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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 420 · 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 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 36 (c) 15 (d) 64
  2. 2.What is the sum of all the whole numbers from 1 to 72? (a) 2556 (b) 2592 (c) 2628 (d) 5256
  3. 3.Which term of the AP 3, 7, 11, 15, … is 147? (a) 38th (b) 39th (c) 36th (d) 37th
  4. 4.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 529 (c) 45 (d) 552
  5. 5.What is the 17th term of the AP 16, 25, 34, 43, …? (a) 160 (b) 169 (c) 153 (d) 144
  6. 6.Which term of the AP 20, 22, 24, 26, … is 68? (a) 24th (b) 34th (c) 26th (d) 25th
  7. 7.What is the missing term in the AP 13, 18, ?, 28, 33? (a) 22 (b) 24 (c) 23 (d) 28
  8. 8.What is the sum of the first 10 terms of the AP 10, 14, 18, …? (a) 46 (b) 280 (c) 560 (d) 300
  9. 9.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 31 (c) 136 (d) 256
  10. 10.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 33 (b) 147 (c) 161 (d) 294
  11. 11.What is the missing term in the AP 4, 12, 20, ?, 36? (a) 29 (b) 36 (c) 27 (d) 28
  12. 12.Which term of the AP 18, 24, 30, 36, … is 222? (a) 34th (b) 36th (c) 37th (d) 35th
  13. 13.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 135 (b) 22 (c) 252 (d) 126
  14. 14.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 289 (c) 33 (d) 306
  15. 15.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 264 (b) 51 (c) 240 (d) 480
  16. 16.What is the missing term in the AP 18, 21, ?, 27, 30? (a) 27 (b) 25 (c) 23 (d) 24
  17. 17.What is the 10th term of the AP 7, 10, 13, 16, …? (a) 37 (b) 30 (c) 27 (d) 34
  18. 18.What is the 16th term of the AP 19, 24, 29, 34, …? (a) 75 (b) 99 (c) 94 (d) 80
  19. 19.What is the sum of the first 10 terms of the AP 1, 5, 9, …? (a) 210 (b) 37 (c) 190 (d) 380
  20. 20.What is the 13th term of the AP 8, 15, 22, 29, …? (a) 92 (b) 91 (c) 84 (d) 99
  21. 21.What is the 28th term of the AP 6, 9, 12, 15, …? (a) 90 (b) 84 (c) 81 (d) 87
  22. 22.What is the 18th term of the AP 5, 10, 15, 20, …? (a) 95 (b) 90 (c) 91 (d) 85
  23. 23.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 342 (c) 324 (d) 171
  24. 24.What is the 16th term of the AP 4, 9, 14, 19, …? (a) 84 (b) 79 (c) 75 (d) 80
  25. 25.What is the sum of all the whole numbers from 1 to 51? (a) 1327 (b) 1275 (c) 1326 (d) 2652
  26. 26.What is the 11th term of the AP 5, 12, 19, 26, …? (a) 70 (b) 75 (c) 82 (d) 77
  27. 27.What is the 10th term of the AP 14, 17, 20, 23, …? (a) 27 (b) 44 (c) 41 (d) 30
  28. 28.What is the missing term in the AP 9, 12, ?, 18, 21? (a) 15 (b) 14 (c) 16 (d) 18
  29. 29.What is the missing term in the AP 10, 18, ?, 34, 42? (a) 25 (b) 27 (c) 34 (d) 26
  30. 30.What is the sum of all the whole numbers from 1 to 83? (a) 3403 (b) 3487 (c) 6972 (d) 3486
  31. 31.What is the 39th term of the AP 15, 24, 33, 42, …? (a) 342 (b) 351 (c) 366 (d) 357
  32. 32.What is the 29th term of the AP 1, 5, 9, 13, …? (a) 117 (b) 112 (c) 113 (d) 116
  33. 33.What is the 29th term of the AP 14, 20, 26, 32, …? (a) 174 (b) 188 (c) 182 (d) 168
  34. 34.What is the missing term in the AP 14, 20, 26, ?, 38? (a) 32 (b) 31 (c) 33 (d) 38
  35. 35.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 378 (c) 729 (d) 756
  36. 36.What is the 16th term of the AP 3, 6, 9, 12, …? (a) 51 (b) 49 (c) 45 (d) 48
  37. 37.What is the 34th term of the AP 1, 10, 19, 28, …? (a) 306 (b) 307 (c) 297 (d) 298
  38. 38.What is the 11th term of the AP 18, 25, 32, 39, …? (a) 88 (b) 77 (c) 95 (d) 70
  39. 39.Which term of the AP 5, 7, 9, 11, … is 27? (a) 11th (b) 13th (c) 14th (d) 12th
  40. 40.Which term of the AP 9, 16, 23, 30, … is 79? (a) 12th (b) 11th (c) 13th (d) 10th

Answer key

  1. 64
  2. 2628
  3. 37th
  4. 529
  5. 160
  6. 25th
  7. 23
  8. 280
  9. 256
  10. 147
  11. 28
  12. 35th
  13. 126
  14. 289
  15. 240
  16. 24
  17. 34
  18. 94
  19. 190
  20. 92
  21. 87
  22. 90
  23. 324
  24. 79
  25. 1326
  26. 75
  27. 41
  28. 15
  29. 26
  30. 3486
  31. 357
  32. 113
  33. 182
  34. 32
  35. 729
  36. 48
  37. 298
  38. 88
  39. 12th
  40. 11th

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