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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 492 · 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 29? (a) 435 (b) 436 (c) 406 (d) 870
  2. 2.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 57 (c) 435 (d) 841
  3. 3.What is the 34th term of the AP 1, 7, 13, 19, …? (a) 198 (b) 204 (c) 205 (d) 199
  4. 4.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 182 (c) 91 (d) 25
  5. 5.What is the missing term in the AP 5, 10, ?, 20, 25? (a) 15 (b) 16 (c) 14 (d) 20
  6. 6.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2312 (c) 2278 (d) 2346
  7. 7.What is the 38th term of the AP 14, 19, 24, 29, …? (a) 204 (b) 185 (c) 199 (d) 190
  8. 8.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 676 (c) 351 (d) 702
  9. 9.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 341 (b) 682 (c) 346 (d) 56
  10. 10.What is the sum of all the whole numbers from 1 to 59? (a) 1770 (b) 3540 (c) 1711 (d) 1771
  11. 11.What is the missing term in the AP 18, ?, 36, 45, 54? (a) 26 (b) 36 (c) 27 (d) 28
  12. 12.What is the sum of all the whole numbers from 1 to 56? (a) 3192 (b) 1568 (c) 1540 (d) 1596
  13. 13.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 196 (b) 46 (c) 392 (d) 217
  14. 14.What is the 17th term of the AP 3, 5, 7, 9, …? (a) 37 (b) 34 (c) 32 (d) 35
  15. 15.What is the 23rd term of the AP 18, 21, 24, 27, …? (a) 69 (b) 84 (c) 66 (d) 87
  16. 16.What is the missing term in the AP 16, 22, ?, 34, 40? (a) 27 (b) 28 (c) 29 (d) 34
  17. 17.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 168 (b) 24 (c) 96 (d) 84
  18. 18.What is the 24th term of the AP 18, 21, 24, 27, …? (a) 72 (b) 69 (c) 87 (d) 90
  19. 19.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 13 (b) 82 (c) 162 (d) 81
  20. 20.What is the missing term in the AP 17, 23, ?, 35, 41? (a) 28 (b) 29 (c) 30 (d) 35
  21. 21.What is the missing term in the AP 20, 29, 38, ?, 56? (a) 48 (b) 56 (c) 47 (d) 46
  22. 22.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2557 (c) 2485 (d) 2556
  23. 23.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 29 (c) 240 (d) 120
  24. 24.Which term of the AP 11, 15, 19, 23, … is 59? (a) 12th (b) 13th (c) 14th (d) 15th
  25. 25.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 13 (b) 49 (c) 56 (d) 98
  26. 26.What is the 25th term of the AP 19, 21, 23, 25, …? (a) 69 (b) 48 (c) 50 (d) 67
  27. 27.What is the missing term in the AP 13, ?, 21, 25, 29? (a) 17 (b) 21 (c) 18 (d) 16
  28. 28.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 200 (b) 400 (c) 38 (d) 220
  29. 29.Which term of the AP 12, 19, 26, 33, … is 278? (a) 39th (b) 41st (c) 40th (d) 38th
  30. 30.Which term of the AP 16, 18, 20, 22, … is 32? (a) 8th (b) 9th (c) 16th (d) 10th
  31. 31.What is the 12th term of the AP 11, 15, 19, 23, …? (a) 44 (b) 55 (c) 48 (d) 59
  32. 32.Which term of the AP 17, 24, 31, 38, … is 192? (a) 27th (b) 28th (c) 26th (d) 25th
  33. 33.What is the missing term in the AP 1, ?, 19, 28, 37? (a) 10 (b) 11 (c) 19 (d) 9
  34. 34.What is the sum of the first 8 terms of the AP 5, 6, 7, …? (a) 68 (b) 136 (c) 12 (d) 72
  35. 35.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 729 (d) 378
  36. 36.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 25 (d) 30
  37. 37.Which term of the AP 4, 10, 16, 22, … is 76? (a) 14th (b) 12th (c) 13th (d) 15th
  38. 38.What is the sum of the first 12 terms of the AP 5, 9, 13, …? (a) 648 (b) 348 (c) 49 (d) 324
  39. 39.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 30 (b) 50 (c) 9 (d) 25
  40. 40.What is the missing term in the AP 7, 15, ?, 31, 39? (a) 22 (b) 24 (c) 23 (d) 31

Answer key

  1. 435
  2. 841
  3. 199
  4. 169
  5. 15
  6. 2346
  7. 199
  8. 676
  9. 341
  10. 1770
  11. 27
  12. 1596
  13. 196
  14. 35
  15. 84
  16. 28
  17. 84
  18. 87
  19. 81
  20. 29
  21. 47
  22. 2556
  23. 225
  24. 13th
  25. 49
  26. 67
  27. 17
  28. 200
  29. 39th
  30. 9th
  31. 55
  32. 26th
  33. 10
  34. 68
  35. 729
  36. 25
  37. 13th
  38. 324
  39. 25
  40. 23

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