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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 128 · 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 sum of the first 11 terms of the AP 1, 4, 7, …? (a) 31 (b) 179 (c) 352 (d) 176
  2. 2.What is the missing term in the AP 20, 22, 24, ?, 28? (a) 27 (b) 25 (c) 28 (d) 26
  3. 3.What is the sum of the first 8 terms of the AP 6, 9, 12, …? (a) 144 (b) 264 (c) 27 (d) 132
  4. 4.What is the 24th term of the AP 4, 11, 18, 25, …? (a) 165 (b) 172 (c) 161 (d) 168
  5. 5.What is the missing term in the AP 17, ?, 27, 32, 37? (a) 22 (b) 23 (c) 27 (d) 21
  6. 6.What is the sum of all the whole numbers from 1 to 89? (a) 4005 (b) 4006 (c) 3916 (d) 8010
  7. 7.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 75 (b) 12 (c) 150 (d) 80
  8. 8.What is the 37th term of the AP 17, 24, 31, 38, …? (a) 269 (b) 259 (c) 252 (d) 276
  9. 9.What is the 32nd term of the AP 20, 24, 28, 32, …? (a) 128 (b) 148 (c) 144 (d) 124
  10. 10.What is the sum of the first 10 terms of the AP 5, 7, 9, …? (a) 150 (b) 140 (c) 280 (d) 23
  11. 11.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 294 (b) 312 (c) 588 (d) 41
  12. 12.What is the 31st term of the AP 2, 4, 6, 8, …? (a) 62 (b) 64 (c) 63 (d) 60
  13. 13.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 740 (b) 64 (c) 400 (d) 370
  14. 14.Which term of the AP 17, 20, 23, 26, … is 119? (a) 37th (b) 36th (c) 34th (d) 35th
  15. 15.What is the missing term in the AP 16, ?, 30, 37, 44? (a) 30 (b) 22 (c) 24 (d) 23
  16. 16.What is the 15th term of the AP 15, 17, 19, 21, …? (a) 45 (b) 28 (c) 43 (d) 30
  17. 17.What is the 19th term of the AP 3, 6, 9, 12, …? (a) 60 (b) 58 (c) 54 (d) 57
  18. 18.What is the 10th term of the AP 1, 8, 15, 22, …? (a) 64 (b) 71 (c) 70 (d) 63
  19. 19.What is the 31st term of the AP 12, 20, 28, 36, …? (a) 240 (b) 260 (c) 248 (d) 252
  20. 20.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 484 (c) 43 (d) 506
  21. 21.What is the missing term in the AP 19, 26, ?, 40, 47? (a) 33 (b) 40 (c) 34 (d) 32
  22. 22.What is the 37th term of the AP 2, 10, 18, 26, …? (a) 298 (b) 290 (c) 296 (d) 288
  23. 23.What is the 40th term of the AP 12, 20, 28, 36, …? (a) 312 (b) 320 (c) 332 (d) 324
  24. 24.What is the 39th term of the AP 9, 12, 15, 18, …? (a) 126 (b) 123 (c) 117 (d) 114
  25. 25.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 41 (c) 462 (d) 231
  26. 26.What is the 30th term of the AP 18, 22, 26, 30, …? (a) 120 (b) 134 (c) 116 (d) 138
  27. 27.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 45 (c) 17 (d) 81
  28. 28.Which term of the AP 20, 27, 34, 41, … is 83? (a) 9th (b) 12th (c) 10th (d) 11th
  29. 29.What is the 33rd term of the AP 15, 23, 31, 39, …? (a) 256 (b) 279 (c) 271 (d) 264
  30. 30.What is the 25th term of the AP 13, 20, 27, 34, …? (a) 181 (b) 188 (c) 175 (d) 168
  31. 31.What is the 35th term of the AP 17, 25, 33, 41, …? (a) 297 (b) 272 (c) 280 (d) 289
  32. 32.Which term of the AP 14, 17, 20, 23, … is 35? (a) 10th (b) 8th (c) 9th (d) 7th
  33. 33.What is the 38th term of the AP 18, 25, 32, 39, …? (a) 259 (b) 266 (c) 284 (d) 277
  34. 34.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 4851 (c) 9900 (d) 4950
  35. 35.What is the 24th term of the AP 3, 9, 15, 21, …? (a) 144 (b) 138 (c) 141 (d) 147
  36. 36.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 13 (b) 10 (c) 11 (d) 12
  37. 37.Which term of the AP 2, 4, 6, 8, … is 30? (a) 15th (b) 14th (c) 16th (d) 17th
  38. 38.What is the 17th term of the AP 7, 13, 19, 25, …? (a) 103 (b) 109 (c) 102 (d) 96
  39. 39.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 360 (b) 183 (c) 32 (d) 180
  40. 40.What is the sum of the first 9 terms of the AP 6, 12, 18, …? (a) 297 (b) 54 (c) 540 (d) 270

Answer key

  1. 176
  2. 26
  3. 132
  4. 165
  5. 22
  6. 4005
  7. 75
  8. 269
  9. 144
  10. 140
  11. 294
  12. 62
  13. 370
  14. 35th
  15. 23
  16. 43
  17. 57
  18. 64
  19. 252
  20. 484
  21. 33
  22. 290
  23. 324
  24. 123
  25. 441
  26. 134
  27. 81
  28. 10th
  29. 271
  30. 181
  31. 289
  32. 8th
  33. 277
  34. 4950
  35. 141
  36. 11
  37. 15th
  38. 103
  39. 180
  40. 270

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