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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 371 · 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 missing term in the AP 3, 5, ?, 9, 11? (a) 8 (b) 9 (c) 6 (d) 7
  2. 2.What is the sum of the first 7 terms of the AP 5, 10, 15, …? (a) 35 (b) 280 (c) 145 (d) 140
  3. 3.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 34 (b) 201 (c) 198 (d) 396
  4. 4.What is the 28th term of the AP 3, 6, 9, 12, …? (a) 81 (b) 85 (c) 84 (d) 87
  5. 5.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 92 (b) 182 (c) 91 (d) 16
  6. 6.What is the 20th term of the AP 11, 17, 23, 29, …? (a) 114 (b) 125 (c) 131 (d) 120
  7. 7.What is the missing term in the AP 8, 12, 16, ?, 24? (a) 21 (b) 19 (c) 24 (d) 20
  8. 8.What is the 18th term of the AP 18, 23, 28, 33, …? (a) 90 (b) 85 (c) 108 (d) 103
  9. 9.What is the 38th term of the AP 6, 11, 16, 21, …? (a) 196 (b) 185 (c) 190 (d) 191
  10. 10.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 7 (b) 5 (c) 6 (d) 4
  11. 11.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 28 (b) 266 (c) 136 (d) 133
  12. 12.What is the missing term in the AP 3, 5, 7, ?, 11? (a) 8 (b) 9 (c) 11 (d) 10
  13. 13.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 121 (c) 240 (d) 120
  14. 14.What is the missing term in the AP 10, ?, 24, 31, 38? (a) 17 (b) 18 (c) 16 (d) 24
  15. 15.What is the sum of the first 11 terms of the AP 4, 8, 12, …? (a) 528 (b) 44 (c) 264 (d) 286
  16. 16.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 4186 (c) 4095 (d) 8372
  17. 17.What is the 31st term of the AP 13, 18, 23, 28, …? (a) 168 (b) 150 (c) 163 (d) 155
  18. 18.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 120 (b) 18 (c) 60 (d) 63
  19. 19.What is the sum of all the whole numbers from 1 to 69? (a) 2346 (b) 2415 (c) 4830 (d) 2416
  20. 20.What is the 23rd term of the AP 15, 21, 27, 33, …? (a) 132 (b) 153 (c) 138 (d) 147
  21. 21.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 220 (b) 110 (c) 15 (d) 111
  22. 22.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 122 (b) 16 (c) 121 (d) 242
  23. 23.What is the missing term in the AP 1, 8, ?, 22, 29? (a) 14 (b) 22 (c) 16 (d) 15
  24. 24.What is the sum of all the whole numbers from 1 to 49? (a) 1226 (b) 2450 (c) 1176 (d) 1225
  25. 25.What is the sum of the first 9 terms of the AP 7, 12, 17, …? (a) 486 (b) 243 (c) 47 (d) 248
  26. 26.What is the 33rd term of the AP 1, 7, 13, 19, …? (a) 192 (b) 199 (c) 198 (d) 193
  27. 27.What is the 28th term of the AP 17, 19, 21, 23, …? (a) 73 (b) 71 (c) 56 (d) 54
  28. 28.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 25 (d) 30
  29. 29.What is the 12th term of the AP 13, 17, 21, 25, …? (a) 44 (b) 61 (c) 48 (d) 57
  30. 30.What is the 23rd term of the AP 4, 12, 20, 28, …? (a) 180 (b) 184 (c) 176 (d) 188
  31. 31.What is the missing term in the AP 12, 18, 24, ?, 36? (a) 29 (b) 31 (c) 36 (d) 30
  32. 32.What is the missing term in the AP 9, 12, 15, ?, 21? (a) 21 (b) 17 (c) 18 (d) 19
  33. 33.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 150 (b) 78 (c) 15 (d) 75
  34. 34.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 144 (b) 18 (c) 286 (d) 143
  35. 35.What is the 13th term of the AP 3, 9, 15, 21, …? (a) 78 (b) 75 (c) 72 (d) 81
  36. 36.What is the 39th term of the AP 19, 24, 29, 34, …? (a) 214 (b) 190 (c) 209 (d) 195
  37. 37.What is the 22nd term of the AP 5, 14, 23, 32, …? (a) 194 (b) 189 (c) 198 (d) 203
  38. 38.What is the 36th term of the AP 15, 24, 33, 42, …? (a) 315 (b) 330 (c) 324 (d) 339
  39. 39.What is the 18th term of the AP 5, 14, 23, 32, …? (a) 167 (b) 158 (c) 162 (d) 153
  40. 40.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 756 (d) 729

Answer key

  1. 7
  2. 140
  3. 198
  4. 84
  5. 91
  6. 125
  7. 20
  8. 103
  9. 191
  10. 5
  11. 133
  12. 9
  13. 120
  14. 17
  15. 264
  16. 4186
  17. 163
  18. 60
  19. 2415
  20. 147
  21. 110
  22. 121
  23. 15
  24. 1225
  25. 243
  26. 193
  27. 71
  28. 25
  29. 57
  30. 180
  31. 30
  32. 18
  33. 75
  34. 143
  35. 75
  36. 209
  37. 194
  38. 330
  39. 158
  40. 729

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