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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 877 · 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 14th term of the AP 11, 20, 29, 38, …? (a) 126 (b) 117 (c) 137 (d) 128
  2. 2.Which term of the AP 13, 20, 27, 34, … is 153? (a) 21st (b) 22nd (c) 23rd (d) 20th
  3. 3.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 100 (b) 95 (c) 190 (d) 29
  4. 4.What is the 13th term of the AP 17, 26, 35, 44, …? (a) 125 (b) 108 (c) 134 (d) 117
  5. 5.What is the missing term in the AP 17, 24, 31, ?, 45? (a) 39 (b) 45 (c) 37 (d) 38
  6. 6.What is the missing term in the AP 1, ?, 13, 19, 25? (a) 8 (b) 7 (c) 6 (d) 13
  7. 7.What is the 17th term of the AP 19, 25, 31, 37, …? (a) 115 (b) 96 (c) 121 (d) 102
  8. 8.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 231 (c) 441 (d) 41
  9. 9.What is the 20th term of the AP 13, 15, 17, 19, …? (a) 51 (b) 40 (c) 38 (d) 53
  10. 10.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 506 (c) 253 (d) 231
  11. 11.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 169 (c) 25 (d) 182
  12. 12.What is the missing term in the AP 8, 16, 24, ?, 40? (a) 31 (b) 32 (c) 40 (d) 33
  13. 13.What is the missing term in the AP 3, 11, ?, 27, 35? (a) 20 (b) 19 (c) 18 (d) 27
  14. 14.What is the 26th term of the AP 7, 16, 25, 34, …? (a) 225 (b) 232 (c) 241 (d) 234
  15. 15.What is the 18th term of the AP 15, 17, 19, 21, …? (a) 49 (b) 36 (c) 34 (d) 51
  16. 16.What is the sum of all the whole numbers from 1 to 82? (a) 3362 (b) 3321 (c) 6806 (d) 3403
  17. 17.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 25 (b) 224 (c) 115 (d) 112
  18. 18.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 51 (b) 54 (c) 11 (d) 102
  19. 19.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 126 (b) 31 (c) 111 (d) 222
  20. 20.What is the 34th term of the AP 14, 20, 26, 32, …? (a) 204 (b) 198 (c) 212 (d) 218
  21. 21.What is the 23rd term of the AP 6, 11, 16, 21, …? (a) 116 (b) 115 (c) 110 (d) 121
  22. 22.What is the 38th term of the AP 19, 26, 33, 40, …? (a) 259 (b) 278 (c) 285 (d) 266
  23. 23.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 180 (b) 360 (c) 32 (d) 183
  24. 24.What is the 32nd term of the AP 8, 17, 26, 35, …? (a) 287 (b) 288 (c) 279 (d) 296
  25. 25.What is the 40th term of the AP 6, 15, 24, 33, …? (a) 366 (b) 357 (c) 360 (d) 351
  26. 26.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 380 (b) 62 (c) 700 (d) 350
  27. 27.Which term of the AP 18, 27, 36, 45, … is 126? (a) 14th (b) 12th (c) 13th (d) 15th
  28. 28.What is the 25th term of the AP 18, 20, 22, 24, …? (a) 66 (b) 48 (c) 50 (d) 68
  29. 29.What is the 29th term of the AP 12, 20, 28, 36, …? (a) 236 (b) 232 (c) 244 (d) 224
  30. 30.Which term of the AP 6, 15, 24, 33, … is 276? (a) 31st (b) 33rd (c) 32nd (d) 30th
  31. 31.What is the 27th term of the AP 8, 12, 16, 20, …? (a) 116 (b) 104 (c) 112 (d) 108
  32. 32.What is the 36th term of the AP 3, 6, 9, 12, …? (a) 111 (b) 105 (c) 109 (d) 108
  33. 33.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 96 (b) 114 (c) 192 (d) 31
  34. 34.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100
  35. 35.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 180 (b) 27 (c) 360 (d) 190
  36. 36.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 37 (c) 380 (d) 190
  37. 37.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 306 (c) 33 (d) 153
  38. 38.What is the 11th term of the AP 20, 27, 34, 41, …? (a) 97 (b) 70 (c) 77 (d) 90
  39. 39.Which term of the AP 19, 25, 31, 37, … is 79? (a) 13th (b) 10th (c) 11th (d) 12th
  40. 40.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 35 (b) 189 (c) 342 (d) 171

Answer key

  1. 128
  2. 21st
  3. 95
  4. 125
  5. 38
  6. 7
  7. 115
  8. 441
  9. 51
  10. 253
  11. 169
  12. 32
  13. 19
  14. 232
  15. 49
  16. 3403
  17. 112
  18. 51
  19. 111
  20. 212
  21. 116
  22. 278
  23. 180
  24. 287
  25. 357
  26. 350
  27. 13th
  28. 66
  29. 236
  30. 31st
  31. 112
  32. 108
  33. 96
  34. 100
  35. 180
  36. 361
  37. 289
  38. 90
  39. 11th
  40. 171

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