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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 85 · 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 33rd term of the AP 11, 14, 17, 20, …? (a) 99 (b) 96 (c) 110 (d) 107
  2. 2.What is the sum of all the whole numbers from 1 to 61? (a) 1830 (b) 1891 (c) 3782 (d) 1892
  3. 3.What is the sum of all the whole numbers from 1 to 13? (a) 92 (b) 182 (c) 91 (d) 78
  4. 4.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 50 (b) 25 (c) 9 (d) 30
  5. 5.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 126 (b) 64 (c) 63 (d) 11
  6. 6.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 45 (b) 90 (c) 11 (d) 46
  7. 7.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 31 (b) 126 (c) 111 (d) 222
  8. 8.Which term of the AP 12, 18, 24, 30, … is 66? (a) 11th (b) 9th (c) 12th (d) 10th
  9. 9.What is the missing term in the AP 13, ?, 17, 19, 21? (a) 16 (b) 17 (c) 15 (d) 14
  10. 10.What is the 14th term of the AP 2, 4, 6, 8, …? (a) 29 (b) 30 (c) 28 (d) 26
  11. 11.What is the 20th term of the AP 2, 4, 6, 8, …? (a) 38 (b) 42 (c) 41 (d) 40
  12. 12.What is the sum of all the whole numbers from 1 to 12? (a) 156 (b) 66 (c) 78 (d) 72
  13. 13.What is the 20th term of the AP 19, 22, 25, 28, …? (a) 79 (b) 76 (c) 57 (d) 60
  14. 14.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 276 (c) 45 (d) 552
  15. 15.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 144 (b) 84 (c) 72 (d) 22
  16. 16.What is the sum of the first 11 terms of the AP 3, 8, 13, …? (a) 53 (b) 313 (c) 616 (d) 308
  17. 17.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 37 (c) 361 (d) 190
  18. 18.Which term of the AP 12, 20, 28, 36, … is 148? (a) 20th (b) 18th (c) 19th (d) 17th
  19. 19.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 400 (c) 210 (d) 420
  20. 20.What is the 13th term of the AP 17, 21, 25, 29, …? (a) 69 (b) 52 (c) 48 (d) 65
  21. 21.What is the sum of the first 8 terms of the AP 1, 6, 11, …? (a) 148 (b) 168 (c) 36 (d) 296
  22. 22.What is the missing term in the AP 16, 18, ?, 22, 24? (a) 21 (b) 20 (c) 19 (d) 22
  23. 23.What is the 34th term of the AP 18, 24, 30, 36, …? (a) 198 (b) 204 (c) 216 (d) 222
  24. 24.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 138 (b) 19 (c) 78 (d) 69
  25. 25.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 306 (c) 154 (d) 153
  26. 26.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 66 (b) 36 (c) 8 (d) 33
  27. 27.What is the 11th term of the AP 5, 14, 23, 32, …? (a) 99 (b) 104 (c) 90 (d) 95
  28. 28.What is the missing term in the AP 17, ?, 35, 44, 53? (a) 25 (b) 35 (c) 27 (d) 26
  29. 29.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 272 (b) 248 (c) 496 (d) 52
  30. 30.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 63 (b) 112 (c) 56 (d) 14
  31. 31.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 21 (d) 132
  32. 32.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 3540 (c) 1711 (d) 1770
  33. 33.Which term of the AP 11, 17, 23, 29, … is 179? (a) 29th (b) 30th (c) 28th (d) 31st
  34. 34.What is the sum of all the whole numbers from 1 to 65? (a) 2145 (b) 2146 (c) 2080 (d) 4290
  35. 35.What is the sum of the first 11 terms of the AP 9, 12, 15, …? (a) 39 (b) 267 (c) 264 (d) 528
  36. 36.What is the missing term in the AP 4, 8, ?, 16, 20? (a) 16 (b) 12 (c) 11 (d) 13
  37. 37.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 930 (c) 435 (d) 465
  38. 38.Which term of the AP 20, 26, 32, 38, … is 98? (a) 16th (b) 14th (c) 15th (d) 13th
  39. 39.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
  40. 40.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 28 (c) 49 (d) 13

Answer key

  1. 107
  2. 1891
  3. 91
  4. 25
  5. 63
  6. 45
  7. 111
  8. 10th
  9. 15
  10. 28
  11. 40
  12. 78
  13. 76
  14. 529
  15. 72
  16. 308
  17. 361
  18. 18th
  19. 400
  20. 65
  21. 148
  22. 20
  23. 216
  24. 69
  25. 153
  26. 33
  27. 95
  28. 26
  29. 248
  30. 56
  31. 121
  32. 1770
  33. 29th
  34. 2145
  35. 264
  36. 12
  37. 465
  38. 14th
  39. 25
  40. 49

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