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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 901 · 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 14th term of the AP 9, 17, 25, 33, …? (a) 104 (b) 113 (c) 112 (d) 121
  2. 2.What is the 13th term of the AP 2, 4, 6, 8, …? (a) 24 (b) 26 (c) 28 (d) 27
  3. 3.What is the sum of the first 9 terms of the AP 2, 5, 8, …? (a) 126 (b) 129 (c) 26 (d) 252
  4. 4.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 66 (c) 55 (d) 67
  5. 5.What is the 30th term of the AP 4, 8, 12, 16, …? (a) 121 (b) 120 (c) 116 (d) 124
  6. 6.What is the sum of all the whole numbers from 1 to 75? (a) 2775 (b) 2851 (c) 2850 (d) 5700
  7. 7.What is the missing term in the AP 10, ?, 24, 31, 38? (a) 24 (b) 16 (c) 17 (d) 18
  8. 8.What is the 11th term of the AP 20, 27, 34, 41, …? (a) 77 (b) 70 (c) 90 (d) 97
  9. 9.What is the 28th term of the AP 20, 23, 26, 29, …? (a) 81 (b) 101 (c) 84 (d) 104
  10. 10.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 85 (b) 80 (c) 26 (d) 160
  11. 11.What is the 10th term of the AP 14, 18, 22, 26, …? (a) 50 (b) 54 (c) 36 (d) 40
  12. 12.What is the sum of the first 8 terms of the AP 4, 8, 12, …? (a) 288 (b) 32 (c) 144 (d) 160
  13. 13.What is the 40th term of the AP 13, 21, 29, 37, …? (a) 320 (b) 312 (c) 325 (d) 333
  14. 14.What is the 19th term of the AP 5, 14, 23, 32, …? (a) 162 (b) 171 (c) 176 (d) 167
  15. 15.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1432 (c) 1431 (d) 1378
  16. 16.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 180 (b) 20 (c) 90 (d) 96
  17. 17.What is the missing term in the AP 8, 16, ?, 32, 40? (a) 24 (b) 25 (c) 23 (d) 32
  18. 18.What is the 29th term of the AP 9, 12, 15, 18, …? (a) 96 (b) 87 (c) 84 (d) 93
  19. 19.What is the missing term in the AP 3, 11, ?, 27, 35? (a) 27 (b) 18 (c) 20 (d) 19
  20. 20.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 361 (c) 37 (d) 380
  21. 21.Which term of the AP 17, 19, 21, 23, … is 73? (a) 30th (b) 29th (c) 31st (d) 28th
  22. 22.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 26 (b) 25 (c) 50 (d) 7
  23. 23.What is the 10th term of the AP 2, 11, 20, 29, …? (a) 92 (b) 90 (c) 81 (d) 83
  24. 24.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 45 (b) 90 (c) 55 (d) 17
  25. 25.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 77 (b) 12 (c) 154 (d) 78
  26. 26.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 529 (d) 552
  27. 27.What is the 20th term of the AP 9, 16, 23, 30, …? (a) 133 (b) 149 (c) 140 (d) 142
  28. 28.Which term of the AP 3, 10, 17, 24, … is 199? (a) 30th (b) 28th (c) 31st (d) 29th
  29. 29.What is the missing term in the AP 16, ?, 28, 34, 40? (a) 21 (b) 23 (c) 28 (d) 22
  30. 30.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 870 (d) 841
  31. 31.What is the 18th term of the AP 16, 25, 34, 43, …? (a) 153 (b) 162 (c) 178 (d) 169
  32. 32.What is the missing term in the AP 16, 18, ?, 22, 24? (a) 21 (b) 22 (c) 20 (d) 19
  33. 33.What is the sum of the first 8 terms of the AP 3, 7, 11, …? (a) 31 (b) 152 (c) 136 (d) 272
  34. 34.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 3741 (c) 7482 (d) 3655
  35. 35.What is the 35th term of the AP 20, 23, 26, 29, …? (a) 125 (b) 105 (c) 102 (d) 122
  36. 36.What is the missing term in the AP 13, 17, 21, ?, 29? (a) 26 (b) 24 (c) 29 (d) 25
  37. 37.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 84 (b) 48 (c) 42 (d) 12
  38. 38.What is the 12th term of the AP 9, 17, 25, 33, …? (a) 97 (b) 105 (c) 96 (d) 88
  39. 39.What is the sum of all the whole numbers from 1 to 35? (a) 595 (b) 631 (c) 1260 (d) 630
  40. 40.What is the sum of all the whole numbers from 1 to 91? (a) 4095 (b) 8372 (c) 4187 (d) 4186

Answer key

  1. 113
  2. 26
  3. 126
  4. 66
  5. 120
  6. 2850
  7. 17
  8. 90
  9. 101
  10. 80
  11. 50
  12. 144
  13. 325
  14. 167
  15. 1431
  16. 90
  17. 24
  18. 93
  19. 19
  20. 361
  21. 29th
  22. 25
  23. 83
  24. 45
  25. 77
  26. 529
  27. 142
  28. 29th
  29. 22
  30. 841
  31. 169
  32. 20
  33. 136
  34. 3741
  35. 122
  36. 25
  37. 42
  38. 97
  39. 630
  40. 4186

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