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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 153 · 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 8 terms of the AP 3, 5, 7, …? (a) 160 (b) 17 (c) 88 (d) 80
  2. 2.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 91 (c) 25 (d) 169
  3. 3.What is the missing term in the AP 6, 15, 24, ?, 42? (a) 34 (b) 42 (c) 33 (d) 32
  4. 4.What is the sum of all the whole numbers from 1 to 93? (a) 4278 (b) 8742 (c) 4372 (d) 4371
  5. 5.What is the 35th term of the AP 17, 25, 33, 41, …? (a) 297 (b) 289 (c) 280 (d) 272
  6. 6.What is the sum of all the whole numbers from 1 to 87? (a) 3828 (b) 3741 (c) 3829 (d) 7656
  7. 7.What is the 15th term of the AP 15, 24, 33, 42, …? (a) 126 (b) 135 (c) 141 (d) 150
  8. 8.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 78 (c) 23 (d) 156
  9. 9.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 121 (b) 122 (c) 242 (d) 16
  10. 10.Which term of the AP 11, 15, 19, 23, … is 67? (a) 15th (b) 17th (c) 14th (d) 16th
  11. 11.What is the 32nd term of the AP 3, 6, 9, 12, …? (a) 93 (b) 97 (c) 96 (d) 99
  12. 12.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 171 (c) 342 (d) 35
  13. 13.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 31 (b) 30 (c) 60 (d) 8
  14. 14.What is the missing term in the AP 17, ?, 27, 32, 37? (a) 21 (b) 27 (c) 22 (d) 23
  15. 15.What is the 33rd term of the AP 5, 7, 9, 11, …? (a) 64 (b) 69 (c) 66 (d) 71
  16. 16.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 4970 (c) 2485 (d) 2415
  17. 17.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 49 (c) 13 (d) 56
  18. 18.What is the 28th term of the AP 20, 23, 26, 29, …? (a) 81 (b) 104 (c) 84 (d) 101
  19. 19.What is the 19th term of the AP 8, 10, 12, 14, …? (a) 46 (b) 36 (c) 44 (d) 38
  20. 20.What is the sum of the first 9 terms of the AP 8, 14, 20, …? (a) 288 (b) 576 (c) 315 (d) 56
  21. 21.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 216 (b) 28 (c) 120 (d) 108
  22. 22.What is the sum of all the whole numbers from 1 to 64? (a) 4160 (b) 2048 (c) 2016 (d) 2080
  23. 23.What is the sum of all the whole numbers from 1 to 75? (a) 2851 (b) 2775 (c) 5700 (d) 2850
  24. 24.Which term of the AP 3, 6, 9, 12, … is 42? (a) 15th (b) 16th (c) 14th (d) 13th
  25. 25.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 289 (d) 306
  26. 26.What is the 39th term of the AP 3, 6, 9, 12, …? (a) 118 (b) 114 (c) 117 (d) 120
  27. 27.What is the sum of the first 9 terms of the AP 9, 11, 13, …? (a) 153 (b) 306 (c) 162 (d) 25
  28. 28.Which term of the AP 17, 24, 31, 38, … is 87? (a) 13th (b) 12th (c) 10th (d) 11th
  29. 29.What is the missing term in the AP 5, 7, 9, ?, 13? (a) 10 (b) 13 (c) 11 (d) 12
  30. 30.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 33 (b) 36 (c) 66 (d) 8
  31. 31.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 126 (b) 13 (c) 66 (d) 63
  32. 32.Which term of the AP 17, 25, 33, 41, … is 97? (a) 12th (b) 13th (c) 10th (d) 11th
  33. 33.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 37 (d) 190
  34. 34.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 294 (b) 33 (c) 147 (d) 161
  35. 35.What is the 16th term of the AP 13, 20, 27, 34, …? (a) 112 (b) 105 (c) 118 (d) 125
  36. 36.What is the missing term in the AP 5, ?, 13, 17, 21? (a) 9 (b) 10 (c) 8 (d) 13
  37. 37.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 333 (b) 612 (c) 58 (d) 306
  38. 38.What is the missing term in the AP 17, ?, 31, 38, 45? (a) 23 (b) 31 (c) 24 (d) 25
  39. 39.What is the 36th term of the AP 9, 18, 27, 36, …? (a) 325 (b) 333 (c) 315 (d) 324
  40. 40.What is the 29th term of the AP 18, 27, 36, 45, …? (a) 252 (b) 270 (c) 261 (d) 279

Answer key

  1. 80
  2. 169
  3. 33
  4. 4371
  5. 289
  6. 3828
  7. 141
  8. 144
  9. 121
  10. 15th
  11. 96
  12. 324
  13. 30
  14. 22
  15. 69
  16. 2485
  17. 49
  18. 101
  19. 44
  20. 288
  21. 108
  22. 2080
  23. 2850
  24. 14th
  25. 289
  26. 117
  27. 153
  28. 11th
  29. 11
  30. 33
  31. 63
  32. 11th
  33. 361
  34. 147
  35. 118
  36. 9
  37. 306
  38. 24
  39. 324
  40. 270

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