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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 416 · 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 18th term of the AP 17, 19, 21, 23, …? (a) 51 (b) 53 (c) 34 (d) 36
  2. 2.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 10 (b) 15 (c) 11 (d) 12
  3. 3.What is the 12th term of the AP 14, 18, 22, 26, …? (a) 48 (b) 62 (c) 44 (d) 58
  4. 4.What is the 15th term of the AP 12, 16, 20, 24, …? (a) 56 (b) 68 (c) 60 (d) 72
  5. 5.What is the 16th term of the AP 4, 10, 16, 22, …? (a) 96 (b) 100 (c) 94 (d) 90
  6. 6.Which term of the AP 4, 6, 8, 10, … is 52? (a) 26th (b) 24th (c) 25th (d) 27th
  7. 7.What is the sum of the first 9 terms of the AP 4, 10, 16, …? (a) 252 (b) 279 (c) 52 (d) 504
  8. 8.What is the missing term in the AP 1, 4, ?, 10, 13? (a) 10 (b) 8 (c) 6 (d) 7
  9. 9.What is the sum of all the whole numbers from 1 to 59? (a) 1711 (b) 3540 (c) 1770 (d) 1771
  10. 10.What is the sum of all the whole numbers from 1 to 74? (a) 2701 (b) 2738 (c) 5550 (d) 2775
  11. 11.What is the 35th term of the AP 8, 13, 18, 23, …? (a) 183 (b) 170 (c) 175 (d) 178
  12. 12.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 46 (b) 90 (c) 9 (d) 45
  13. 13.What is the sum of all the whole numbers from 1 to 95? (a) 4465 (b) 9120 (c) 4561 (d) 4560
  14. 14.What is the missing term in the AP 12, 15, 18, ?, 24? (a) 20 (b) 22 (c) 21 (d) 24
  15. 15.What is the missing term in the AP 7, ?, 11, 13, 15? (a) 9 (b) 11 (c) 8 (d) 10
  16. 16.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 368 (b) 184 (c) 44 (d) 208
  17. 17.What is the 33rd term of the AP 15, 17, 19, 21, …? (a) 79 (b) 81 (c) 64 (d) 66
  18. 18.What is the missing term in the AP 3, 5, 7, ?, 11? (a) 9 (b) 11 (c) 8 (d) 10
  19. 19.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 72 (b) 8 (c) 36 (d) 40
  20. 20.What is the sum of all the whole numbers from 1 to 27? (a) 378 (b) 379 (c) 756 (d) 351
  21. 21.What is the 32nd term of the AP 3, 10, 17, 24, …? (a) 227 (b) 217 (c) 224 (d) 220
  22. 22.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 22 (b) 70 (c) 80 (d) 140
  23. 23.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 15 (c) 30 (d) 9
  24. 24.What is the sum of the first 10 terms of the AP 5, 10, 15, …? (a) 50 (b) 550 (c) 275 (d) 300
  25. 25.What is the 11th term of the AP 9, 18, 27, 36, …? (a) 108 (b) 90 (c) 100 (d) 99
  26. 26.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 784 (c) 406 (d) 812
  27. 27.What is the 21st term of the AP 18, 21, 24, 27, …? (a) 60 (b) 81 (c) 78 (d) 63
  28. 28.What is the 23rd term of the AP 12, 17, 22, 27, …? (a) 115 (b) 127 (c) 122 (d) 110
  29. 29.What is the 31st term of the AP 11, 14, 17, 20, …? (a) 104 (b) 90 (c) 93 (d) 101
  30. 30.Which term of the AP 7, 14, 21, 28, … is 98? (a) 16th (b) 15th (c) 14th (d) 13th
  31. 31.What is the 34th term of the AP 16, 21, 26, 31, …? (a) 186 (b) 165 (c) 170 (d) 181
  32. 32.Which term of the AP 8, 12, 16, 20, … is 84? (a) 21st (b) 22nd (c) 19th (d) 20th
  33. 33.What is the 14th term of the AP 9, 17, 25, 33, …? (a) 113 (b) 112 (c) 121 (d) 104
  34. 34.What is the missing term in the AP 6, ?, 18, 24, 30? (a) 12 (b) 18 (c) 11 (d) 13
  35. 35.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 156 (d) 144
  36. 36.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 572 (b) 308 (c) 286 (d) 46
  37. 37.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 84 (b) 90 (c) 19 (d) 168
  38. 38.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 14 (b) 12 (c) 13 (d) 15
  39. 39.What is the 28th term of the AP 6, 11, 16, 21, …? (a) 146 (b) 140 (c) 141 (d) 135
  40. 40.Which term of the AP 4, 12, 20, 28, … is 148? (a) 20th (b) 21st (c) 19th (d) 18th

Answer key

  1. 51
  2. 11
  3. 58
  4. 68
  5. 94
  6. 25th
  7. 252
  8. 7
  9. 1770
  10. 2775
  11. 178
  12. 45
  13. 4560
  14. 21
  15. 9
  16. 184
  17. 79
  18. 9
  19. 36
  20. 378
  21. 220
  22. 70
  23. 25
  24. 275
  25. 99
  26. 784
  27. 78
  28. 122
  29. 101
  30. 14th
  31. 181
  32. 20th
  33. 113
  34. 12
  35. 144
  36. 286
  37. 84
  38. 13
  39. 141
  40. 19th

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