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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 967 · 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 73? (a) 5402 (b) 2702 (c) 2701 (d) 2628
  2. 2.What is the sum of the first 6 terms of the AP 8, 10, 12, …? (a) 156 (b) 18 (c) 84 (d) 78
  3. 3.What is the 25th term of the AP 11, 16, 21, 26, …? (a) 120 (b) 125 (c) 136 (d) 131
  4. 4.What is the 11th term of the AP 8, 17, 26, 35, …? (a) 98 (b) 99 (c) 90 (d) 107
  5. 5.What is the missing term in the AP 18, 20, 22, ?, 26? (a) 24 (b) 25 (c) 26 (d) 23
  6. 6.What is the 28th term of the AP 16, 22, 28, 34, …? (a) 168 (b) 184 (c) 178 (d) 162
  7. 7.What is the 34th term of the AP 4, 7, 10, 13, …? (a) 103 (b) 99 (c) 106 (d) 102
  8. 8.What is the missing term in the AP 7, 11, ?, 19, 23? (a) 14 (b) 19 (c) 15 (d) 16
  9. 9.What is the missing term in the AP 4, ?, 12, 16, 20? (a) 7 (b) 12 (c) 9 (d) 8
  10. 10.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 45 (c) 90 (d) 17
  11. 11.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 14 (b) 120 (c) 61 (d) 60
  12. 12.What is the 22nd term of the AP 9, 13, 17, 21, …? (a) 97 (b) 93 (c) 88 (d) 84
  13. 13.Which term of the AP 12, 20, 28, 36, … is 196? (a) 25th (b) 23rd (c) 26th (d) 24th
  14. 14.What is the 36th term of the AP 12, 20, 28, 36, …? (a) 300 (b) 288 (c) 292 (d) 280
  15. 15.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 120 (b) 30 (c) 105 (d) 210
  16. 16.What is the 11th term of the AP 5, 9, 13, 17, …? (a) 44 (b) 49 (c) 40 (d) 45
  17. 17.What is the missing term in the AP 12, 18, 24, ?, 36? (a) 29 (b) 36 (c) 31 (d) 30
  18. 18.What is the sum of the first 5 terms of the AP 1, 6, 11, …? (a) 60 (b) 55 (c) 110 (d) 21
  19. 19.What is the 25th term of the AP 12, 17, 22, 27, …? (a) 132 (b) 125 (c) 120 (d) 137
  20. 20.What is the 38th term of the AP 8, 14, 20, 26, …? (a) 222 (b) 228 (c) 236 (d) 230
  21. 21.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 120 (b) 22 (c) 60 (d) 65
  22. 22.What is the sum of all the whole numbers from 1 to 83? (a) 6972 (b) 3486 (c) 3487 (d) 3403
  23. 23.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 276 (b) 17 (c) 144 (d) 138
  24. 24.What is the missing term in the AP 20, 23, ?, 29, 32? (a) 27 (b) 25 (c) 29 (d) 26
  25. 25.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 25 (c) 182 (d) 91
  26. 26.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 10 (b) 41 (c) 80 (d) 40
  27. 27.What is the 21st term of the AP 12, 19, 26, 33, …? (a) 147 (b) 159 (c) 152 (d) 140
  28. 28.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 164 (b) 328 (c) 38 (d) 184
  29. 29.What is the 12th term of the AP 12, 20, 28, 36, …? (a) 108 (b) 100 (c) 96 (d) 88
  30. 30.Which term of the AP 2, 10, 18, 26, … is 218? (a) 29th (b) 27th (c) 28th (d) 30th
  31. 31.What is the sum of the first 7 terms of the AP 7, 12, 17, …? (a) 308 (b) 154 (c) 37 (d) 159
  32. 32.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 595 (c) 631 (d) 1260
  33. 33.What is the 13th term of the AP 3, 8, 13, 18, …? (a) 60 (b) 68 (c) 65 (d) 63
  34. 34.What is the sum of all the whole numbers from 1 to 57? (a) 1653 (b) 3306 (c) 1596 (d) 1654
  35. 35.What is the sum of all the whole numbers from 1 to 36? (a) 666 (b) 630 (c) 648 (d) 1332
  36. 36.What is the 18th term of the AP 8, 14, 20, 26, …? (a) 116 (b) 110 (c) 102 (d) 108
  37. 37.What is the 16th term of the AP 16, 24, 32, 40, …? (a) 128 (b) 136 (c) 120 (d) 144
  38. 38.What is the sum of the first 7 terms of the AP 4, 10, 16, …? (a) 40 (b) 308 (c) 175 (d) 154
  39. 39.What is the sum of the first 9 terms of the AP 8, 12, 16, …? (a) 234 (b) 40 (c) 216 (d) 432
  40. 40.What is the sum of all the whole numbers from 1 to 86? (a) 3655 (b) 3741 (c) 7482 (d) 3698

Answer key

  1. 2701
  2. 78
  3. 131
  4. 98
  5. 24
  6. 178
  7. 103
  8. 15
  9. 8
  10. 81
  11. 60
  12. 93
  13. 24th
  14. 292
  15. 105
  16. 45
  17. 30
  18. 55
  19. 132
  20. 230
  21. 60
  22. 3486
  23. 138
  24. 26
  25. 169
  26. 40
  27. 152
  28. 164
  29. 100
  30. 28th
  31. 154
  32. 630
  33. 63
  34. 1653
  35. 666
  36. 110
  37. 136
  38. 154
  39. 216
  40. 3741

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