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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 749 · 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 19, ?, 25, 28, 31? (a) 21 (b) 25 (c) 22 (d) 23
  2. 2.Which term of the AP 5, 7, 9, 11, … is 19? (a) 10th (b) 7th (c) 9th (d) 8th
  3. 3.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 78 (b) 12 (c) 154 (d) 77
  4. 4.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 378 (c) 53 (d) 756
  5. 5.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 13 (b) 162 (c) 81 (d) 82
  6. 6.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 22 (b) 94 (c) 182 (d) 91
  7. 7.What is the 10th term of the AP 13, 17, 21, 25, …? (a) 36 (b) 49 (c) 40 (d) 53
  8. 8.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 41 (b) 588 (c) 312 (d) 294
  9. 9.What is the 14th term of the AP 3, 10, 17, 24, …? (a) 91 (b) 98 (c) 94 (d) 101
  10. 10.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 14 (b) 55 (c) 100 (d) 50
  11. 11.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 130 (b) 11 (c) 65 (d) 70
  12. 12.What is the sum of the first 9 terms of the AP 8, 13, 18, …? (a) 257 (b) 252 (c) 504 (d) 48
  13. 13.Which term of the AP 7, 15, 23, 31, … is 175? (a) 21st (b) 23rd (c) 24th (d) 22nd
  14. 14.Which term of the AP 17, 21, 25, 29, … is 165? (a) 40th (b) 37th (c) 38th (d) 39th
  15. 15.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 870 (d) 841
  16. 16.What is the 34th term of the AP 17, 24, 31, 38, …? (a) 231 (b) 255 (c) 238 (d) 248
  17. 17.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 9506 (c) 4753 (d) 4656
  18. 18.Which term of the AP 17, 25, 33, 41, … is 89? (a) 11th (b) 12th (c) 10th (d) 9th
  19. 19.What is the 11th term of the AP 15, 21, 27, 33, …? (a) 66 (b) 60 (c) 81 (d) 75
  20. 20.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 55 (c) 110 (d) 19
  21. 21.What is the sum of the first 11 terms of the AP 7, 12, 17, …? (a) 357 (b) 57 (c) 704 (d) 352
  22. 22.What is the sum of the first 7 terms of the AP 4, 10, 16, …? (a) 175 (b) 308 (c) 154 (d) 40
  23. 23.What is the 17th term of the AP 9, 18, 27, 36, …? (a) 144 (b) 154 (c) 153 (d) 162
  24. 24.What is the sum of the first 6 terms of the AP 3, 6, 9, …? (a) 18 (b) 126 (c) 72 (d) 63
  25. 25.What is the 29th term of the AP 12, 21, 30, 39, …? (a) 264 (b) 273 (c) 252 (d) 261
  26. 26.What is the missing term in the AP 1, 4, ?, 10, 13? (a) 10 (b) 7 (c) 8 (d) 6
  27. 27.What is the sum of all the whole numbers from 1 to 61? (a) 1891 (b) 1830 (c) 1892 (d) 3782
  28. 28.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 124 (b) 32 (c) 119 (d) 238
  29. 29.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 96 (b) 168 (c) 84 (d) 24
  30. 30.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 25 (c) 30 (d) 9
  31. 31.What is the 14th term of the AP 16, 18, 20, 22, …? (a) 44 (b) 26 (c) 42 (d) 28
  32. 32.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 25 (b) 7 (c) 26 (d) 50
  33. 33.What is the missing term in the AP 11, ?, 15, 17, 19? (a) 12 (b) 13 (c) 14 (d) 15
  34. 34.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 15 (b) 22 (c) 16 (d) 14
  35. 35.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 650 (d) 625
  36. 36.Which term of the AP 9, 16, 23, 30, … is 261? (a) 37th (b) 36th (c) 39th (d) 38th
  37. 37.What is the sum of the first 11 terms of the AP 10, 14, 18, …? (a) 50 (b) 352 (c) 660 (d) 330
  38. 38.What is the sum of all the whole numbers from 1 to 79? (a) 3160 (b) 6320 (c) 3081 (d) 3161
  39. 39.What is the 27th term of the AP 8, 11, 14, 17, …? (a) 81 (b) 89 (c) 78 (d) 86
  40. 40.What is the 30th term of the AP 7, 14, 21, 28, …? (a) 210 (b) 211 (c) 217 (d) 203

Answer key

  1. 22
  2. 8th
  3. 77
  4. 729
  5. 81
  6. 91
  7. 49
  8. 294
  9. 94
  10. 50
  11. 65
  12. 252
  13. 22nd
  14. 38th
  15. 841
  16. 248
  17. 4753
  18. 10th
  19. 75
  20. 100
  21. 352
  22. 154
  23. 153
  24. 63
  25. 264
  26. 7
  27. 1891
  28. 119
  29. 84
  30. 25
  31. 42
  32. 25
  33. 13
  34. 15
  35. 625
  36. 37th
  37. 330
  38. 3160
  39. 86
  40. 210

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