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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 737 · 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 20th term of the AP 3, 12, 21, 30, …? (a) 174 (b) 171 (c) 183 (d) 180
  2. 2.What is the 15th term of the AP 6, 10, 14, 18, …? (a) 56 (b) 60 (c) 66 (d) 62
  3. 3.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 66 (b) 8 (c) 33 (d) 36
  4. 4.What is the sum of the first 6 terms of the AP 10, 15, 20, …? (a) 150 (b) 135 (c) 270 (d) 35
  5. 5.What is the 25th term of the AP 13, 22, 31, 40, …? (a) 238 (b) 229 (c) 225 (d) 216
  6. 6.Which term of the AP 6, 12, 18, 24, … is 132? (a) 23rd (b) 22nd (c) 24th (d) 21st
  7. 7.What is the 13th term of the AP 6, 11, 16, 21, …? (a) 60 (b) 71 (c) 66 (d) 65
  8. 8.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 74 (b) 528 (c) 984 (d) 492
  9. 9.What is the 26th term of the AP 17, 21, 25, 29, …? (a) 121 (b) 100 (c) 117 (d) 104
  10. 10.What is the sum of all the whole numbers from 1 to 67? (a) 2279 (b) 2278 (c) 2211 (d) 4556
  11. 11.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 8 (b) 70 (c) 36 (d) 35
  12. 12.What is the 14th term of the AP 16, 20, 24, 28, …? (a) 72 (b) 52 (c) 68 (d) 56
  13. 13.Which term of the AP 11, 18, 25, 32, … is 158? (a) 21st (b) 23rd (c) 24th (d) 22nd
  14. 14.Which term of the AP 18, 25, 32, 39, … is 179? (a) 23rd (b) 26th (c) 25th (d) 24th
  15. 15.What is the missing term in the AP 2, 6, 10, ?, 18? (a) 14 (b) 15 (c) 18 (d) 13
  16. 16.What is the sum of the first 12 terms of the AP 9, 14, 19, …? (a) 468 (b) 438 (c) 64 (d) 876
  17. 17.What is the 12th term of the AP 7, 9, 11, 13, …? (a) 29 (b) 31 (c) 24 (d) 22
  18. 18.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 360 (b) 180 (c) 190 (d) 27
  19. 19.Which term of the AP 5, 11, 17, 23, … is 47? (a) 9th (b) 8th (c) 7th (d) 10th
  20. 20.Which term of the AP 15, 23, 31, 39, … is 303? (a) 36th (b) 37th (c) 38th (d) 39th
  21. 21.What is the missing term in the AP 12, 17, 22, ?, 32? (a) 28 (b) 26 (c) 27 (d) 32
  22. 22.Which term of the AP 5, 10, 15, 20, … is 70? (a) 15th (b) 14th (c) 13th (d) 16th
  23. 23.What is the 32nd term of the AP 19, 22, 25, 28, …? (a) 115 (b) 93 (c) 96 (d) 112
  24. 24.What is the 32nd term of the AP 15, 21, 27, 33, …? (a) 192 (b) 207 (c) 201 (d) 186
  25. 25.What is the missing term in the AP 12, ?, 30, 39, 48? (a) 20 (b) 30 (c) 22 (d) 21
  26. 26.What is the 28th term of the AP 19, 24, 29, 34, …? (a) 135 (b) 154 (c) 140 (d) 159
  27. 27.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 638 (b) 49 (c) 341 (d) 319
  28. 28.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 200 (b) 105 (c) 30 (d) 100
  29. 29.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 300 (c) 576 (d) 600
  30. 30.What is the missing term in the AP 5, ?, 19, 26, 33? (a) 13 (b) 11 (c) 12 (d) 19
  31. 31.What is the 25th term of the AP 7, 14, 21, 28, …? (a) 182 (b) 176 (c) 168 (d) 175
  32. 32.What is the 39th term of the AP 16, 19, 22, 25, …? (a) 114 (b) 133 (c) 130 (d) 117
  33. 33.What is the 38th term of the AP 4, 11, 18, 25, …? (a) 263 (b) 266 (c) 259 (d) 270
  34. 34.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 306 (c) 33 (d) 289
  35. 35.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 132 (d) 66
  36. 36.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 7 (b) 28 (c) 29 (d) 56
  37. 37.What is the 29th term of the AP 3, 7, 11, 15, …? (a) 112 (b) 115 (c) 119 (d) 116
  38. 38.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 3655 (c) 7482 (d) 3741
  39. 39.What is the 17th term of the AP 14, 19, 24, 29, …? (a) 80 (b) 85 (c) 99 (d) 94
  40. 40.What is the 26th term of the AP 16, 19, 22, 25, …? (a) 94 (b) 78 (c) 75 (d) 91

Answer key

  1. 174
  2. 62
  3. 33
  4. 135
  5. 229
  6. 22nd
  7. 66
  8. 492
  9. 117
  10. 2278
  11. 35
  12. 68
  13. 22nd
  14. 24th
  15. 14
  16. 438
  17. 29
  18. 180
  19. 8th
  20. 37th
  21. 27
  22. 14th
  23. 112
  24. 201
  25. 21
  26. 154
  27. 319
  28. 100
  29. 576
  30. 12
  31. 175
  32. 130
  33. 263
  34. 289
  35. 121
  36. 28
  37. 115
  38. 3741
  39. 94
  40. 91

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