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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 592 · 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 11 terms of the AP 1, 6, 11, …? (a) 291 (b) 286 (c) 51 (d) 572
  2. 2.What is the 17th term of the AP 7, 13, 19, 25, …? (a) 102 (b) 103 (c) 96 (d) 109
  3. 3.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 256 (b) 144 (c) 30 (d) 128
  4. 4.What is the 36th term of the AP 17, 25, 33, 41, …? (a) 305 (b) 288 (c) 297 (d) 280
  5. 5.What is the 20th term of the AP 20, 22, 24, 26, …? (a) 60 (b) 40 (c) 58 (d) 38
  6. 6.What is the missing term in the AP 17, ?, 33, 41, 49? (a) 24 (b) 26 (c) 33 (d) 25
  7. 7.Which term of the AP 20, 29, 38, 47, … is 119? (a) 11th (b) 13th (c) 14th (d) 12th
  8. 8.Which term of the AP 16, 19, 22, 25, … is 124? (a) 37th (b) 36th (c) 38th (d) 39th
  9. 9.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 91 (c) 92 (d) 78
  10. 10.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 90 (b) 30 (c) 180 (d) 105
  11. 11.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 306 (d) 289
  12. 12.What is the missing term in the AP 7, 14, ?, 28, 35? (a) 28 (b) 20 (c) 21 (d) 22
  13. 13.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 361 (d) 380
  14. 14.What is the 38th term of the AP 15, 22, 29, 36, …? (a) 259 (b) 266 (c) 274 (d) 281
  15. 15.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 105 (c) 91 (d) 210
  16. 16.What is the sum of all the whole numbers from 1 to 57? (a) 1653 (b) 1654 (c) 1596 (d) 3306
  17. 17.What is the sum of the first 12 terms of the AP 5, 10, 15, …? (a) 780 (b) 390 (c) 420 (d) 60
  18. 18.What is the 17th term of the AP 18, 20, 22, 24, …? (a) 34 (b) 50 (c) 52 (d) 32
  19. 19.What is the 34th term of the AP 8, 11, 14, 17, …? (a) 99 (b) 102 (c) 110 (d) 107
  20. 20.What is the 23rd term of the AP 2, 11, 20, 29, …? (a) 209 (b) 200 (c) 198 (d) 207
  21. 21.What is the missing term in the AP 20, 26, 32, ?, 44? (a) 44 (b) 39 (c) 37 (d) 38
  22. 22.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 66 (d) 121
  23. 23.What is the 18th term of the AP 17, 21, 25, 29, …? (a) 68 (b) 72 (c) 85 (d) 89
  24. 24.What is the missing term in the AP 8, ?, 14, 17, 20? (a) 12 (b) 10 (c) 11 (d) 14
  25. 25.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 52 (b) 302 (c) 297 (d) 594
  26. 26.Which term of the AP 11, 19, 27, 35, … is 299? (a) 36th (b) 39th (c) 37th (d) 38th
  27. 27.What is the 24th term of the AP 17, 21, 25, 29, …? (a) 113 (b) 109 (c) 96 (d) 92
  28. 28.What is the 27th term of the AP 5, 13, 21, 29, …? (a) 216 (b) 213 (c) 208 (d) 221
  29. 29.What is the 17th term of the AP 13, 15, 17, 19, …? (a) 32 (b) 45 (c) 34 (d) 47
  30. 30.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 43 (c) 253 (d) 506
  31. 31.What is the sum of the first 8 terms of the AP 9, 10, 11, …? (a) 100 (b) 200 (c) 104 (d) 16
  32. 32.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 441 (c) 41 (d) 231
  33. 33.What is the 31st term of the AP 18, 22, 26, 30, …? (a) 142 (b) 124 (c) 138 (d) 120
  34. 34.What is the 12th term of the AP 17, 22, 27, 32, …? (a) 77 (b) 55 (c) 72 (d) 60
  35. 35.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 196 (b) 216 (c) 42 (d) 392
  36. 36.What is the missing term in the AP 6, 13, 20, ?, 34? (a) 27 (b) 26 (c) 34 (d) 28
  37. 37.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 25 (b) 27 (c) 26 (d) 33
  38. 38.What is the 10th term of the AP 1, 9, 17, 25, …? (a) 72 (b) 73 (c) 81 (d) 80
  39. 39.What is the 19th term of the AP 2, 7, 12, 17, …? (a) 92 (b) 95 (c) 90 (d) 97
  40. 40.What is the 12th term of the AP 5, 13, 21, 29, …? (a) 96 (b) 93 (c) 88 (d) 101

Answer key

  1. 286
  2. 103
  3. 128
  4. 297
  5. 58
  6. 25
  7. 12th
  8. 37th
  9. 91
  10. 90
  11. 289
  12. 21
  13. 361
  14. 274
  15. 105
  16. 1653
  17. 390
  18. 50
  19. 107
  20. 200
  21. 38
  22. 121
  23. 85
  24. 11
  25. 297
  26. 37th
  27. 109
  28. 213
  29. 45
  30. 484
  31. 100
  32. 441
  33. 138
  34. 72
  35. 196
  36. 27
  37. 26
  38. 73
  39. 92
  40. 93

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