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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 594 · 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 32nd term of the AP 12, 17, 22, 27, …? (a) 172 (b) 155 (c) 167 (d) 160
  2. 2.Which term of the AP 4, 8, 12, 16, … is 80? (a) 20th (b) 22nd (c) 21st (d) 19th
  3. 3.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 30 (b) 165 (c) 162 (d) 324
  4. 4.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 562 (c) 528 (d) 561
  5. 5.What is the 35th term of the AP 20, 26, 32, 38, …? (a) 224 (b) 230 (c) 210 (d) 204
  6. 6.Which term of the AP 4, 7, 10, 13, … is 61? (a) 19th (b) 22nd (c) 21st (d) 20th
  7. 7.What is the sum of all the whole numbers from 1 to 11? (a) 55 (b) 67 (c) 132 (d) 66
  8. 8.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 25 (c) 9 (d) 30
  9. 9.What is the sum of the first 11 terms of the AP 1, 7, 13, …? (a) 374 (b) 682 (c) 341 (d) 61
  10. 10.What is the 40th term of the AP 18, 24, 30, 36, …? (a) 258 (b) 234 (c) 240 (d) 252
  11. 11.What is the 23rd term of the AP 1, 7, 13, 19, …? (a) 138 (b) 139 (c) 133 (d) 132
  12. 12.What is the 10th term of the AP 2, 6, 10, 14, …? (a) 36 (b) 42 (c) 40 (d) 38
  13. 13.What is the sum of all the whole numbers from 1 to 90? (a) 4050 (b) 8190 (c) 4005 (d) 4095
  14. 14.Which term of the AP 12, 15, 18, 21, … is 129? (a) 40th (b) 41st (c) 43rd (d) 39th
  15. 15.What is the sum of the first 9 terms of the AP 1, 4, 7, …? (a) 120 (b) 25 (c) 117 (d) 234
  16. 16.What is the 22nd term of the AP 11, 18, 25, 32, …? (a) 147 (b) 165 (c) 154 (d) 158
  17. 17.What is the 24th term of the AP 10, 17, 24, 31, …? (a) 161 (b) 178 (c) 168 (d) 171
  18. 18.Which term of the AP 16, 24, 32, 40, … is 288? (a) 35th (b) 36th (c) 34th (d) 37th
  19. 19.Which term of the AP 14, 21, 28, 35, … is 84? (a) 11th (b) 12th (c) 13th (d) 10th
  20. 20.What is the 12th term of the AP 5, 13, 21, 29, …? (a) 93 (b) 96 (c) 88 (d) 101
  21. 21.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 144 (d) 23
  22. 22.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 196 (b) 46 (c) 217 (d) 392
  23. 23.What is the 34th term of the AP 7, 12, 17, 22, …? (a) 165 (b) 170 (c) 172 (d) 177
  24. 24.What is the 38th term of the AP 4, 11, 18, 25, …? (a) 263 (b) 266 (c) 259 (d) 270
  25. 25.What is the missing term in the AP 4, 10, ?, 22, 28? (a) 17 (b) 22 (c) 16 (d) 15
  26. 26.What is the 12th term of the AP 13, 20, 27, 34, …? (a) 77 (b) 97 (c) 90 (d) 84
  27. 27.What is the 38th term of the AP 5, 12, 19, 26, …? (a) 271 (b) 264 (c) 259 (d) 266
  28. 28.Which term of the AP 9, 14, 19, 24, … is 204? (a) 41st (b) 42nd (c) 40th (d) 39th
  29. 29.What is the missing term in the AP 19, ?, 27, 31, 35? (a) 24 (b) 27 (c) 23 (d) 22
  30. 30.What is the missing term in the AP 13, ?, 21, 25, 29? (a) 16 (b) 17 (c) 21 (d) 18
  31. 31.What is the missing term in the AP 16, ?, 30, 37, 44? (a) 30 (b) 23 (c) 24 (d) 22
  32. 32.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 26 (b) 196 (c) 98 (d) 112
  33. 33.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 325 (c) 650 (d) 49
  34. 34.What is the 10th term of the AP 4, 7, 10, 13, …? (a) 31 (b) 30 (c) 34 (d) 27
  35. 35.What is the 13th term of the AP 10, 13, 16, 19, …? (a) 36 (b) 39 (c) 46 (d) 49
  36. 36.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 63 (b) 70 (c) 15 (d) 126
  37. 37.What is the 20th term of the AP 20, 23, 26, 29, …? (a) 57 (b) 60 (c) 77 (d) 80
  38. 38.What is the 39th term of the AP 8, 17, 26, 35, …? (a) 351 (b) 342 (c) 350 (d) 359
  39. 39.What is the missing term in the AP 11, ?, 17, 20, 23? (a) 13 (b) 17 (c) 14 (d) 15
  40. 40.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 49 (d) 28

Answer key

  1. 167
  2. 20th
  3. 162
  4. 561
  5. 224
  6. 20th
  7. 66
  8. 25
  9. 341
  10. 252
  11. 133
  12. 38
  13. 4095
  14. 40th
  15. 117
  16. 158
  17. 171
  18. 35th
  19. 11th
  20. 93
  21. 144
  22. 196
  23. 172
  24. 263
  25. 16
  26. 90
  27. 264
  28. 40th
  29. 23
  30. 17
  31. 23
  32. 98
  33. 625
  34. 31
  35. 46
  36. 63
  37. 77
  38. 350
  39. 14
  40. 49

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