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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 345 · 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 40th term of the AP 18, 21, 24, 27, …? (a) 120 (b) 135 (c) 117 (d) 138
  2. 2.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 165 (b) 176 (c) 330 (d) 25
  3. 3.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 60 (b) 30 (c) 31 (d) 8
  4. 4.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 60 (b) 120 (c) 15 (d) 66
  5. 5.What is the missing term in the AP 18, 24, ?, 36, 42? (a) 36 (b) 29 (c) 31 (d) 30
  6. 6.What is the 16th term of the AP 19, 23, 27, 31, …? (a) 60 (b) 83 (c) 79 (d) 64
  7. 7.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 441 (d) 231
  8. 8.What is the sum of the first 9 terms of the AP 5, 8, 11, …? (a) 156 (b) 306 (c) 153 (d) 29
  9. 9.What is the missing term in the AP 5, 11, ?, 23, 29? (a) 17 (b) 18 (c) 16 (d) 23
  10. 10.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 105 (c) 240 (d) 120
  11. 11.What is the 10th term of the AP 7, 10, 13, 16, …? (a) 30 (b) 37 (c) 27 (d) 34
  12. 12.What is the 29th term of the AP 4, 6, 8, 10, …? (a) 60 (b) 62 (c) 58 (d) 56
  13. 13.What is the 38th term of the AP 16, 24, 32, 40, …? (a) 320 (b) 312 (c) 304 (d) 296
  14. 14.What is the sum of the first 11 terms of the AP 5, 9, 13, …? (a) 297 (b) 550 (c) 275 (d) 45
  15. 15.What is the 27th term of the AP 7, 13, 19, 25, …? (a) 169 (b) 156 (c) 163 (d) 162
  16. 16.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 190 (c) 37 (d) 380
  17. 17.What is the sum of the first 11 terms of the AP 10, 15, 20, …? (a) 60 (b) 385 (c) 390 (d) 770
  18. 18.What is the 25th term of the AP 20, 29, 38, 47, …? (a) 236 (b) 245 (c) 225 (d) 216
  19. 19.What is the missing term in the AP 13, 22, ?, 40, 49? (a) 32 (b) 30 (c) 40 (d) 31
  20. 20.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 31 (b) 190 (c) 110 (d) 95
  21. 21.Which term of the AP 20, 22, 24, 26, … is 52? (a) 18th (b) 16th (c) 26th (d) 17th
  22. 22.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 189 (b) 41 (c) 378 (d) 194
  23. 23.What is the missing term in the AP 3, 6, ?, 12, 15? (a) 10 (b) 9 (c) 12 (d) 8
  24. 24.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 11 (b) 36 (c) 72 (d) 42
  25. 25.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 56 (b) 112 (c) 57 (d) 11
  26. 26.What is the 11th term of the AP 2, 11, 20, 29, …? (a) 99 (b) 101 (c) 90 (d) 92
  27. 27.What is the sum of the first 12 terms of the AP 6, 10, 14, …? (a) 50 (b) 336 (c) 672 (d) 360
  28. 28.What is the 16th term of the AP 4, 9, 14, 19, …? (a) 84 (b) 80 (c) 79 (d) 75
  29. 29.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 5 (b) 7 (c) 3 (d) 4
  30. 30.What is the 10th term of the AP 20, 23, 26, 29, …? (a) 30 (b) 47 (c) 50 (d) 27
  31. 31.What is the 26th term of the AP 5, 11, 17, 23, …? (a) 150 (b) 156 (c) 155 (d) 161
  32. 32.What is the 28th term of the AP 4, 13, 22, 31, …? (a) 243 (b) 247 (c) 256 (d) 252
  33. 33.What is the 15th term of the AP 2, 9, 16, 23, …? (a) 105 (b) 107 (c) 100 (d) 98
  34. 34.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 63 (b) 14 (c) 56 (d) 112
  35. 35.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 176 (b) 96 (c) 18 (d) 88
  36. 36.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 25 (b) 105 (c) 210 (d) 114
  37. 37.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 78 (b) 9 (c) 39 (d) 42
  38. 38.What is the 11th term of the AP 19, 26, 33, 40, …? (a) 96 (b) 77 (c) 89 (d) 70
  39. 39.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2312 (c) 2346 (d) 2278
  40. 40.What is the 27th term of the AP 18, 21, 24, 27, …? (a) 99 (b) 78 (c) 96 (d) 81

Answer key

  1. 135
  2. 165
  3. 30
  4. 60
  5. 30
  6. 79
  7. 441
  8. 153
  9. 17
  10. 120
  11. 34
  12. 60
  13. 312
  14. 275
  15. 163
  16. 361
  17. 385
  18. 236
  19. 31
  20. 95
  21. 17th
  22. 189
  23. 9
  24. 36
  25. 56
  26. 92
  27. 336
  28. 79
  29. 4
  30. 47
  31. 155
  32. 247
  33. 100
  34. 56
  35. 88
  36. 105
  37. 39
  38. 89
  39. 2346
  40. 96

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