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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 37 · 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 87? (a) 3741 (b) 3828 (c) 3829 (d) 7656
  2. 2.What is the missing term in the AP 10, 12, 14, ?, 18? (a) 17 (b) 15 (c) 16 (d) 18
  3. 3.What is the 20th term of the AP 7, 9, 11, 13, …? (a) 38 (b) 40 (c) 47 (d) 45
  4. 4.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 27 (b) 126 (c) 129 (d) 252
  5. 5.What is the sum of all the whole numbers from 1 to 26? (a) 338 (b) 325 (c) 702 (d) 351
  6. 6.What is the 10th term of the AP 4, 11, 18, 25, …? (a) 67 (b) 74 (c) 70 (d) 63
  7. 7.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 28 (d) 56
  8. 8.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 77 (b) 154 (c) 17 (d) 84
  9. 9.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 17 (b) 216 (c) 112 (d) 108
  10. 10.Which term of the AP 7, 10, 13, 16, … is 100? (a) 33rd (b) 31st (c) 34th (d) 32nd
  11. 11.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 42 (b) 6 (c) 21 (d) 24
  12. 12.What is the 40th term of the AP 13, 18, 23, 28, …? (a) 213 (b) 208 (c) 195 (d) 200
  13. 13.Which term of the AP 15, 19, 23, 27, … is 155? (a) 35th (b) 38th (c) 37th (d) 36th
  14. 14.What is the missing term in the AP 9, 16, 23, ?, 37? (a) 37 (b) 29 (c) 30 (d) 31
  15. 15.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 756 (c) 729 (d) 53
  16. 16.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 192 (b) 31 (c) 96 (d) 114
  17. 17.What is the sum of the first 10 terms of the AP 7, 10, 13, …? (a) 205 (b) 220 (c) 34 (d) 410
  18. 18.What is the 15th term of the AP 9, 17, 25, 33, …? (a) 112 (b) 129 (c) 120 (d) 121
  19. 19.What is the missing term in the AP 18, 27, 36, ?, 54? (a) 44 (b) 54 (c) 46 (d) 45
  20. 20.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2080 (c) 2145 (d) 2146
  21. 21.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 4950 (c) 9900 (d) 4851
  22. 22.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 105 (c) 210 (d) 91
  23. 23.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 21 (b) 242 (c) 121 (d) 132
  24. 24.What is the missing term in the AP 12, 15, ?, 21, 24? (a) 19 (b) 17 (c) 18 (d) 21
  25. 25.What is the 25th term of the AP 18, 23, 28, 33, …? (a) 143 (b) 138 (c) 125 (d) 120
  26. 26.What is the 22nd term of the AP 1, 5, 9, 13, …? (a) 88 (b) 84 (c) 89 (d) 85
  27. 27.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 360 (b) 32 (c) 183 (d) 180
  28. 28.What is the 20th term of the AP 4, 12, 20, 28, …? (a) 152 (b) 164 (c) 156 (d) 160
  29. 29.What is the 25th term of the AP 5, 13, 21, 29, …? (a) 197 (b) 205 (c) 192 (d) 200
  30. 30.Which term of the AP 15, 23, 31, 39, … is 247? (a) 30th (b) 29th (c) 31st (d) 32nd
  31. 31.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 187 (b) 26 (c) 176 (d) 352
  32. 32.What is the 11th term of the AP 1, 8, 15, 22, …? (a) 71 (b) 77 (c) 70 (d) 78
  33. 33.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 42 (c) 11 (d) 21
  34. 34.What is the 18th term of the AP 20, 27, 34, 41, …? (a) 126 (b) 139 (c) 146 (d) 119
  35. 35.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 28 (b) 29 (c) 56 (d) 7
  36. 36.Which term of the AP 17, 21, 25, 29, … is 81? (a) 17th (b) 18th (c) 16th (d) 19th
  37. 37.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 15 (b) 16 (c) 22 (d) 14
  38. 38.What is the sum of all the whole numbers from 1 to 82? (a) 3321 (b) 3362 (c) 3403 (d) 6806
  39. 39.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 31 (b) 41 (c) 32 (d) 33
  40. 40.What is the 20th term of the AP 2, 4, 6, 8, …? (a) 40 (b) 41 (c) 38 (d) 42

Answer key

  1. 3828
  2. 16
  3. 45
  4. 126
  5. 351
  6. 67
  7. 49
  8. 77
  9. 108
  10. 32nd
  11. 21
  12. 208
  13. 36th
  14. 30
  15. 729
  16. 96
  17. 205
  18. 121
  19. 45
  20. 2145
  21. 4950
  22. 105
  23. 121
  24. 18
  25. 138
  26. 85
  27. 180
  28. 156
  29. 197
  30. 30th
  31. 176
  32. 71
  33. 36
  34. 139
  35. 28
  36. 17th
  37. 15
  38. 3403
  39. 32
  40. 40

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