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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 476 · 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 11 terms of the AP 4, 5, 6, …? (a) 100 (b) 99 (c) 198 (d) 14
  2. 2.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 26 (b) 119 (c) 238 (d) 122
  3. 3.Which term of the AP 5, 7, 9, 11, … is 39? (a) 18th (b) 19th (c) 20th (d) 17th
  4. 4.What is the 21st term of the AP 7, 9, 11, 13, …? (a) 49 (b) 40 (c) 47 (d) 42
  5. 5.Which term of the AP 9, 14, 19, 24, … is 74? (a) 16th (b) 13th (c) 15th (d) 14th
  6. 6.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 8 (b) 10 (c) 6 (d) 7
  7. 7.Which term of the AP 10, 19, 28, 37, … is 208? (a) 24th (b) 25th (c) 22nd (d) 23rd
  8. 8.What is the sum of all the whole numbers from 1 to 87? (a) 3828 (b) 7656 (c) 3829 (d) 3741
  9. 9.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 625 (c) 49 (d) 650
  10. 10.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 352 (b) 26 (c) 176 (d) 187
  11. 11.What is the 30th term of the AP 1, 6, 11, 16, …? (a) 150 (b) 145 (c) 151 (d) 146
  12. 12.What is the sum of all the whole numbers from 1 to 18? (a) 342 (b) 153 (c) 162 (d) 171
  13. 13.What is the 17th term of the AP 16, 19, 22, 25, …? (a) 48 (b) 64 (c) 67 (d) 51
  14. 14.What is the sum of all the whole numbers from 1 to 24? (a) 600 (b) 288 (c) 300 (d) 276
  15. 15.What is the sum of all the whole numbers from 1 to 19? (a) 190 (b) 191 (c) 380 (d) 171
  16. 16.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 144 (b) 288 (c) 162 (d) 39
  17. 17.Which term of the AP 20, 24, 28, 32, … is 60? (a) 11th (b) 10th (c) 12th (d) 15th
  18. 18.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 28 (b) 160 (c) 95 (d) 80
  19. 19.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 25 (d) 9
  20. 20.What is the missing term in the AP 10, 12, ?, 16, 18? (a) 16 (b) 14 (c) 13 (d) 15
  21. 21.What is the 15th term of the AP 10, 16, 22, 28, …? (a) 100 (b) 94 (c) 84 (d) 90
  22. 22.Which term of the AP 14, 16, 18, 20, … is 30? (a) 8th (b) 10th (c) 15th (d) 9th
  23. 23.What is the sum of the first 8 terms of the AP 7, 13, 19, …? (a) 224 (b) 49 (c) 248 (d) 448
  24. 24.What is the sum of all the whole numbers from 1 to 74? (a) 2701 (b) 2738 (c) 5550 (d) 2775
  25. 25.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 138 (b) 27 (c) 270 (d) 135
  26. 26.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 812 (d) 784
  27. 27.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 186 (b) 192 (c) 21 (d) 372
  28. 28.Which term of the AP 3, 12, 21, 30, … is 255? (a) 29th (b) 31st (c) 30th (d) 28th
  29. 29.What is the 35th term of the AP 3, 8, 13, 18, …? (a) 178 (b) 175 (c) 173 (d) 170
  30. 30.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 57 (c) 435 (d) 870
  31. 31.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 11 (d) 36
  32. 32.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 16 (b) 92 (c) 91 (d) 182
  33. 33.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 63 (b) 126 (c) 15 (d) 70
  34. 34.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 154 (b) 23 (c) 286 (d) 143
  35. 35.What is the 19th term of the AP 7, 9, 11, 13, …? (a) 36 (b) 38 (c) 43 (d) 45
  36. 36.What is the 27th term of the AP 16, 23, 30, 37, …? (a) 205 (b) 189 (c) 182 (d) 198
  37. 37.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 225 (b) 414 (c) 207 (d) 39
  38. 38.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 47 (c) 600 (d) 300
  39. 39.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 16 (b) 72 (c) 144 (d) 80
  40. 40.Which term of the AP 3, 11, 19, 27, … is 139? (a) 19th (b) 17th (c) 20th (d) 18th

Answer key

  1. 99
  2. 119
  3. 18th
  4. 47
  5. 14th
  6. 7
  7. 23rd
  8. 3828
  9. 625
  10. 176
  11. 146
  12. 171
  13. 64
  14. 300
  15. 190
  16. 144
  17. 11th
  18. 80
  19. 25
  20. 14
  21. 94
  22. 9th
  23. 224
  24. 2775
  25. 135
  26. 784
  27. 186
  28. 29th
  29. 173
  30. 841
  31. 36
  32. 91
  33. 63
  34. 143
  35. 43
  36. 198
  37. 207
  38. 576
  39. 72
  40. 18th

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