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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 439 · 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 14? (a) 98 (b) 105 (c) 91 (d) 210
  2. 2.Which term of the AP 11, 13, 15, 17, … is 87? (a) 40th (b) 41st (c) 39th (d) 38th
  3. 3.What is the 30th term of the AP 16, 20, 24, 28, …? (a) 120 (b) 136 (c) 116 (d) 132
  4. 4.What is the 11th term of the AP 9, 16, 23, 30, …? (a) 70 (b) 77 (c) 79 (d) 86
  5. 5.What is the 17th term of the AP 1, 10, 19, 28, …? (a) 154 (b) 144 (c) 145 (d) 153
  6. 6.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 64 (d) 72
  7. 7.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 4970 (c) 2450 (d) 2485
  8. 8.What is the sum of the first 12 terms of the AP 4, 10, 16, …? (a) 480 (b) 888 (c) 70 (d) 444
  9. 9.What is the 11th term of the AP 17, 26, 35, 44, …? (a) 107 (b) 99 (c) 90 (d) 116
  10. 10.Which term of the AP 14, 16, 18, 20, … is 68? (a) 28th (b) 34th (c) 29th (d) 27th
  11. 11.What is the 31st term of the AP 10, 16, 22, 28, …? (a) 196 (b) 186 (c) 180 (d) 190
  12. 12.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 444 (b) 35 (c) 222 (d) 240
  13. 13.What is the 11th term of the AP 3, 5, 7, 9, …? (a) 25 (b) 20 (c) 23 (d) 22
  14. 14.What is the 26th term of the AP 19, 25, 31, 37, …? (a) 175 (b) 150 (c) 169 (d) 156
  15. 15.Which term of the AP 2, 5, 8, 11, … is 98? (a) 32nd (b) 35th (c) 34th (d) 33rd
  16. 16.What is the sum of all the whole numbers from 1 to 11? (a) 67 (b) 132 (c) 66 (d) 55
  17. 17.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 98 (b) 13 (c) 49 (d) 56
  18. 18.What is the missing term in the AP 20, ?, 38, 47, 56? (a) 30 (b) 29 (c) 38 (d) 28
  19. 19.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 33 (b) 126 (c) 216 (d) 108
  20. 20.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 45 (c) 55 (d) 110
  21. 21.What is the 33rd term of the AP 8, 11, 14, 17, …? (a) 99 (b) 104 (c) 96 (d) 107
  22. 22.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 144 (c) 156 (d) 23
  23. 23.What is the 27th term of the AP 3, 6, 9, 12, …? (a) 84 (b) 78 (c) 82 (d) 81
  24. 24.What is the 19th term of the AP 17, 19, 21, 23, …? (a) 38 (b) 36 (c) 53 (d) 55
  25. 25.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 27 (b) 102 (c) 174 (d) 87
  26. 26.Which term of the AP 11, 19, 27, 35, … is 235? (a) 28th (b) 29th (c) 30th (d) 31st
  27. 27.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 216 (b) 24 (c) 120 (d) 108
  28. 28.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 625 (d) 650
  29. 29.What is the 24th term of the AP 17, 24, 31, 38, …? (a) 185 (b) 178 (c) 168 (d) 161
  30. 30.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 45 (b) 90 (c) 17 (d) 55
  31. 31.What is the 37th term of the AP 5, 8, 11, 14, …? (a) 108 (b) 116 (c) 113 (d) 111
  32. 32.What is the 32nd term of the AP 6, 12, 18, 24, …? (a) 198 (b) 193 (c) 186 (d) 192
  33. 33.What is the 28th term of the AP 6, 12, 18, 24, …? (a) 168 (b) 162 (c) 174 (d) 169
  34. 34.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 37 (c) 361 (d) 190
  35. 35.What is the 14th term of the AP 4, 12, 20, 28, …? (a) 112 (b) 104 (c) 116 (d) 108
  36. 36.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 78 (b) 12 (c) 77 (d) 154
  37. 37.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 16 (b) 12 (c) 13 (d) 14
  38. 38.What is the 38th term of the AP 4, 6, 8, 10, …? (a) 76 (b) 80 (c) 74 (d) 78
  39. 39.What is the missing term in the AP 8, ?, 12, 14, 16? (a) 10 (b) 12 (c) 11 (d) 9
  40. 40.Which term of the AP 5, 7, 9, 11, … is 23? (a) 10th (b) 11th (c) 12th (d) 9th

Answer key

  1. 105
  2. 39th
  3. 132
  4. 79
  5. 145
  6. 64
  7. 2485
  8. 444
  9. 107
  10. 28th
  11. 190
  12. 222
  13. 23
  14. 169
  15. 33rd
  16. 66
  17. 49
  18. 29
  19. 108
  20. 55
  21. 104
  22. 144
  23. 81
  24. 53
  25. 87
  26. 29th
  27. 108
  28. 625
  29. 178
  30. 45
  31. 113
  32. 192
  33. 168
  34. 361
  35. 108
  36. 77
  37. 13
  38. 78
  39. 10
  40. 10th

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