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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 613 · 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 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 900 (c) 930 (d) 465
  2. 2.Which term of the AP 3, 6, 9, 12, … is 27? (a) 11th (b) 8th (c) 10th (d) 9th
  3. 3.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 110 (b) 58 (c) 55 (d) 17
  4. 4.Which term of the AP 20, 23, 26, 29, … is 62? (a) 16th (b) 15th (c) 17th (d) 14th
  5. 5.What is the 38th term of the AP 12, 14, 16, 18, …? (a) 76 (b) 88 (c) 86 (d) 74
  6. 6.Which term of the AP 4, 8, 12, 16, … is 132? (a) 34th (b) 35th (c) 33rd (d) 32nd
  7. 7.What is the 13th term of the AP 14, 20, 26, 32, …? (a) 92 (b) 72 (c) 78 (d) 86
  8. 8.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 441 (c) 41 (d) 462
  9. 9.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 120 (b) 63 (c) 60 (d) 18
  10. 10.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 552 (d) 529
  11. 11.Which term of the AP 15, 22, 29, 36, … is 92? (a) 12th (b) 11th (c) 14th (d) 13th
  12. 12.What is the 13th term of the AP 9, 16, 23, 30, …? (a) 100 (b) 84 (c) 91 (d) 93
  13. 13.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 130 (b) 70 (c) 23 (d) 65
  14. 14.What is the 14th term of the AP 15, 18, 21, 24, …? (a) 54 (b) 42 (c) 39 (d) 57
  15. 15.What is the missing term in the AP 20, ?, 26, 29, 32? (a) 26 (b) 24 (c) 22 (d) 23
  16. 16.What is the 26th term of the AP 19, 24, 29, 34, …? (a) 130 (b) 149 (c) 125 (d) 144
  17. 17.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 1056 (c) 496 (d) 528
  18. 18.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 55 (b) 279 (c) 306 (d) 558
  19. 19.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 13 (b) 96 (c) 48 (d) 54
  20. 20.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 14 (b) 63 (c) 112 (d) 56
  21. 21.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 50 (b) 9 (c) 30 (d) 25
  22. 22.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 5 (b) 8 (c) 7 (d) 6
  23. 23.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 650 (c) 625 (d) 325
  24. 24.Which term of the AP 1, 9, 17, 25, … is 161? (a) 23rd (b) 20th (c) 22nd (d) 21st
  25. 25.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 190 (b) 31 (c) 350 (d) 175
  26. 26.What is the 38th term of the AP 10, 12, 14, 16, …? (a) 74 (b) 84 (c) 86 (d) 76
  27. 27.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 13 (b) 88 (c) 89 (d) 176
  28. 28.What is the 22nd term of the AP 9, 18, 27, 36, …? (a) 207 (b) 199 (c) 189 (d) 198
  29. 29.What is the sum of all the whole numbers from 1 to 62? (a) 3906 (b) 1891 (c) 1922 (d) 1953
  30. 30.What is the missing term in the AP 2, ?, 12, 17, 22? (a) 12 (b) 6 (c) 7 (d) 8
  31. 31.What is the missing term in the AP 13, 17, ?, 25, 29? (a) 22 (b) 20 (c) 25 (d) 21
  32. 32.Which term of the AP 1, 10, 19, 28, … is 127? (a) 17th (b) 15th (c) 16th (d) 14th
  33. 33.What is the sum of the first 10 terms of the AP 5, 9, 13, …? (a) 460 (b) 250 (c) 41 (d) 230
  34. 34.Which term of the AP 16, 23, 30, 37, … is 184? (a) 27th (b) 24th (c) 26th (d) 25th
  35. 35.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 676 (c) 51 (d) 702
  36. 36.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 140 (b) 16 (c) 77 (d) 70
  37. 37.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 200 (b) 105 (c) 100 (d) 30
  38. 38.What is the missing term in the AP 15, 20, ?, 30, 35? (a) 25 (b) 26 (c) 24 (d) 30
  39. 39.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 37 (c) 190 (d) 361
  40. 40.Which term of the AP 2, 5, 8, 11, … is 116? (a) 41st (b) 39th (c) 38th (d) 40th

Answer key

  1. 900
  2. 9th
  3. 55
  4. 15th
  5. 86
  6. 33rd
  7. 86
  8. 441
  9. 60
  10. 529
  11. 12th
  12. 93
  13. 65
  14. 54
  15. 23
  16. 144
  17. 528
  18. 279
  19. 48
  20. 56
  21. 25
  22. 6
  23. 625
  24. 21st
  25. 175
  26. 84
  27. 88
  28. 198
  29. 1953
  30. 7
  31. 21
  32. 15th
  33. 230
  34. 25th
  35. 676
  36. 70
  37. 100
  38. 25
  39. 361
  40. 39th

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