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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 31 · 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.Which term of the AP 19, 27, 35, 43, … is 115? (a) 13th (b) 14th (c) 12th (d) 15th
  2. 2.What is the sum of all the whole numbers from 1 to 61? (a) 1830 (b) 1891 (c) 3782 (d) 1892
  3. 3.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 900 (c) 59 (d) 930
  4. 4.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 102 (b) 11 (c) 54 (d) 51
  5. 5.What is the missing term in the AP 5, 11, ?, 23, 29? (a) 23 (b) 16 (c) 17 (d) 18
  6. 6.Which term of the AP 9, 18, 27, 36, … is 261? (a) 29th (b) 31st (c) 30th (d) 28th
  7. 7.What is the missing term in the AP 2, 11, ?, 29, 38? (a) 19 (b) 21 (c) 29 (d) 20
  8. 8.What is the 15th term of the AP 17, 22, 27, 32, …? (a) 92 (b) 70 (c) 75 (d) 87
  9. 9.What is the 39th term of the AP 11, 17, 23, 29, …? (a) 239 (b) 234 (c) 245 (d) 228
  10. 10.What is the 27th term of the AP 8, 13, 18, 23, …? (a) 138 (b) 130 (c) 135 (d) 143
  11. 11.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 286 (b) 143 (c) 144 (d) 18
  12. 12.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 13 (b) 176 (c) 88 (d) 89
  13. 13.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 22 (b) 65 (c) 60 (d) 120
  14. 14.What is the sum of all the whole numbers from 1 to 86? (a) 3655 (b) 3741 (c) 3698 (d) 7482
  15. 15.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 160 (b) 17 (c) 88 (d) 80
  16. 16.Which term of the AP 14, 23, 32, 41, … is 221? (a) 23rd (b) 26th (c) 25th (d) 24th
  17. 17.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 120 (c) 240 (d) 225
  18. 18.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 13 (b) 14 (c) 12 (d) 15
  19. 19.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 198 (b) 99 (c) 100 (d) 14
  20. 20.What is the missing term in the AP 20, ?, 34, 41, 48? (a) 28 (b) 26 (c) 34 (d) 27
  21. 21.What is the 17th term of the AP 13, 19, 25, 31, …? (a) 115 (b) 109 (c) 96 (d) 102
  22. 22.Which term of the AP 8, 14, 20, 26, … is 188? (a) 30th (b) 33rd (c) 31st (d) 32nd
  23. 23.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 2485 (c) 2415 (d) 4970
  24. 24.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 612 (b) 333 (c) 58 (d) 306
  25. 25.What is the 25th term of the AP 8, 15, 22, 29, …? (a) 175 (b) 183 (c) 176 (d) 168
  26. 26.What is the 40th term of the AP 12, 17, 22, 27, …? (a) 212 (b) 207 (c) 195 (d) 200
  27. 27.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 180 (b) 190 (c) 360 (d) 27
  28. 28.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 741 (c) 703 (d) 1482
  29. 29.What is the 34th term of the AP 18, 20, 22, 24, …? (a) 84 (b) 68 (c) 66 (d) 86
  30. 30.What is the 20th term of the AP 17, 24, 31, 38, …? (a) 140 (b) 133 (c) 157 (d) 150
  31. 31.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 22 (b) 80 (c) 70 (d) 140
  32. 32.What is the sum of all the whole numbers from 1 to 71? (a) 5112 (b) 2485 (c) 2557 (d) 2556
  33. 33.What is the missing term in the AP 1, ?, 11, 16, 21? (a) 5 (b) 11 (c) 6 (d) 7
  34. 34.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 88 (b) 18 (c) 96 (d) 176
  35. 35.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 17 (b) 57 (c) 114 (d) 66
  36. 36.Which term of the AP 16, 22, 28, 34, … is 226? (a) 36th (b) 35th (c) 38th (d) 37th
  37. 37.What is the 36th term of the AP 8, 10, 12, 14, …? (a) 72 (b) 70 (c) 78 (d) 80
  38. 38.What is the missing term in the AP 14, ?, 20, 23, 26? (a) 16 (b) 17 (c) 20 (d) 18
  39. 39.What is the 33rd term of the AP 11, 15, 19, 23, …? (a) 128 (b) 132 (c) 143 (d) 139
  40. 40.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 248 (b) 272 (c) 496 (d) 52

Answer key

  1. 13th
  2. 1891
  3. 900
  4. 51
  5. 17
  6. 29th
  7. 20
  8. 87
  9. 239
  10. 138
  11. 143
  12. 88
  13. 60
  14. 3741
  15. 80
  16. 24th
  17. 225
  18. 13
  19. 99
  20. 27
  21. 109
  22. 31st
  23. 2485
  24. 306
  25. 176
  26. 207
  27. 180
  28. 741
  29. 84
  30. 150
  31. 70
  32. 2556
  33. 6
  34. 88
  35. 57
  36. 36th
  37. 78
  38. 17
  39. 139
  40. 248

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