the AP 18, 27, 36, 45, …? (a) 234 (b) 216 (c) 243 (d) 225
  30. 30.What is the 23rd term of the AP 17, 23, 29, 35, …? (a) 155 (b) 132 (c) 149 (d) 138
  31. 31.What is the 35th term of the AP 18, 23, 28, 33, …? (a) 170 (b) 193 (c) 188 (d) 175
  32. 32.Which term of the AP 17, 20, 23, 26, … is 119? (a) 34th (b) 35th (c) 37th (d) 36th
  33. 33.What is the sum of the first 10 terms of the AP 5, 9, 13, …? (a) 460 (b) 41 (c) 250 (d) 230
  34. 34.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 38 (b) 256 (c) 253 (d) 506
  35. 35.What is the missing term in the AP 6, ?, 18, 24, 30? (a) 12 (b) 18 (c) 13 (d) 11
  36. 36.What is the missing term in the AP 3, 9, 15, ?, 27? (a) 22 (b) 20 (c) 21 (d) 27
  37. 37.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 1431 (c) 2862 (d) 1432
  38. 38.What is the missing term in the AP 9, 15, 21, ?, 33? (a) 33 (b) 28 (c) 27 (d) 26
  39. 39.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 240 (d) 225
  40. 40.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 216 (b) 109 (c) 108 (d) 16

Answer key

  1. 78
  2. 159
  3. 126
  4. 34
  5. 15th
  6. 189
  7. 127
  8. 625
  9. 288
  10. 149
  11. 60
  12. 61
  13. 378
  14. 122
  15. 195
  16. 18
  17. 407
  18. 190
  19. 169
  20. 277
  21. 105
  22. 36
  23. 56
  24. 18
  25. 256
  26. 33
  27. 200
  28. 21
  29. 234
  30. 149
  31. 188
  32. 35th
  33. 230
  34. 253
  35. 12
  36. 21
  37. 1431
  38. 27
  39. 225
  40. 108

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