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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 358 · 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 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 37 (c) 190 (d) 361
  2. 2.What is the sum of all the whole numbers from 1 to 75? (a) 2775 (b) 5700 (c) 2850 (d) 2851
  3. 3.What is the sum of all the whole numbers from 1 to 50? (a) 1250 (b) 1275 (c) 1225 (d) 2550
  4. 4.What is the 24th term of the AP 16, 20, 24, 28, …? (a) 96 (b) 112 (c) 108 (d) 92
  5. 5.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 99 (b) 19 (c) 108 (d) 198
  6. 6.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 306 (c) 153 (d) 154
  7. 7.What is the sum of all the whole numbers from 1 to 56? (a) 1540 (b) 1568 (c) 3192 (d) 1596
  8. 8.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 154 (b) 17 (c) 84 (d) 77
  9. 9.What is the sum of all the whole numbers from 1 to 61? (a) 3782 (b) 1891 (c) 1892 (d) 1830
  10. 10.What is the 30th term of the AP 17, 25, 33, 41, …? (a) 249 (b) 257 (c) 232 (d) 240
  11. 11.What is the missing term in the AP 10, ?, 22, 28, 34? (a) 15 (b) 17 (c) 22 (d) 16
  12. 12.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 408 (b) 67 (c) 444 (d) 816
  13. 13.Which term of the AP 13, 17, 21, 25, … is 133? (a) 33rd (b) 32nd (c) 31st (d) 30th
  14. 14.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 406 (c) 812 (d) 784
  15. 15.What is the sum of all the whole numbers from 1 to 86? (a) 3741 (b) 7482 (c) 3655 (d) 3698
  16. 16.Which term of the AP 6, 11, 16, 21, … is 86? (a) 16th (b) 18th (c) 17th (d) 19th
  17. 17.What is the 16th term of the AP 11, 14, 17, 20, …? (a) 45 (b) 56 (c) 48 (d) 59
  18. 18.What is the sum of the first 7 terms of the AP 5, 8, 11, …? (a) 98 (b) 101 (c) 23 (d) 196
  19. 19.What is the sum of the first 7 terms of the AP 4, 9, 14, …? (a) 266 (b) 138 (c) 34 (d) 133
  20. 20.What is the 26th term of the AP 9, 12, 15, 18, …? (a) 75 (b) 84 (c) 78 (d) 87
  21. 21.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 25 (d) 15
  22. 22.What is the 22nd term of the AP 6, 9, 12, 15, …? (a) 66 (b) 72 (c) 69 (d) 63
  23. 23.What is the 23rd term of the AP 3, 5, 7, 9, …? (a) 46 (b) 44 (c) 47 (d) 49
  24. 24.What is the 29th term of the AP 17, 22, 27, 32, …? (a) 162 (b) 145 (c) 140 (d) 157
  25. 25.What is the missing term in the AP 3, 5, ?, 9, 11? (a) 7 (b) 6 (c) 8 (d) 9
  26. 26.Which term of the AP 13, 16, 19, 22, … is 61? (a) 16th (b) 19th (c) 18th (d) 17th
  27. 27.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 23 (b) 136 (c) 128 (d) 256
  28. 28.What is the missing term in the AP 20, ?, 24, 26, 28? (a) 24 (b) 22 (c) 23 (d) 21
  29. 29.Which term of the AP 11, 13, 15, 17, … is 77? (a) 35th (b) 34th (c) 33rd (d) 36th
  30. 30.What is the missing term in the AP 12, 20, ?, 36, 44? (a) 27 (b) 36 (c) 28 (d) 29
  31. 31.What is the sum of all the whole numbers from 1 to 34? (a) 578 (b) 595 (c) 561 (d) 1190
  32. 32.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 132 (d) 66
  33. 33.What is the 30th term of the AP 12, 18, 24, 30, …? (a) 174 (b) 186 (c) 180 (d) 192
  34. 34.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 81 (b) 90 (c) 162 (d) 17
  35. 35.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 78 (c) 66 (d) 156
  36. 36.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 40 (b) 36 (c) 72 (d) 8
  37. 37.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 56 (b) 10 (c) 52 (d) 104
  38. 38.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 49 (d) 28
  39. 39.What is the 30th term of the AP 16, 21, 26, 31, …? (a) 150 (b) 145 (c) 166 (d) 161
  40. 40.What is the missing term in the AP 8, 12, ?, 20, 24? (a) 17 (b) 16 (c) 20 (d) 15

Answer key

  1. 361
  2. 2850
  3. 1275
  4. 108
  5. 99
  6. 153
  7. 1596
  8. 77
  9. 1891
  10. 249
  11. 16
  12. 408
  13. 31st
  14. 784
  15. 3741
  16. 17th
  17. 56
  18. 98
  19. 133
  20. 84
  21. 25
  22. 69
  23. 47
  24. 157
  25. 7
  26. 17th
  27. 128
  28. 22
  29. 34th
  30. 28
  31. 595
  32. 121
  33. 186
  34. 81
  35. 78
  36. 36
  37. 52
  38. 49
  39. 161
  40. 16

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