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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 612 · 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 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 225 (c) 240 (d) 29
  2. 2.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 200 (b) 180 (c) 40 (d) 360
  3. 3.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 34 (b) 324 (c) 162 (d) 180
  4. 4.What is the 10th term of the AP 13, 20, 27, 34, …? (a) 70 (b) 76 (c) 63 (d) 83
  5. 5.What is the 18th term of the AP 15, 17, 19, 21, …? (a) 49 (b) 36 (c) 51 (d) 34
  6. 6.What is the 29th term of the AP 1, 3, 5, 7, …? (a) 58 (b) 56 (c) 57 (d) 59
  7. 7.What is the 21st term of the AP 7, 13, 19, 25, …? (a) 126 (b) 120 (c) 133 (d) 127
  8. 8.Which term of the AP 3, 11, 19, 27, … is 283? (a) 38th (b) 36th (c) 37th (d) 35th
  9. 9.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 78 (c) 156 (d) 23
  10. 10.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 324 (b) 168 (c) 162 (d) 19
  11. 11.What is the sum of all the whole numbers from 1 to 42? (a) 861 (b) 882 (c) 1806 (d) 903
  12. 12.Which term of the AP 20, 25, 30, 35, … is 120? (a) 21st (b) 20th (c) 22nd (d) 24th
  13. 13.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 6 (b) 5 (c) 7 (d) 4
  14. 14.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 14 (b) 60 (c) 54 (d) 108
  15. 15.Which term of the AP 1, 3, 5, 7, … is 25? (a) 15th (b) 12th (c) 13th (d) 14th
  16. 16.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 13 (b) 12 (c) 11 (d) 15
  17. 17.What is the sum of the first 10 terms of the AP 6, 9, 12, …? (a) 33 (b) 195 (c) 210 (d) 390
  18. 18.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 91 (b) 182 (c) 22 (d) 94
  19. 19.What is the sum of all the whole numbers from 1 to 52? (a) 1326 (b) 2756 (c) 1378 (d) 1352
  20. 20.What is the 17th term of the AP 4, 8, 12, 16, …? (a) 69 (b) 68 (c) 64 (d) 72
  21. 21.What is the missing term in the AP 18, 23, 28, ?, 38? (a) 34 (b) 33 (c) 38 (d) 32
  22. 22.What is the sum of all the whole numbers from 1 to 54? (a) 2970 (b) 1458 (c) 1431 (d) 1485
  23. 23.What is the 16th term of the AP 16, 24, 32, 40, …? (a) 120 (b) 136 (c) 144 (d) 128
  24. 24.What is the sum of all the whole numbers from 1 to 98? (a) 9702 (b) 4802 (c) 4851 (d) 4753
  25. 25.Which term of the AP 3, 8, 13, 18, … is 98? (a) 21st (b) 22nd (c) 20th (d) 19th
  26. 26.What is the 35th term of the AP 9, 14, 19, 24, …? (a) 175 (b) 170 (c) 184 (d) 179
  27. 27.What is the sum of the first 12 terms of the AP 5, 8, 11, …? (a) 276 (b) 516 (c) 258 (d) 38
  28. 28.What is the 11th term of the AP 9, 15, 21, 27, …? (a) 66 (b) 60 (c) 75 (d) 69
  29. 29.What is the 20th term of the AP 2, 4, 6, 8, …? (a) 38 (b) 40 (c) 41 (d) 42
  30. 30.What is the 16th term of the AP 5, 9, 13, 17, …? (a) 64 (b) 65 (c) 69 (d) 60
  31. 31.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 39 (b) 42 (c) 9 (d) 78
  32. 32.What is the 20th term of the AP 16, 20, 24, 28, …? (a) 80 (b) 96 (c) 76 (d) 92
  33. 33.What is the missing term in the AP 19, 25, ?, 37, 43? (a) 32 (b) 31 (c) 37 (d) 30
  34. 34.Which term of the AP 4, 7, 10, 13, … is 94? (a) 30th (b) 32nd (c) 33rd (d) 31st
  35. 35.Which term of the AP 14, 18, 22, 26, … is 46? (a) 11th (b) 9th (c) 8th (d) 10th
  36. 36.What is the 35th term of the AP 6, 13, 20, 27, …? (a) 244 (b) 238 (c) 245 (d) 251
  37. 37.Which term of the AP 18, 26, 34, 42, … is 306? (a) 38th (b) 39th (c) 36th (d) 37th
  38. 38.What is the 15th term of the AP 15, 22, 29, 36, …? (a) 105 (b) 113 (c) 120 (d) 98
  39. 39.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 3655 (c) 7482 (d) 3741
  40. 40.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 9506 (c) 4753 (d) 4656

Answer key

  1. 225
  2. 180
  3. 162
  4. 76
  5. 49
  6. 57
  7. 127
  8. 36th
  9. 144
  10. 162
  11. 903
  12. 21st
  13. 5
  14. 54
  15. 13th
  16. 12
  17. 195
  18. 91
  19. 1378
  20. 68
  21. 33
  22. 1485
  23. 136
  24. 4851
  25. 20th
  26. 179
  27. 258
  28. 69
  29. 40
  30. 65
  31. 39
  32. 92
  33. 31
  34. 31st
  35. 9th
  36. 244
  37. 37th
  38. 113
  39. 3741
  40. 4753

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