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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 12 · 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 all the whole numbers from 1 to 92? (a) 4278 (b) 4186 (c) 4232 (d) 8556
  2. 2.What is the 11th term of the AP 18, 23, 28, 33, …? (a) 68 (b) 50 (c) 73 (d) 55
  3. 3.What is the 18th term of the AP 17, 20, 23, 26, …? (a) 51 (b) 71 (c) 68 (d) 54
  4. 4.What is the 13th term of the AP 14, 19, 24, 29, …? (a) 65 (b) 74 (c) 79 (d) 60
  5. 5.Which term of the AP 7, 14, 21, 28, … is 63? (a) 9th (b) 8th (c) 11th (d) 10th
  6. 6.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 25 (c) 15 (d) 9
  7. 7.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 210 (c) 462 (d) 231
  8. 8.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 31 (b) 266 (c) 147 (d) 133
  9. 9.What is the missing term in the AP 11, 18, ?, 32, 39? (a) 25 (b) 24 (c) 26 (d) 32
  10. 10.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 43 (b) 253 (c) 275 (d) 506
  11. 11.What is the 36th term of the AP 6, 12, 18, 24, …? (a) 210 (b) 222 (c) 217 (d) 216
  12. 12.What is the missing term in the AP 15, ?, 29, 36, 43? (a) 22 (b) 23 (c) 29 (d) 21
  13. 13.What is the sum of all the whole numbers from 1 to 41? (a) 820 (b) 862 (c) 1722 (d) 861
  14. 14.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 105 (b) 25 (c) 114 (d) 210
  15. 15.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 16 (b) 30 (c) 15 (d) 5
  16. 16.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 306 (d) 289
  17. 17.What is the missing term in the AP 11, ?, 23, 29, 35? (a) 18 (b) 23 (c) 16 (d) 17
  18. 18.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 26 (b) 81 (c) 162 (d) 96
  19. 19.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 666 (c) 630 (d) 648
  20. 20.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 324 (c) 35 (d) 171
  21. 21.What is the 10th term of the AP 4, 12, 20, 28, …? (a) 80 (b) 72 (c) 84 (d) 76
  22. 22.What is the 14th term of the AP 12, 16, 20, 24, …? (a) 64 (b) 68 (c) 56 (d) 52
  23. 23.What is the sum of the first 10 terms of the AP 5, 11, 17, …? (a) 320 (b) 640 (c) 350 (d) 59
  24. 24.What is the missing term in the AP 15, ?, 23, 27, 31? (a) 20 (b) 18 (c) 23 (d) 19
  25. 25.Which term of the AP 1, 7, 13, 19, … is 121? (a) 21st (b) 23rd (c) 22nd (d) 20th
  26. 26.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 378 (c) 406 (d) 812
  27. 27.What is the 10th term of the AP 3, 8, 13, 18, …? (a) 48 (b) 45 (c) 53 (d) 50
  28. 28.What is the 37th term of the AP 18, 21, 24, 27, …? (a) 108 (b) 126 (c) 129 (d) 111
  29. 29.What is the missing term in the AP 5, 10, 15, ?, 25? (a) 21 (b) 25 (c) 20 (d) 19
  30. 30.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 15 (b) 78 (c) 75 (d) 150
  31. 31.What is the 39th term of the AP 12, 14, 16, 18, …? (a) 78 (b) 76 (c) 88 (d) 90
  32. 32.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 182 (b) 22 (c) 94 (d) 91
  33. 33.Which term of the AP 20, 28, 36, 44, … is 156? (a) 18th (b) 19th (c) 20th (d) 17th
  34. 34.Which term of the AP 10, 17, 24, 31, … is 234? (a) 33rd (b) 34th (c) 32nd (d) 35th
  35. 35.What is the sum of all the whole numbers from 1 to 71? (a) 2557 (b) 5112 (c) 2556 (d) 2485
  36. 36.What is the 35th term of the AP 14, 23, 32, 41, …? (a) 320 (b) 306 (c) 315 (d) 329
  37. 37.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 182 (c) 25 (d) 91
  38. 38.What is the 15th term of the AP 9, 11, 13, 15, …? (a) 39 (b) 37 (c) 28 (d) 30
  39. 39.What is the 12th term of the AP 12, 17, 22, 27, …? (a) 60 (b) 67 (c) 55 (d) 72
  40. 40.Which term of the AP 5, 7, 9, 11, … is 79? (a) 38th (b) 37th (c) 39th (d) 40th

Answer key

  1. 4278
  2. 68
  3. 68
  4. 74
  5. 9th
  6. 25
  7. 231
  8. 133
  9. 25
  10. 253
  11. 216
  12. 22
  13. 861
  14. 105
  15. 15
  16. 289
  17. 17
  18. 81
  19. 666
  20. 324
  21. 76
  22. 64
  23. 320
  24. 19
  25. 21st
  26. 406
  27. 48
  28. 126
  29. 20
  30. 75
  31. 88
  32. 91
  33. 18th
  34. 33rd
  35. 2556
  36. 320
  37. 169
  38. 37
  39. 67
  40. 38th

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