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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 930 · 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 missing term in the AP 2, ?, 20, 29, 38? (a) 10 (b) 11 (c) 12 (d) 20
  2. 2.What is the sum of the first 10 terms of the AP 4, 9, 14, …? (a) 49 (b) 265 (c) 290 (d) 530
  3. 3.What is the 24th term of the AP 17, 20, 23, 26, …? (a) 72 (b) 69 (c) 89 (d) 86
  4. 4.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 64 (c) 15 (d) 72
  5. 5.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 13 (b) 12 (c) 15 (d) 14
  6. 6.What is the 17th term of the AP 5, 11, 17, 23, …? (a) 101 (b) 96 (c) 102 (d) 107
  7. 7.What is the missing term in the AP 11, 13, ?, 17, 19? (a) 16 (b) 17 (c) 15 (d) 14
  8. 8.Which term of the AP 5, 9, 13, 17, … is 41? (a) 12th (b) 9th (c) 11th (d) 10th
  9. 9.What is the missing term in the AP 8, 13, ?, 23, 28? (a) 19 (b) 17 (c) 23 (d) 18
  10. 10.What is the missing term in the AP 17, 22, ?, 32, 37? (a) 28 (b) 26 (c) 27 (d) 32
  11. 11.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 144 (c) 156 (d) 78
  12. 12.What is the missing term in the AP 13, 15, ?, 19, 21? (a) 18 (b) 17 (c) 19 (d) 16
  13. 13.What is the 17th term of the AP 4, 8, 12, 16, …? (a) 72 (b) 64 (c) 69 (d) 68
  14. 14.What is the sum of all the whole numbers from 1 to 70? (a) 2485 (b) 2450 (c) 4970 (d) 2415
  15. 15.What is the 26th term of the AP 20, 26, 32, 38, …? (a) 156 (b) 170 (c) 176 (d) 150
  16. 16.What is the 20th term of the AP 1, 4, 7, 10, …? (a) 61 (b) 57 (c) 58 (d) 60
  17. 17.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 240 (d) 225
  18. 18.What is the sum of all the whole numbers from 1 to 76? (a) 5852 (b) 2850 (c) 2926 (d) 2888
  19. 19.Which term of the AP 16, 20, 24, 28, … is 120? (a) 30th (b) 28th (c) 27th (d) 26th
  20. 20.What is the 17th term of the AP 6, 10, 14, 18, …? (a) 68 (b) 64 (c) 74 (d) 70
  21. 21.Which term of the AP 15, 21, 27, 33, … is 99? (a) 14th (b) 16th (c) 17th (d) 15th
  22. 22.What is the 34th term of the AP 20, 28, 36, 44, …? (a) 284 (b) 292 (c) 264 (d) 272
  23. 23.What is the 32nd term of the AP 6, 13, 20, 27, …? (a) 217 (b) 230 (c) 223 (d) 224
  24. 24.What is the missing term in the AP 4, 8, ?, 16, 20? (a) 16 (b) 12 (c) 13 (d) 11
  25. 25.What is the sum of all the whole numbers from 1 to 74? (a) 2701 (b) 2738 (c) 2775 (d) 5550
  26. 26.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 110 (b) 10 (c) 60 (d) 55
  27. 27.What is the missing term in the AP 2, 6, 10, ?, 18? (a) 14 (b) 15 (c) 13 (d) 18
  28. 28.What is the 17th term of the AP 12, 15, 18, 21, …? (a) 48 (b) 51 (c) 63 (d) 60
  29. 29.What is the 22nd term of the AP 7, 14, 21, 28, …? (a) 154 (b) 155 (c) 161 (d) 147
  30. 30.What is the 35th term of the AP 7, 11, 15, 19, …? (a) 136 (b) 147 (c) 140 (d) 143
  31. 31.What is the missing term in the AP 2, ?, 8, 11, 14? (a) 5 (b) 4 (c) 8 (d) 6
  32. 32.What is the 31st term of the AP 9, 16, 23, 30, …? (a) 217 (b) 219 (c) 210 (d) 226
  33. 33.What is the 30th term of the AP 10, 14, 18, 22, …? (a) 130 (b) 116 (c) 126 (d) 120
  34. 34.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 48 (b) 12 (c) 42 (d) 84
  35. 35.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 110 (c) 19 (d) 55
  36. 36.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 150 (b) 75 (c) 85 (d) 23
  37. 37.What is the 35th term of the AP 15, 21, 27, 33, …? (a) 210 (b) 204 (c) 219 (d) 225
  38. 38.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 13 (c) 56 (d) 28
  39. 39.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 702 (c) 676 (d) 351
  40. 40.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 462 (c) 231 (d) 232

Answer key

  1. 11
  2. 265
  3. 86
  4. 64
  5. 13
  6. 101
  7. 15
  8. 10th
  9. 18
  10. 27
  11. 144
  12. 17
  13. 68
  14. 2485
  15. 170
  16. 58
  17. 225
  18. 2926
  19. 27th
  20. 70
  21. 15th
  22. 284
  23. 223
  24. 12
  25. 2775
  26. 55
  27. 14
  28. 60
  29. 154
  30. 143
  31. 5
  32. 219
  33. 126
  34. 42
  35. 100
  36. 75
  37. 219
  38. 49
  39. 676
  40. 231

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