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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 324 · 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 2, 5, 8, …? (a) 100 (b) 200 (c) 23 (d) 112
  2. 2.What is the missing term in the AP 5, 11, 17, ?, 29? (a) 23 (b) 29 (c) 22 (d) 24
  3. 3.What is the sum of the first 11 terms of the AP 5, 11, 17, …? (a) 770 (b) 418 (c) 65 (d) 385
  4. 4.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 264 (b) 22 (c) 143 (d) 132
  5. 5.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 117 (b) 31 (c) 112 (d) 224
  6. 6.What is the sum of all the whole numbers from 1 to 87? (a) 3741 (b) 3829 (c) 7656 (d) 3828
  7. 7.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 2080 (c) 2016 (d) 4160
  8. 8.What is the 11th term of the AP 2, 6, 10, 14, …? (a) 46 (b) 40 (c) 42 (d) 44
  9. 9.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 48 (b) 96 (c) 13 (d) 54
  10. 10.Which term of the AP 5, 14, 23, 32, … is 104? (a) 13th (b) 14th (c) 12th (d) 11th
  11. 11.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 150 (b) 132 (c) 37 (d) 264
  12. 12.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 120 (b) 105 (c) 30 (d) 210
  13. 13.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 400 (d) 39
  14. 14.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 41 (c) 231 (d) 462
  15. 15.What is the 35th term of the AP 9, 11, 13, 15, …? (a) 77 (b) 68 (c) 79 (d) 70
  16. 16.What is the 27th term of the AP 4, 8, 12, 16, …? (a) 104 (b) 112 (c) 109 (d) 108
  17. 17.What is the 17th term of the AP 2, 9, 16, 23, …? (a) 112 (b) 119 (c) 114 (d) 121
  18. 18.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 104 (b) 184 (c) 22 (d) 92
  19. 19.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 96 (b) 31 (c) 114 (d) 192
  20. 20.What is the 30th term of the AP 3, 10, 17, 24, …? (a) 206 (b) 203 (c) 213 (d) 210
  21. 21.What is the 31st term of the AP 5, 12, 19, 26, …? (a) 217 (b) 222 (c) 210 (d) 215
  22. 22.What is the sum of the first 6 terms of the AP 3, 6, 9, …? (a) 18 (b) 72 (c) 63 (d) 126
  23. 23.What is the sum of all the whole numbers from 1 to 23? (a) 277 (b) 552 (c) 276 (d) 253
  24. 24.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 294 (b) 39 (c) 168 (d) 147
  25. 25.What is the missing term in the AP 16, 25, 34, ?, 52? (a) 44 (b) 52 (c) 42 (d) 43
  26. 26.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 13 (b) 14 (c) 16 (d) 12
  27. 27.What is the 25th term of the AP 18, 21, 24, 27, …? (a) 75 (b) 72 (c) 90 (d) 93
  28. 28.What is the missing term in the AP 15, ?, 33, 42, 51? (a) 23 (b) 33 (c) 25 (d) 24
  29. 29.What is the missing term in the AP 9, 13, 17, ?, 25? (a) 25 (b) 20 (c) 21 (d) 22
  30. 30.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 396 (b) 63 (c) 726 (d) 363
  31. 31.What is the 13th term of the AP 2, 4, 6, 8, …? (a) 24 (b) 27 (c) 26 (d) 28
  32. 32.What is the missing term in the AP 3, 8, 13, ?, 23? (a) 23 (b) 19 (c) 17 (d) 18
  33. 33.What is the missing term in the AP 5, 13, 21, ?, 37? (a) 37 (b) 29 (c) 30 (d) 28
  34. 34.What is the 26th term of the AP 19, 26, 33, 40, …? (a) 175 (b) 201 (c) 182 (d) 194
  35. 35.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 228 (b) 29 (c) 216 (d) 432
  36. 36.What is the 31st term of the AP 11, 18, 25, 32, …? (a) 221 (b) 210 (c) 217 (d) 228
  37. 37.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 23 (c) 78 (d) 156
  38. 38.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 102 (b) 204 (c) 114 (d) 27
  39. 39.What is the 35th term of the AP 14, 20, 26, 32, …? (a) 224 (b) 204 (c) 210 (d) 218
  40. 40.What is the 21st term of the AP 17, 19, 21, 23, …? (a) 59 (b) 40 (c) 57 (d) 42

Answer key

  1. 100
  2. 23
  3. 385
  4. 132
  5. 112
  6. 3828
  7. 2080
  8. 42
  9. 48
  10. 12th
  11. 132
  12. 105
  13. 400
  14. 441
  15. 77
  16. 108
  17. 114
  18. 92
  19. 96
  20. 206
  21. 215
  22. 63
  23. 276
  24. 147
  25. 43
  26. 13
  27. 90
  28. 24
  29. 21
  30. 363
  31. 26
  32. 18
  33. 29
  34. 194
  35. 216
  36. 221
  37. 144
  38. 102
  39. 218
  40. 57

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