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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 289 · 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 9 terms of the AP 7, 9, 11, …? (a) 135 (b) 23 (c) 144 (d) 270
  2. 2.What is the 38th term of the AP 4, 12, 20, 28, …? (a) 296 (b) 308 (c) 304 (d) 300
  3. 3.What is the 27th term of the AP 14, 21, 28, 35, …? (a) 182 (b) 196 (c) 189 (d) 203
  4. 4.Which term of the AP 1, 4, 7, 10, … is 34? (a) 11th (b) 12th (c) 13th (d) 14th
  5. 5.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 21 (c) 36 (d) 11
  6. 6.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 120 (b) 29 (c) 240 (d) 136
  7. 7.What is the 14th term of the AP 6, 9, 12, 15, …? (a) 48 (b) 39 (c) 45 (d) 42
  8. 8.What is the 22nd term of the AP 4, 11, 18, 25, …? (a) 154 (b) 158 (c) 151 (d) 147
  9. 9.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 90 (c) 17 (d) 45
  10. 10.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 360 (b) 200 (c) 180 (d) 40
  11. 11.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 21 (c) 121 (d) 66
  12. 12.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 35 (c) 324 (d) 171
  13. 13.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 72 (b) 36 (c) 11 (d) 42
  14. 14.What is the missing term in the AP 8, ?, 18, 23, 28? (a) 14 (b) 13 (c) 12 (d) 18
  15. 15.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 406 (c) 784 (d) 812
  16. 16.What is the 14th term of the AP 20, 24, 28, 32, …? (a) 56 (b) 72 (c) 52 (d) 76
  17. 17.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 154 (c) 136 (d) 153
  18. 18.What is the sum of all the whole numbers from 1 to 85? (a) 3655 (b) 7310 (c) 3656 (d) 3570
  19. 19.What is the 23rd term of the AP 2, 5, 8, 11, …? (a) 68 (b) 69 (c) 66 (d) 71
  20. 20.What is the 35th term of the AP 1, 7, 13, 19, …? (a) 205 (b) 210 (c) 204 (d) 211
  21. 21.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 561 (c) 562 (d) 528
  22. 22.What is the missing term in the AP 19, ?, 23, 25, 27? (a) 22 (b) 23 (c) 20 (d) 21
  23. 23.What is the sum of the first 10 terms of the AP 7, 12, 17, …? (a) 590 (b) 320 (c) 52 (d) 295
  24. 24.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 41 (b) 194 (c) 189 (d) 378
  25. 25.What is the 37th term of the AP 2, 11, 20, 29, …? (a) 335 (b) 333 (c) 324 (d) 326
  26. 26.What is the 18th term of the AP 4, 12, 20, 28, …? (a) 136 (b) 148 (c) 144 (d) 140
  27. 27.What is the missing term in the AP 13, 18, ?, 28, 33? (a) 22 (b) 28 (c) 24 (d) 23
  28. 28.What is the 12th term of the AP 10, 13, 16, 19, …? (a) 43 (b) 46 (c) 33 (d) 36
  29. 29.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 252 (b) 33 (c) 126 (d) 131
  30. 30.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 420 (c) 210 (d) 39
  31. 31.What is the sum of the first 7 terms of the AP 4, 9, 14, …? (a) 138 (b) 133 (c) 266 (d) 34
  32. 32.What is the 27th term of the AP 8, 11, 14, 17, …? (a) 86 (b) 78 (c) 81 (d) 89
  33. 33.What is the missing term in the AP 7, 16, ?, 34, 43? (a) 34 (b) 24 (c) 25 (d) 26
  34. 34.Which term of the AP 9, 12, 15, 18, … is 54? (a) 17th (b) 16th (c) 15th (d) 18th
  35. 35.Which term of the AP 13, 17, 21, 25, … is 113? (a) 25th (b) 27th (c) 28th (d) 26th
  36. 36.What is the sum of all the whole numbers from 1 to 69? (a) 2416 (b) 2346 (c) 2415 (d) 4830
  37. 37.What is the 38th term of the AP 17, 25, 33, 41, …? (a) 304 (b) 296 (c) 321 (d) 313
  38. 38.What is the 35th term of the AP 7, 10, 13, 16, …? (a) 105 (b) 109 (c) 112 (d) 102
  39. 39.What is the missing term in the AP 6, 8, 10, ?, 14? (a) 11 (b) 13 (c) 12 (d) 14
  40. 40.What is the sum of the first 9 terms of the AP 8, 10, 12, …? (a) 288 (b) 24 (c) 153 (d) 144

Answer key

  1. 135
  2. 300
  3. 196
  4. 12th
  5. 36
  6. 120
  7. 45
  8. 151
  9. 81
  10. 180
  11. 121
  12. 324
  13. 36
  14. 13
  15. 784
  16. 72
  17. 153
  18. 3655
  19. 68
  20. 205
  21. 561
  22. 21
  23. 295
  24. 189
  25. 326
  26. 140
  27. 23
  28. 43
  29. 126
  30. 400
  31. 133
  32. 86
  33. 25
  34. 16th
  35. 26th
  36. 2415
  37. 313
  38. 109
  39. 12
  40. 144

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