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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 729 · 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 11th term of the AP 19, 24, 29, 34, …? (a) 69 (b) 55 (c) 50 (d) 74
  2. 2.What is the missing term in the AP 13, ?, 23, 28, 33? (a) 23 (b) 17 (c) 18 (d) 19
  3. 3.What is the 13th term of the AP 18, 21, 24, 27, …? (a) 39 (b) 36 (c) 57 (d) 54
  4. 4.What is the 37th term of the AP 7, 12, 17, 22, …? (a) 185 (b) 187 (c) 192 (d) 180
  5. 5.What is the 30th term of the AP 6, 11, 16, 21, …? (a) 150 (b) 156 (c) 145 (d) 151
  6. 6.What is the 19th term of the AP 1, 5, 9, 13, …? (a) 77 (b) 73 (c) 72 (d) 76
  7. 7.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 231 (c) 253 (d) 506
  8. 8.What is the 22nd term of the AP 19, 21, 23, 25, …? (a) 42 (b) 61 (c) 63 (d) 44
  9. 9.What is the sum of the first 11 terms of the AP 10, 13, 16, …? (a) 278 (b) 275 (c) 550 (d) 40
  10. 10.What is the missing term in the AP 17, ?, 33, 41, 49? (a) 33 (b) 26 (c) 25 (d) 24
  11. 11.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 552 (c) 276 (d) 529
  12. 12.What is the sum of the first 8 terms of the AP 4, 10, 16, …? (a) 400 (b) 46 (c) 224 (d) 200
  13. 13.Which term of the AP 20, 28, 36, 44, … is 292? (a) 37th (b) 34th (c) 35th (d) 36th
  14. 14.What is the sum of all the whole numbers from 1 to 85? (a) 7310 (b) 3570 (c) 3656 (d) 3655
  15. 15.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 380 (c) 171 (d) 190
  16. 16.What is the 40th term of the AP 16, 19, 22, 25, …? (a) 133 (b) 117 (c) 136 (d) 120
  17. 17.What is the 27th term of the AP 19, 21, 23, 25, …? (a) 73 (b) 52 (c) 54 (d) 71
  18. 18.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 144 (d) 156
  19. 19.What is the 18th term of the AP 8, 16, 24, 32, …? (a) 152 (b) 136 (c) 144 (d) 145
  20. 20.What is the 16th term of the AP 6, 10, 14, 18, …? (a) 64 (b) 70 (c) 66 (d) 60
  21. 21.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 296 (b) 160 (c) 29 (d) 148
  22. 22.What is the missing term in the AP 4, ?, 8, 10, 12? (a) 8 (b) 6 (c) 7 (d) 5
  23. 23.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 182 (c) 91 (d) 25
  24. 24.What is the 31st term of the AP 1, 5, 9, 13, …? (a) 120 (b) 125 (c) 121 (d) 124
  25. 25.What is the 13th term of the AP 11, 14, 17, 20, …? (a) 50 (b) 36 (c) 47 (d) 39
  26. 26.What is the missing term in the AP 6, ?, 22, 30, 38? (a) 15 (b) 14 (c) 22 (d) 13
  27. 27.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 57 (c) 435 (d) 870
  28. 28.What is the sum of the first 11 terms of the AP 9, 12, 15, …? (a) 39 (b) 264 (c) 528 (d) 267
  29. 29.What is the sum of all the whole numbers from 1 to 87? (a) 3829 (b) 7656 (c) 3741 (d) 3828
  30. 30.What is the missing term in the AP 15, ?, 27, 33, 39? (a) 20 (b) 27 (c) 22 (d) 21
  31. 31.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 756 (c) 729 (d) 53
  32. 32.What is the missing term in the AP 8, ?, 14, 17, 20? (a) 12 (b) 11 (c) 14 (d) 10
  33. 33.What is the 32nd term of the AP 18, 27, 36, 45, …? (a) 279 (b) 288 (c) 306 (d) 297
  34. 34.What is the missing term in the AP 13, 19, 25, ?, 37? (a) 37 (b) 31 (c) 32 (d) 30
  35. 35.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 119 (b) 238 (c) 122 (d) 26
  36. 36.What is the missing term in the AP 6, 15, ?, 33, 42? (a) 23 (b) 24 (c) 33 (d) 25
  37. 37.Which term of the AP 14, 23, 32, 41, … is 275? (a) 31st (b) 29th (c) 32nd (d) 30th
  38. 38.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 2211 (c) 4556 (d) 2279
  39. 39.What is the 12th term of the AP 11, 20, 29, 38, …? (a) 119 (b) 108 (c) 110 (d) 99
  40. 40.What is the sum of the first 12 terms of the AP 1, 2, 3, …? (a) 84 (b) 156 (c) 78 (d) 12

Answer key

  1. 69
  2. 18
  3. 54
  4. 187
  5. 151
  6. 73
  7. 253
  8. 61
  9. 275
  10. 25
  11. 529
  12. 200
  13. 35th
  14. 3655
  15. 190
  16. 133
  17. 71
  18. 144
  19. 144
  20. 66
  21. 148
  22. 6
  23. 169
  24. 121
  25. 47
  26. 14
  27. 841
  28. 264
  29. 3828
  30. 21
  31. 729
  32. 11
  33. 297
  34. 31
  35. 119
  36. 24
  37. 30th
  38. 2278
  39. 110
  40. 78

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