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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 916 · 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 11 terms of the AP 1, 7, 13, …? (a) 341 (b) 374 (c) 61 (d) 682
  2. 2.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 12 (b) 14 (c) 13 (d) 16
  3. 3.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 277 (c) 552 (d) 276
  4. 4.What is the missing term in the AP 14, ?, 26, 32, 38? (a) 26 (b) 20 (c) 19 (d) 21
  5. 5.What is the missing term in the AP 7, ?, 25, 34, 43? (a) 15 (b) 16 (c) 17 (d) 25
  6. 6.What is the 38th term of the AP 12, 15, 18, 21, …? (a) 111 (b) 126 (c) 123 (d) 114
  7. 7.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 300 (c) 325 (d) 650
  8. 8.What is the 36th term of the AP 16, 23, 30, 37, …? (a) 252 (b) 268 (c) 261 (d) 245
  9. 9.What is the sum of all the whole numbers from 1 to 81? (a) 3240 (b) 6642 (c) 3322 (d) 3321
  10. 10.What is the 40th term of the AP 2, 5, 8, 11, …? (a) 120 (b) 117 (c) 122 (d) 119
  11. 11.What is the 16th term of the AP 3, 10, 17, 24, …? (a) 105 (b) 115 (c) 112 (d) 108
  12. 12.What is the 14th term of the AP 15, 19, 23, 27, …? (a) 71 (b) 52 (c) 56 (d) 67
  13. 13.What is the 32nd term of the AP 7, 11, 15, 19, …? (a) 131 (b) 135 (c) 128 (d) 124
  14. 14.What is the sum of all the whole numbers from 1 to 24? (a) 300 (b) 288 (c) 600 (d) 276
  15. 15.What is the 12th term of the AP 4, 11, 18, 25, …? (a) 84 (b) 88 (c) 81 (d) 77
  16. 16.What is the sum of all the whole numbers from 1 to 34? (a) 561 (b) 595 (c) 1190 (d) 578
  17. 17.What is the sum of all the whole numbers from 1 to 60? (a) 3660 (b) 1800 (c) 1830 (d) 1770
  18. 18.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 92 (b) 96 (c) 15 (d) 184
  19. 19.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 100 (c) 110 (d) 55
  20. 20.What is the 27th term of the AP 8, 11, 14, 17, …? (a) 78 (b) 86 (c) 89 (d) 81
  21. 21.Which term of the AP 7, 13, 19, 25, … is 217? (a) 36th (b) 37th (c) 35th (d) 38th
  22. 22.What is the 10th term of the AP 16, 22, 28, 34, …? (a) 54 (b) 76 (c) 70 (d) 60
  23. 23.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 26 (b) 7 (c) 25 (d) 50
  24. 24.What is the missing term in the AP 12, 21, ?, 39, 48? (a) 31 (b) 39 (c) 30 (d) 29
  25. 25.What is the missing term in the AP 17, ?, 31, 38, 45? (a) 25 (b) 31 (c) 23 (d) 24
  26. 26.What is the 37th term of the AP 7, 10, 13, 16, …? (a) 115 (b) 111 (c) 118 (d) 108
  27. 27.Which term of the AP 1, 6, 11, 16, … is 141? (a) 29th (b) 28th (c) 31st (d) 30th
  28. 28.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 120 (b) 14 (c) 60 (d) 61
  29. 29.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 156 (d) 144
  30. 30.What is the 22nd term of the AP 7, 13, 19, 25, …? (a) 132 (b) 133 (c) 126 (d) 139
  31. 31.What is the 36th term of the AP 12, 20, 28, 36, …? (a) 300 (b) 280 (c) 288 (d) 292
  32. 32.What is the 19th term of the AP 19, 28, 37, 46, …? (a) 181 (b) 162 (c) 190 (d) 171
  33. 33.What is the missing term in the AP 3, 12, 21, ?, 39? (a) 39 (b) 31 (c) 29 (d) 30
  34. 34.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 210 (b) 27 (c) 119 (d) 105
  35. 35.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 24 (b) 23 (c) 26 (d) 22
  36. 36.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 21 (b) 120 (c) 224 (d) 112
  37. 37.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 756 (c) 378 (d) 53
  38. 38.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 31 (b) 266 (c) 133 (d) 147
  39. 39.What is the 20th term of the AP 14, 23, 32, 41, …? (a) 194 (b) 180 (c) 171 (d) 185
  40. 40.What is the sum of all the whole numbers from 1 to 35? (a) 1260 (b) 595 (c) 630 (d) 631

Answer key

  1. 341
  2. 13
  3. 276
  4. 20
  5. 16
  6. 123
  7. 325
  8. 261
  9. 3321
  10. 119
  11. 108
  12. 67
  13. 131
  14. 300
  15. 81
  16. 595
  17. 1830
  18. 92
  19. 100
  20. 86
  21. 36th
  22. 70
  23. 25
  24. 30
  25. 24
  26. 115
  27. 29th
  28. 60
  29. 144
  30. 133
  31. 292
  32. 181
  33. 30
  34. 105
  35. 23
  36. 112
  37. 729
  38. 133
  39. 185
  40. 630

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