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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 964 · 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 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 33 (c) 306 (d) 153
  2. 2.What is the sum of all the whole numbers from 1 to 56? (a) 1540 (b) 3192 (c) 1568 (d) 1596
  3. 3.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 45 (d) 17
  4. 4.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 105 (c) 196 (d) 27
  5. 5.What is the 18th term of the AP 11, 17, 23, 29, …? (a) 108 (b) 119 (c) 113 (d) 102
  6. 6.What is the 14th term of the AP 3, 9, 15, 21, …? (a) 78 (b) 84 (c) 81 (d) 87
  7. 7.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 240 (b) 45 (c) 440 (d) 220
  8. 8.What is the 22nd term of the AP 10, 16, 22, 28, …? (a) 142 (b) 136 (c) 132 (d) 126
  9. 9.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 368 (b) 726 (c) 363 (d) 58
  10. 10.What is the 15th term of the AP 13, 18, 23, 28, …? (a) 75 (b) 88 (c) 70 (d) 83
  11. 11.What is the 39th term of the AP 12, 17, 22, 27, …? (a) 207 (b) 190 (c) 195 (d) 202
  12. 12.What is the sum of all the whole numbers from 1 to 40? (a) 1640 (b) 780 (c) 820 (d) 800
  13. 13.What is the missing term in the AP 1, 4, 7, ?, 13? (a) 10 (b) 11 (c) 13 (d) 9
  14. 14.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 372 (b) 186 (c) 192 (d) 21
  15. 15.What is the 15th term of the AP 7, 13, 19, 25, …? (a) 84 (b) 97 (c) 90 (d) 91
  16. 16.What is the sum of the first 6 terms of the AP 10, 15, 20, …? (a) 135 (b) 35 (c) 150 (d) 270
  17. 17.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 378 (d) 729
  18. 18.What is the 32nd term of the AP 19, 26, 33, 40, …? (a) 224 (b) 217 (c) 243 (d) 236
  19. 19.What is the 18th term of the AP 6, 9, 12, 15, …? (a) 51 (b) 54 (c) 57 (d) 60
  20. 20.Which term of the AP 3, 9, 15, 21, … is 99? (a) 19th (b) 17th (c) 16th (d) 18th
  21. 21.Which term of the AP 8, 15, 22, 29, … is 78? (a) 10th (b) 11th (c) 13th (d) 12th
  22. 22.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 140 (b) 75 (c) 70 (d) 18
  23. 23.What is the sum of all the whole numbers from 1 to 23? (a) 277 (b) 552 (c) 253 (d) 276
  24. 24.What is the sum of the first 11 terms of the AP 5, 11, 17, …? (a) 770 (b) 418 (c) 65 (d) 385
  25. 25.What is the sum of all the whole numbers from 1 to 75? (a) 2775 (b) 2850 (c) 5700 (d) 2851
  26. 26.What is the 31st term of the AP 18, 22, 26, 30, …? (a) 124 (b) 120 (c) 138 (d) 142
  27. 27.What is the missing term in the AP 1, 10, 19, ?, 37? (a) 37 (b) 28 (c) 27 (d) 29
  28. 28.What is the 29th term of the AP 14, 20, 26, 32, …? (a) 182 (b) 188 (c) 174 (d) 168
  29. 29.Which term of the AP 7, 9, 11, 13, … is 73? (a) 33rd (b) 34th (c) 35th (d) 36th
  30. 30.What is the sum of all the whole numbers from 1 to 73? (a) 2628 (b) 5402 (c) 2702 (d) 2701
  31. 31.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 56 (b) 104 (c) 10 (d) 52
  32. 32.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 200 (b) 380 (c) 190 (d) 28
  33. 33.What is the 12th term of the AP 1, 10, 19, 28, …? (a) 109 (b) 108 (c) 99 (d) 100
  34. 34.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 12 (b) 9 (c) 10 (d) 8
  35. 35.What is the missing term in the AP 8, 12, 16, ?, 24? (a) 20 (b) 21 (c) 24 (d) 19
  36. 36.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 231 (c) 232 (d) 462
  37. 37.What is the sum of the first 7 terms of the AP 1, 4, 7, …? (a) 70 (b) 140 (c) 19 (d) 73
  38. 38.What is the missing term in the AP 3, 10, ?, 24, 31? (a) 16 (b) 17 (c) 24 (d) 18
  39. 39.What is the 31st term of the AP 7, 16, 25, 34, …? (a) 286 (b) 277 (c) 279 (d) 270
  40. 40.What is the 28th term of the AP 14, 18, 22, 26, …? (a) 126 (b) 108 (c) 122 (d) 112

Answer key

  1. 289
  2. 1596
  3. 81
  4. 196
  5. 113
  6. 81
  7. 220
  8. 136
  9. 363
  10. 83
  11. 202
  12. 820
  13. 10
  14. 186
  15. 91
  16. 135
  17. 729
  18. 236
  19. 57
  20. 17th
  21. 11th
  22. 70
  23. 276
  24. 385
  25. 2850
  26. 138
  27. 28
  28. 182
  29. 34th
  30. 2701
  31. 52
  32. 190
  33. 100
  34. 9
  35. 20
  36. 231
  37. 70
  38. 17
  39. 277
  40. 122

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