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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 519 · 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 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 153 (c) 33 (d) 289
  2. 2.What is the 26th term of the AP 13, 20, 27, 34, …? (a) 182 (b) 195 (c) 175 (d) 188
  3. 3.What is the 33rd term of the AP 6, 10, 14, 18, …? (a) 138 (b) 132 (c) 128 (d) 134
  4. 4.What is the sum of all the whole numbers from 1 to 49? (a) 1225 (b) 1226 (c) 1176 (d) 2450
  5. 5.What is the 32nd term of the AP 9, 12, 15, 18, …? (a) 93 (b) 102 (c) 105 (d) 96
  6. 6.What is the 25th term of the AP 6, 10, 14, 18, …? (a) 102 (b) 100 (c) 106 (d) 96
  7. 7.What is the sum of all the whole numbers from 1 to 56? (a) 3192 (b) 1596 (c) 1568 (d) 1540
  8. 8.Which term of the AP 14, 18, 22, 26, … is 50? (a) 12th (b) 11th (c) 10th (d) 9th
  9. 9.What is the 10th term of the AP 2, 7, 12, 17, …? (a) 50 (b) 47 (c) 52 (d) 45
  10. 10.What is the missing term in the AP 11, 15, ?, 23, 27? (a) 18 (b) 19 (c) 23 (d) 20
  11. 11.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 368 (b) 44 (c) 208 (d) 184
  12. 12.What is the 28th term of the AP 5, 10, 15, 20, …? (a) 145 (b) 135 (c) 140 (d) 141
  13. 13.What is the sum of all the whole numbers from 1 to 46? (a) 1058 (b) 1035 (c) 1081 (d) 2162
  14. 14.What is the 32nd term of the AP 3, 5, 7, 9, …? (a) 65 (b) 67 (c) 64 (d) 62
  15. 15.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 15 (c) 30 (d) 25
  16. 16.Which term of the AP 1, 9, 17, 25, … is 305? (a) 40th (b) 38th (c) 39th (d) 41st
  17. 17.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 13 (b) 85 (c) 90 (d) 170
  18. 18.What is the sum of all the whole numbers from 1 to 55? (a) 1485 (b) 3080 (c) 1540 (d) 1541
  19. 19.Which term of the AP 8, 14, 20, 26, … is 74? (a) 14th (b) 12th (c) 11th (d) 13th
  20. 20.What is the 27th term of the AP 18, 20, 22, 24, …? (a) 72 (b) 70 (c) 52 (d) 54
  21. 21.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 40 (b) 70 (c) 35 (d) 11
  22. 22.What is the sum of all the whole numbers from 1 to 38? (a) 703 (b) 741 (c) 722 (d) 1482
  23. 23.What is the missing term in the AP 5, ?, 11, 14, 17? (a) 7 (b) 11 (c) 8 (d) 9
  24. 24.What is the 40th term of the AP 8, 12, 16, 20, …? (a) 168 (b) 156 (c) 160 (d) 164
  25. 25.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 14 (b) 16 (c) 12 (d) 13
  26. 26.What is the missing term in the AP 2, 7, 12, ?, 22? (a) 16 (b) 17 (c) 18 (d) 22
  27. 27.What is the 14th term of the AP 2, 4, 6, 8, …? (a) 29 (b) 30 (c) 28 (d) 26
  28. 28.What is the 13th term of the AP 9, 11, 13, 15, …? (a) 24 (b) 26 (c) 33 (d) 35
  29. 29.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 21 (d) 121
  30. 30.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 4753 (c) 4754 (d) 9506
  31. 31.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 210 (b) 114 (c) 25 (d) 105
  32. 32.What is the 21st term of the AP 3, 7, 11, 15, …? (a) 87 (b) 84 (c) 83 (d) 80
  33. 33.Which term of the AP 16, 24, 32, 40, … is 304? (a) 39th (b) 36th (c) 38th (d) 37th
  34. 34.What is the 30th term of the AP 7, 16, 25, 34, …? (a) 268 (b) 277 (c) 261 (d) 270
  35. 35.Which term of the AP 1, 3, 5, 7, … is 23? (a) 13th (b) 12th (c) 11th (d) 14th
  36. 36.Which term of the AP 8, 13, 18, 23, … is 108? (a) 20th (b) 21st (c) 22nd (d) 23rd
  37. 37.What is the 24th term of the AP 19, 25, 31, 37, …? (a) 163 (b) 138 (c) 157 (d) 144
  38. 38.What is the sum of the first 10 terms of the AP 5, 6, 7, …? (a) 100 (b) 95 (c) 14 (d) 190
  39. 39.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 561 (c) 562 (d) 528
  40. 40.What is the 33rd term of the AP 5, 12, 19, 26, …? (a) 236 (b) 231 (c) 224 (d) 229

Answer key

  1. 289
  2. 188
  3. 134
  4. 1225
  5. 102
  6. 102
  7. 1596
  8. 10th
  9. 47
  10. 19
  11. 184
  12. 140
  13. 1081
  14. 65
  15. 25
  16. 39th
  17. 85
  18. 1540
  19. 12th
  20. 70
  21. 35
  22. 741
  23. 8
  24. 164
  25. 13
  26. 17
  27. 28
  28. 33
  29. 121
  30. 4753
  31. 105
  32. 83
  33. 37th
  34. 268
  35. 12th
  36. 21st
  37. 157
  38. 95
  39. 561
  40. 229

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