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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 119 · 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 missing term in the AP 4, 13, 22, ?, 40? (a) 40 (b) 31 (c) 32 (d) 30
  2. 2.What is the 33rd term of the AP 14, 19, 24, 29, …? (a) 179 (b) 160 (c) 165 (d) 174
  3. 3.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 112 (b) 120 (c) 224 (d) 21
  4. 4.What is the 24th term of the AP 17, 25, 33, 41, …? (a) 184 (b) 192 (c) 209 (d) 201
  5. 5.What is the 28th term of the AP 20, 22, 24, 26, …? (a) 76 (b) 74 (c) 56 (d) 54
  6. 6.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 50 (b) 100 (c) 18 (d) 60
  7. 7.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 114 (b) 96 (c) 192 (d) 31
  8. 8.Which term of the AP 7, 16, 25, 34, … is 358? (a) 42nd (b) 41st (c) 39th (d) 40th
  9. 9.What is the missing term in the AP 9, 11, 13, ?, 17? (a) 17 (b) 15 (c) 14 (d) 16
  10. 10.What is the 26th term of the AP 11, 17, 23, 29, …? (a) 167 (b) 161 (c) 156 (d) 150
  11. 11.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 529 (c) 276 (d) 552
  12. 12.What is the sum of the first 5 terms of the AP 4, 8, 12, …? (a) 120 (b) 70 (c) 60 (d) 20
  13. 13.Which term of the AP 12, 17, 22, 27, … is 192? (a) 38th (b) 36th (c) 39th (d) 37th
  14. 14.What is the missing term in the AP 4, 8, 12, ?, 20? (a) 15 (b) 20 (c) 16 (d) 17
  15. 15.Which term of the AP 16, 20, 24, 28, … is 92? (a) 23rd (b) 21st (c) 19th (d) 20th
  16. 16.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 870 (d) 841
  17. 17.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 27 (b) 85 (c) 90 (d) 170
  18. 18.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 126 (b) 18 (c) 252 (d) 127
  19. 19.What is the sum of the first 11 terms of the AP 7, 12, 17, …? (a) 704 (b) 357 (c) 57 (d) 352
  20. 20.What is the 17th term of the AP 14, 17, 20, 23, …? (a) 48 (b) 62 (c) 65 (d) 51
  21. 21.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 50 (b) 90 (c) 13 (d) 45
  22. 22.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 166 (b) 38 (c) 161 (d) 322
  23. 23.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 154 (b) 14 (c) 78 (d) 77
  24. 24.What is the 17th term of the AP 9, 13, 17, 21, …? (a) 77 (b) 68 (c) 73 (d) 64
  25. 25.Which term of the AP 7, 15, 23, 31, … is 279? (a) 35th (b) 36th (c) 37th (d) 34th
  26. 26.What is the missing term in the AP 14, ?, 22, 26, 30? (a) 22 (b) 17 (c) 18 (d) 19
  27. 27.Which term of the AP 7, 9, 11, 13, … is 79? (a) 36th (b) 38th (c) 37th (d) 39th
  28. 28.Which term of the AP 16, 18, 20, 22, … is 40? (a) 12th (b) 14th (c) 20th (d) 13th
  29. 29.What is the 39th term of the AP 11, 17, 23, 29, …? (a) 239 (b) 234 (c) 245 (d) 228
  30. 30.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 180 (b) 360 (c) 32 (d) 183
  31. 31.What is the missing term in the AP 9, ?, 23, 30, 37? (a) 15 (b) 16 (c) 17 (d) 23
  32. 32.What is the 28th term of the AP 3, 6, 9, 12, …? (a) 85 (b) 81 (c) 84 (d) 87
  33. 33.What is the 17th term of the AP 6, 10, 14, 18, …? (a) 68 (b) 70 (c) 64 (d) 74
  34. 34.What is the 38th term of the AP 1, 10, 19, 28, …? (a) 333 (b) 342 (c) 343 (d) 334
  35. 35.What is the sum of the first 7 terms of the AP 7, 13, 19, …? (a) 350 (b) 196 (c) 175 (d) 43
  36. 36.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 7 (b) 9 (c) 8 (d) 6
  37. 37.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 462 (c) 41 (d) 231
  38. 38.What is the 24th term of the AP 4, 13, 22, 31, …? (a) 220 (b) 207 (c) 211 (d) 216
  39. 39.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 984 (b) 528 (c) 74 (d) 492
  40. 40.What is the sum of all the whole numbers from 1 to 41? (a) 820 (b) 1722 (c) 862 (d) 861

Answer key

  1. 31
  2. 174
  3. 112
  4. 201
  5. 74
  6. 50
  7. 96
  8. 40th
  9. 15
  10. 161
  11. 529
  12. 60
  13. 37th
  14. 16
  15. 20th
  16. 841
  17. 85
  18. 126
  19. 352
  20. 62
  21. 45
  22. 161
  23. 77
  24. 73
  25. 35th
  26. 18
  27. 37th
  28. 13th
  29. 239
  30. 180
  31. 16
  32. 84
  33. 70
  34. 334
  35. 175
  36. 7
  37. 441
  38. 211
  39. 492
  40. 861

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