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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 475 · 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 10 terms of the AP 7, 10, 13, …? (a) 220 (b) 34 (c) 410 (d) 205
  2. 2.What is the sum of the first 8 terms of the AP 6, 12, 18, …? (a) 216 (b) 432 (c) 240 (d) 48
  3. 3.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 132 (b) 150 (c) 264 (d) 37
  4. 4.Which term of the AP 19, 24, 29, 34, … is 179? (a) 32nd (b) 33rd (c) 35th (d) 34th
  5. 5.What is the 22nd term of the AP 9, 18, 27, 36, …? (a) 199 (b) 189 (c) 198 (d) 207
  6. 6.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2312 (c) 2278 (d) 2346
  7. 7.What is the 37th term of the AP 13, 15, 17, 19, …? (a) 87 (b) 85 (c) 74 (d) 72
  8. 8.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 156 (c) 66 (d) 78
  9. 9.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 21 (b) 78 (c) 132 (d) 66
  10. 10.Which term of the AP 6, 10, 14, 18, … is 78? (a) 20th (b) 18th (c) 19th (d) 21st
  11. 11.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 41 (c) 231 (d) 462
  12. 12.What is the 11th term of the AP 13, 19, 25, 31, …? (a) 79 (b) 60 (c) 73 (d) 66
  13. 13.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 784 (c) 812 (d) 406
  14. 14.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 41 (b) 322 (c) 161 (d) 182
  15. 15.What is the 21st term of the AP 15, 22, 29, 36, …? (a) 162 (b) 147 (c) 140 (d) 155
  16. 16.What is the sum of all the whole numbers from 1 to 46? (a) 1035 (b) 1058 (c) 2162 (d) 1081
  17. 17.What is the 32nd term of the AP 2, 6, 10, 14, …? (a) 126 (b) 128 (c) 124 (d) 130
  18. 18.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 272 (d) 31
  19. 19.What is the 17th term of the AP 13, 15, 17, 19, …? (a) 32 (b) 47 (c) 34 (d) 45
  20. 20.What is the 38th term of the AP 14, 18, 22, 26, …? (a) 152 (b) 166 (c) 148 (d) 162
  21. 21.What is the missing term in the AP 10, ?, 14, 16, 18? (a) 14 (b) 11 (c) 12 (d) 13
  22. 22.What is the 14th term of the AP 18, 26, 34, 42, …? (a) 104 (b) 122 (c) 130 (d) 112
  23. 23.What is the missing term in the AP 1, ?, 19, 28, 37? (a) 19 (b) 11 (c) 9 (d) 10
  24. 24.What is the sum of all the whole numbers from 1 to 33? (a) 528 (b) 562 (c) 1122 (d) 561
  25. 25.What is the 13th term of the AP 18, 21, 24, 27, …? (a) 57 (b) 36 (c) 54 (d) 39
  26. 26.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 13 (b) 85 (c) 170 (d) 90
  27. 27.What is the 10th term of the AP 18, 27, 36, 45, …? (a) 90 (b) 99 (c) 108 (d) 81
  28. 28.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 576 (c) 300 (d) 47
  29. 29.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 306 (c) 33 (d) 289
  30. 30.What is the 16th term of the AP 13, 20, 27, 34, …? (a) 112 (b) 118 (c) 105 (d) 125
  31. 31.What is the sum of all the whole numbers from 1 to 38? (a) 741 (b) 703 (c) 1482 (d) 722
  32. 32.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 650 (c) 325 (d) 49
  33. 33.Which term of the AP 1, 6, 11, 16, … is 61? (a) 15th (b) 14th (c) 13th (d) 12th
  34. 34.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 7832 (c) 3916 (d) 3828
  35. 35.What is the sum of the first 10 terms of the AP 3, 6, 9, …? (a) 165 (b) 180 (c) 330 (d) 30
  36. 36.What is the 28th term of the AP 18, 27, 36, 45, …? (a) 243 (b) 261 (c) 252 (d) 270
  37. 37.What is the missing term in the AP 18, 23, 28, ?, 38? (a) 38 (b) 32 (c) 33 (d) 34
  38. 38.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 190 (d) 37
  39. 39.What is the missing term in the AP 14, 18, 22, ?, 30? (a) 27 (b) 26 (c) 30 (d) 25
  40. 40.What is the missing term in the AP 8, 12, 16, ?, 24? (a) 21 (b) 19 (c) 24 (d) 20

Answer key

  1. 205
  2. 216
  3. 132
  4. 33rd
  5. 198
  6. 2346
  7. 85
  8. 78
  9. 66
  10. 19th
  11. 441
  12. 73
  13. 784
  14. 161
  15. 155
  16. 1081
  17. 126
  18. 256
  19. 45
  20. 162
  21. 12
  22. 122
  23. 10
  24. 561
  25. 54
  26. 85
  27. 99
  28. 576
  29. 289
  30. 118
  31. 741
  32. 625
  33. 13th
  34. 3916
  35. 165
  36. 261
  37. 33
  38. 361
  39. 26
  40. 20

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