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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 173 · 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 17, ?, 25, 29, 33? (a) 22 (b) 25 (c) 20 (d) 21
  2. 2.What is the sum of the first 10 terms of the AP 9, 14, 19, …? (a) 630 (b) 315 (c) 340 (d) 54
  3. 3.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 238 (b) 133 (c) 29 (d) 119
  4. 4.What is the missing term in the AP 5, ?, 13, 17, 21? (a) 8 (b) 10 (c) 9 (d) 13
  5. 5.What is the 29th term of the AP 4, 6, 8, 10, …? (a) 58 (b) 56 (c) 60 (d) 62
  6. 6.What is the 30th term of the AP 19, 26, 33, 40, …? (a) 222 (b) 210 (c) 229 (d) 203
  7. 7.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 196 (b) 216 (c) 42 (d) 392
  8. 8.What is the 33rd term of the AP 18, 21, 24, 27, …? (a) 96 (b) 117 (c) 99 (d) 114
  9. 9.Which term of the AP 13, 21, 29, 37, … is 285? (a) 37th (b) 36th (c) 35th (d) 34th
  10. 10.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 210 (c) 91 (d) 105
  11. 11.What is the 21st term of the AP 7, 13, 19, 25, …? (a) 120 (b) 133 (c) 127 (d) 126
  12. 12.What is the 13th term of the AP 11, 20, 29, 38, …? (a) 108 (b) 117 (c) 119 (d) 128
  13. 13.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 225 (b) 36 (c) 450 (d) 240
  14. 14.Which term of the AP 2, 5, 8, 11, … is 65? (a) 24th (b) 23rd (c) 22nd (d) 21st
  15. 15.What is the sum of all the whole numbers from 1 to 17? (a) 154 (b) 153 (c) 136 (d) 306
  16. 16.What is the missing term in the AP 3, 10, 17, ?, 31? (a) 25 (b) 31 (c) 24 (d) 23
  17. 17.What is the 22nd term of the AP 15, 17, 19, 21, …? (a) 44 (b) 42 (c) 57 (d) 59
  18. 18.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 14 (b) 16 (c) 13 (d) 12
  19. 19.What is the 26th term of the AP 17, 21, 25, 29, …? (a) 104 (b) 100 (c) 121 (d) 117
  20. 20.What is the 34th term of the AP 9, 11, 13, 15, …? (a) 77 (b) 68 (c) 66 (d) 75
  21. 21.What is the 21st term of the AP 9, 16, 23, 30, …? (a) 147 (b) 156 (c) 149 (d) 140
  22. 22.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 15 (c) 25 (d) 30
  23. 23.What is the sum of the first 7 terms of the AP 6, 11, 16, …? (a) 36 (b) 147 (c) 294 (d) 152
  24. 24.What is the missing term in the AP 20, 28, ?, 44, 52? (a) 37 (b) 35 (c) 44 (d) 36
  25. 25.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 506 (c) 253 (d) 43
  26. 26.What is the 13th term of the AP 8, 15, 22, 29, …? (a) 92 (b) 91 (c) 99 (d) 84
  27. 27.What is the 28th term of the AP 18, 25, 32, 39, …? (a) 189 (b) 196 (c) 214 (d) 207
  28. 28.What is the sum of all the whole numbers from 1 to 46? (a) 2162 (b) 1058 (c) 1035 (d) 1081
  29. 29.What is the 40th term of the AP 16, 19, 22, 25, …? (a) 136 (b) 133 (c) 117 (d) 120
  30. 30.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 225 (c) 240 (d) 120
  31. 31.What is the 30th term of the AP 13, 21, 29, 37, …? (a) 232 (b) 245 (c) 253 (d) 240
  32. 32.What is the missing term in the AP 19, 28, 37, ?, 55? (a) 55 (b) 47 (c) 46 (d) 45
  33. 33.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 93 (b) 108 (c) 186 (d) 28
  34. 34.Which term of the AP 14, 16, 18, 20, … is 50? (a) 18th (b) 20th (c) 19th (d) 25th
  35. 35.What is the 29th term of the AP 14, 22, 30, 38, …? (a) 238 (b) 232 (c) 224 (d) 246
  36. 36.What is the 34th term of the AP 17, 23, 29, 35, …? (a) 215 (b) 198 (c) 204 (d) 221
  37. 37.What is the 28th term of the AP 14, 18, 22, 26, …? (a) 122 (b) 126 (c) 108 (d) 112
  38. 38.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 168 (b) 42 (c) 189 (d) 336
  39. 39.What is the 32nd term of the AP 16, 24, 32, 40, …? (a) 264 (b) 256 (c) 248 (d) 272
  40. 40.What is the missing term in the AP 8, 11, 14, ?, 20? (a) 16 (b) 17 (c) 20 (d) 18

Answer key

  1. 21
  2. 315
  3. 119
  4. 9
  5. 60
  6. 222
  7. 196
  8. 114
  9. 35th
  10. 105
  11. 127
  12. 119
  13. 225
  14. 22nd
  15. 153
  16. 24
  17. 57
  18. 13
  19. 117
  20. 75
  21. 149
  22. 25
  23. 147
  24. 36
  25. 484
  26. 92
  27. 207
  28. 1081
  29. 133
  30. 225
  31. 245
  32. 46
  33. 93
  34. 19th
  35. 238
  36. 215
  37. 122
  38. 168
  39. 264
  40. 17

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