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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 698 · 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 25th term of the AP 6, 12, 18, 24, …? (a) 144 (b) 150 (c) 151 (d) 156
  2. 2.What is the sum of the first 5 terms of the AP 10, 14, 18, …? (a) 90 (b) 100 (c) 180 (d) 26
  3. 3.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 380 (c) 190 (d) 361
  4. 4.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 45 (d) 81
  5. 5.What is the 27th term of the AP 8, 15, 22, 29, …? (a) 182 (b) 190 (c) 189 (d) 197
  6. 6.What is the 12th term of the AP 3, 11, 19, 27, …? (a) 99 (b) 88 (c) 96 (d) 91
  7. 7.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 140 (b) 18 (c) 135 (d) 270
  8. 8.What is the missing term in the AP 6, 11, ?, 21, 26? (a) 17 (b) 15 (c) 21 (d) 16
  9. 9.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 66 (d) 132
  10. 10.Which term of the AP 12, 18, 24, 30, … is 84? (a) 15th (b) 14th (c) 12th (d) 13th
  11. 11.What is the 15th term of the AP 12, 16, 20, 24, …? (a) 72 (b) 56 (c) 60 (d) 68
  12. 12.What is the 15th term of the AP 11, 15, 19, 23, …? (a) 67 (b) 56 (c) 60 (d) 71
  13. 13.What is the 17th term of the AP 17, 22, 27, 32, …? (a) 85 (b) 80 (c) 97 (d) 102
  14. 14.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 91 (c) 105 (d) 210
  15. 15.What is the missing term in the AP 8, ?, 12, 14, 16? (a) 10 (b) 9 (c) 12 (d) 11
  16. 16.What is the 12th term of the AP 1, 3, 5, 7, …? (a) 22 (b) 23 (c) 25 (d) 24
  17. 17.Which term of the AP 2, 5, 8, 11, … is 113? (a) 38th (b) 40th (c) 37th (d) 39th
  18. 18.What is the missing term in the AP 18, 24, ?, 36, 42? (a) 36 (b) 31 (c) 30 (d) 29
  19. 19.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 252 (b) 240 (c) 31 (d) 480
  20. 20.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 33 (b) 216 (c) 108 (d) 126
  21. 21.What is the sum of the first 10 terms of the AP 9, 14, 19, …? (a) 315 (b) 54 (c) 340 (d) 630
  22. 22.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 238 (b) 124 (c) 119 (d) 32
  23. 23.What is the missing term in the AP 13, ?, 21, 25, 29? (a) 21 (b) 18 (c) 17 (d) 16
  24. 24.What is the 35th term of the AP 8, 10, 12, 14, …? (a) 68 (b) 78 (c) 76 (d) 70
  25. 25.What is the 24th term of the AP 7, 12, 17, 22, …? (a) 115 (b) 122 (c) 120 (d) 127
  26. 26.Which term of the AP 17, 22, 27, 32, … is 187? (a) 34th (b) 37th (c) 35th (d) 36th
  27. 27.What is the sum of the first 11 terms of the AP 7, 12, 17, …? (a) 704 (b) 57 (c) 352 (d) 357
  28. 28.What is the sum of all the whole numbers from 1 to 79? (a) 3161 (b) 6320 (c) 3160 (d) 3081
  29. 29.What is the 15th term of the AP 5, 7, 9, 11, …? (a) 30 (b) 28 (c) 33 (d) 35
  30. 30.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 66 (b) 792 (c) 429 (d) 396
  31. 31.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 352 (b) 385 (c) 704 (d) 62
  32. 32.Which term of the AP 15, 24, 33, 42, … is 132? (a) 14th (b) 13th (c) 15th (d) 16th
  33. 33.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 300 (b) 150 (c) 24 (d) 160
  34. 34.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 64 (b) 11 (c) 60 (d) 120
  35. 35.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 44 (b) 48 (c) 9 (d) 88
  36. 36.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 39 (b) 288 (c) 144 (d) 162
  37. 37.What is the sum of all the whole numbers from 1 to 53? (a) 1432 (b) 1431 (c) 1378 (d) 2862
  38. 38.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 418 (b) 212 (c) 209 (d) 34
  39. 39.What is the sum of all the whole numbers from 1 to 43? (a) 903 (b) 1892 (c) 947 (d) 946
  40. 40.What is the 39th term of the AP 7, 14, 21, 28, …? (a) 274 (b) 266 (c) 273 (d) 280

Answer key

  1. 150
  2. 90
  3. 361
  4. 81
  5. 190
  6. 91
  7. 135
  8. 16
  9. 121
  10. 13th
  11. 68
  12. 67
  13. 97
  14. 105
  15. 10
  16. 23
  17. 38th
  18. 30
  19. 240
  20. 108
  21. 315
  22. 119
  23. 17
  24. 76
  25. 122
  26. 35th
  27. 352
  28. 3160
  29. 33
  30. 396
  31. 352
  32. 14th
  33. 150
  34. 60
  35. 44
  36. 144
  37. 1431
  38. 209
  39. 946
  40. 273

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