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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 628 · 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 all the whole numbers from 1 to 44? (a) 990 (b) 968 (c) 946 (d) 1980
  2. 2.What is the 33rd term of the AP 3, 6, 9, 12, …? (a) 100 (b) 96 (c) 99 (d) 102
  3. 3.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 3540 (c) 1711 (d) 1770
  4. 4.What is the 21st term of the AP 19, 27, 35, 43, …? (a) 187 (b) 179 (c) 168 (d) 160
  5. 5.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 196 (d) 105
  6. 6.Which term of the AP 15, 19, 23, 27, … is 119? (a) 29th (b) 26th (c) 27th (d) 28th
  7. 7.What is the sum of all the whole numbers from 1 to 47? (a) 2256 (b) 1129 (c) 1081 (d) 1128
  8. 8.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 80 (b) 150 (c) 75 (d) 12
  9. 9.Which term of the AP 5, 9, 13, 17, … is 81? (a) 21st (b) 20th (c) 22nd (d) 19th
  10. 10.What is the 32nd term of the AP 11, 14, 17, 20, …? (a) 107 (b) 93 (c) 96 (d) 104
  11. 11.Which term of the AP 3, 6, 9, 12, … is 36? (a) 11th (b) 13th (c) 14th (d) 12th
  12. 12.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 59 (c) 930 (d) 465
  13. 13.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 529 (d) 276
  14. 14.What is the 11th term of the AP 15, 20, 25, 30, …? (a) 70 (b) 55 (c) 65 (d) 50
  15. 15.What is the sum of all the whole numbers from 1 to 38? (a) 703 (b) 722 (c) 741 (d) 1482
  16. 16.What is the 16th term of the AP 17, 26, 35, 44, …? (a) 152 (b) 161 (c) 135 (d) 144
  17. 17.What is the sum of the first 12 terms of the AP 4, 6, 8, …? (a) 360 (b) 192 (c) 26 (d) 180
  18. 18.What is the 31st term of the AP 9, 12, 15, 18, …? (a) 90 (b) 93 (c) 102 (d) 99
  19. 19.What is the 27th term of the AP 12, 14, 16, 18, …? (a) 66 (b) 52 (c) 54 (d) 64
  20. 20.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 225 (b) 252 (c) 450 (d) 49
  21. 21.What is the sum of all the whole numbers from 1 to 98? (a) 4753 (b) 9702 (c) 4802 (d) 4851
  22. 22.What is the 26th term of the AP 10, 16, 22, 28, …? (a) 156 (b) 166 (c) 160 (d) 150
  23. 23.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 841 (c) 435 (d) 870
  24. 24.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 108 (b) 55 (c) 54 (d) 10
  25. 25.What is the sum of the first 12 terms of the AP 4, 7, 10, …? (a) 246 (b) 492 (c) 37 (d) 264
  26. 26.What is the sum of the first 7 terms of the AP 5, 10, 15, …? (a) 35 (b) 145 (c) 280 (d) 140
  27. 27.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 11 (b) 120 (c) 64 (d) 60
  28. 28.What is the sum of the first 5 terms of the AP 5, 10, 15, …? (a) 80 (b) 25 (c) 75 (d) 150
  29. 29.What is the 22nd term of the AP 7, 15, 23, 31, …? (a) 183 (b) 168 (c) 175 (d) 176
  30. 30.What is the 26th term of the AP 3, 11, 19, 27, …? (a) 211 (b) 200 (c) 208 (d) 203
  31. 31.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 96 (b) 92 (c) 184 (d) 15
  32. 32.What is the sum of all the whole numbers from 1 to 95? (a) 4465 (b) 4561 (c) 9120 (d) 4560
  33. 33.What is the 10th term of the AP 2, 10, 18, 26, …? (a) 72 (b) 74 (c) 80 (d) 82
  34. 34.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 144 (b) 23 (c) 288 (d) 156
  35. 35.What is the sum of all the whole numbers from 1 to 28? (a) 378 (b) 406 (c) 392 (d) 812
  36. 36.What is the sum of the first 8 terms of the AP 7, 13, 19, …? (a) 224 (b) 248 (c) 49 (d) 448
  37. 37.What is the 13th term of the AP 14, 22, 30, 38, …? (a) 118 (b) 110 (c) 96 (d) 104
  38. 38.Which term of the AP 18, 27, 36, 45, … is 342? (a) 39th (b) 36th (c) 37th (d) 38th
  39. 39.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 140 (b) 70 (c) 80 (d) 22
  40. 40.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 168 (b) 96 (c) 24 (d) 84

Answer key

  1. 990
  2. 99
  3. 1770
  4. 179
  5. 196
  6. 27th
  7. 1128
  8. 75
  9. 20th
  10. 104
  11. 12th
  12. 900
  13. 529
  14. 65
  15. 741
  16. 152
  17. 180
  18. 99
  19. 64
  20. 225
  21. 4851
  22. 160
  23. 841
  24. 54
  25. 246
  26. 140
  27. 60
  28. 75
  29. 175
  30. 203
  31. 92
  32. 4560
  33. 74
  34. 144
  35. 406
  36. 224
  37. 110
  38. 37th
  39. 70
  40. 84

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