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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 936 · 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 10 terms of the AP 6, 7, 8, …? (a) 210 (b) 110 (c) 105 (d) 15
  2. 2.What is the 25th term of the AP 15, 24, 33, 42, …? (a) 240 (b) 216 (c) 225 (d) 231
  3. 3.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 50 (b) 540 (c) 275 (d) 270
  4. 4.What is the 32nd term of the AP 14, 16, 18, 20, …? (a) 64 (b) 62 (c) 78 (d) 76
  5. 5.What is the 25th term of the AP 5, 10, 15, 20, …? (a) 125 (b) 130 (c) 120 (d) 126
  6. 6.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 153 (c) 306 (d) 33
  7. 7.Which term of the AP 3, 12, 21, 30, … is 138? (a) 16th (b) 18th (c) 17th (d) 15th
  8. 8.What is the sum of all the whole numbers from 1 to 50? (a) 1275 (b) 2550 (c) 1250 (d) 1225
  9. 9.Which term of the AP 7, 10, 13, 16, … is 85? (a) 28th (b) 27th (c) 26th (d) 29th
  10. 10.What is the missing term in the AP 18, 21, 24, ?, 30? (a) 28 (b) 26 (c) 30 (d) 27
  11. 11.What is the missing term in the AP 1, 7, 13, ?, 25? (a) 25 (b) 19 (c) 18 (d) 20
  12. 12.What is the missing term in the AP 7, 15, ?, 31, 39? (a) 24 (b) 31 (c) 22 (d) 23
  13. 13.What is the 24th term of the AP 12, 19, 26, 33, …? (a) 173 (b) 161 (c) 168 (d) 180
  14. 14.What is the 10th term of the AP 12, 15, 18, 21, …? (a) 27 (b) 42 (c) 30 (d) 39
  15. 15.What is the 15th term of the AP 2, 10, 18, 26, …? (a) 122 (b) 112 (c) 120 (d) 114
  16. 16.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 155 (b) 154 (c) 19 (d) 308
  17. 17.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 210 (b) 228 (c) 420 (d) 34
  18. 18.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 676 (d) 702
  19. 19.What is the 19th term of the AP 2, 8, 14, 20, …? (a) 110 (b) 108 (c) 116 (d) 114
  20. 20.What is the 16th term of the AP 6, 9, 12, 15, …? (a) 48 (b) 54 (c) 45 (d) 51
  21. 21.What is the sum of all the whole numbers from 1 to 19? (a) 191 (b) 380 (c) 171 (d) 190
  22. 22.What is the 35th term of the AP 16, 18, 20, 22, …? (a) 86 (b) 70 (c) 84 (d) 68
  23. 23.What is the 15th term of the AP 9, 17, 25, 33, …? (a) 129 (b) 112 (c) 121 (d) 120
  24. 24.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 380 (c) 190 (d) 361
  25. 25.What is the sum of all the whole numbers from 1 to 29? (a) 436 (b) 435 (c) 870 (d) 406
  26. 26.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 96 (b) 176 (c) 88 (d) 18
  27. 27.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 324 (b) 162 (c) 180 (d) 34
  28. 28.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 561 (c) 528 (d) 1122
  29. 29.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 16 (b) 80 (c) 144 (d) 72
  30. 30.What is the sum of the first 8 terms of the AP 2, 5, 8, …? (a) 112 (b) 200 (c) 23 (d) 100
  31. 31.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 6480 (c) 3240 (d) 3200
  32. 32.What is the sum of all the whole numbers from 1 to 30? (a) 435 (b) 930 (c) 465 (d) 450
  33. 33.What is the sum of all the whole numbers from 1 to 63? (a) 1953 (b) 2017 (c) 2016 (d) 4032
  34. 34.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 91 (b) 92 (c) 16 (d) 182
  35. 35.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 378 (b) 37 (c) 207 (d) 189
  36. 36.What is the 10th term of the AP 18, 22, 26, 30, …? (a) 58 (b) 36 (c) 54 (d) 40
  37. 37.What is the 25th term of the AP 13, 17, 21, 25, …? (a) 100 (b) 96 (c) 109 (d) 113
  38. 38.What is the 39th term of the AP 16, 24, 32, 40, …? (a) 312 (b) 304 (c) 328 (d) 320
  39. 39.Which term of the AP 6, 10, 14, 18, … is 78? (a) 18th (b) 20th (c) 19th (d) 21st
  40. 40.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 312 (b) 294 (c) 588 (d) 41

Answer key

  1. 105
  2. 231
  3. 270
  4. 76
  5. 125
  6. 289
  7. 16th
  8. 1275
  9. 27th
  10. 27
  11. 19
  12. 23
  13. 173
  14. 39
  15. 114
  16. 154
  17. 210
  18. 676
  19. 110
  20. 51
  21. 190
  22. 84
  23. 121
  24. 361
  25. 435
  26. 88
  27. 162
  28. 561
  29. 72
  30. 100
  31. 3240
  32. 465
  33. 2016
  34. 91
  35. 189
  36. 54
  37. 109
  38. 320
  39. 19th
  40. 294

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