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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 750 · 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 7 terms of the AP 9, 10, 11, …? (a) 168 (b) 15 (c) 85 (d) 84
  2. 2.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 25 (d) 169
  3. 3.What is the 27th term of the AP 7, 10, 13, 16, …? (a) 78 (b) 85 (c) 88 (d) 81
  4. 4.What is the 34th term of the AP 8, 12, 16, 20, …? (a) 136 (b) 132 (c) 144 (d) 140
  5. 5.What is the missing term in the AP 5, 13, ?, 29, 37? (a) 29 (b) 20 (c) 21 (d) 22
  6. 6.What is the 25th term of the AP 2, 5, 8, 11, …? (a) 77 (b) 74 (c) 72 (d) 75
  7. 7.What is the 35th term of the AP 2, 4, 6, 8, …? (a) 72 (b) 68 (c) 71 (d) 70
  8. 8.What is the sum of all the whole numbers from 1 to 93? (a) 4278 (b) 8742 (c) 4372 (d) 4371
  9. 9.What is the 30th term of the AP 8, 14, 20, 26, …? (a) 174 (b) 188 (c) 182 (d) 180
  10. 10.What is the 15th term of the AP 6, 12, 18, 24, …? (a) 96 (b) 90 (c) 91 (d) 84
  11. 11.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 58 (b) 612 (c) 306 (d) 333
  12. 12.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 120 (b) 30 (c) 210 (d) 105
  13. 13.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 100 (b) 170 (c) 29 (d) 85
  14. 14.What is the sum of all the whole numbers from 1 to 51? (a) 1327 (b) 2652 (c) 1275 (d) 1326
  15. 15.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 136 (c) 154 (d) 306
  16. 16.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 11 (d) 36
  17. 17.What is the sum of the first 12 terms of the AP 5, 8, 11, …? (a) 258 (b) 38 (c) 276 (d) 516
  18. 18.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 32 (b) 120 (c) 204 (d) 102
  19. 19.What is the sum of all the whole numbers from 1 to 30? (a) 465 (b) 930 (c) 435 (d) 450
  20. 20.Which term of the AP 5, 14, 23, 32, … is 131? (a) 15th (b) 17th (c) 14th (d) 16th
  21. 21.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 144 (c) 23 (d) 156
  22. 22.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 9 (b) 88 (c) 48 (d) 44
  23. 23.What is the sum of the first 7 terms of the AP 4, 10, 16, …? (a) 175 (b) 40 (c) 154 (d) 308
  24. 24.What is the sum of all the whole numbers from 1 to 75? (a) 2775 (b) 2851 (c) 5700 (d) 2850
  25. 25.What is the sum of the first 8 terms of the AP 2, 5, 8, …? (a) 112 (b) 200 (c) 100 (d) 23
  26. 26.What is the missing term in the AP 9, ?, 15, 18, 21? (a) 11 (b) 13 (c) 15 (d) 12
  27. 27.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 45 (d) 17
  28. 28.What is the sum of all the whole numbers from 1 to 44? (a) 1980 (b) 946 (c) 990 (d) 968
  29. 29.What is the 22nd term of the AP 6, 15, 24, 33, …? (a) 189 (b) 204 (c) 198 (d) 195
  30. 30.What is the sum of all the whole numbers from 1 to 32? (a) 496 (b) 528 (c) 1056 (d) 512
  31. 31.What is the 21st term of the AP 7, 16, 25, 34, …? (a) 187 (b) 196 (c) 180 (d) 189
  32. 32.What is the missing term in the AP 13, 18, ?, 28, 33? (a) 24 (b) 28 (c) 22 (d) 23
  33. 33.What is the sum of the first 10 terms of the AP 5, 6, 7, …? (a) 95 (b) 14 (c) 100 (d) 190
  34. 34.What is the sum of the first 6 terms of the AP 8, 14, 20, …? (a) 156 (b) 38 (c) 276 (d) 138
  35. 35.Which term of the AP 2, 6, 10, 14, … is 110? (a) 30th (b) 29th (c) 27th (d) 28th
  36. 36.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 56 (b) 52 (c) 104 (d) 10
  37. 37.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 240 (b) 30 (c) 456 (d) 228
  38. 38.What is the missing term in the AP 1, 6, ?, 16, 21? (a) 16 (b) 11 (c) 10 (d) 12
  39. 39.Which term of the AP 3, 8, 13, 18, … is 73? (a) 14th (b) 16th (c) 15th (d) 17th
  40. 40.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 35 (c) 171 (d) 342

Answer key

  1. 84
  2. 169
  3. 85
  4. 140
  5. 21
  6. 74
  7. 70
  8. 4371
  9. 182
  10. 90
  11. 306
  12. 105
  13. 85
  14. 1326
  15. 153
  16. 36
  17. 258
  18. 102
  19. 465
  20. 15th
  21. 144
  22. 44
  23. 154
  24. 2850
  25. 100
  26. 12
  27. 81
  28. 990
  29. 195
  30. 528
  31. 187
  32. 23
  33. 95
  34. 138
  35. 28th
  36. 52
  37. 228
  38. 11
  39. 15th
  40. 324

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