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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 560 · 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 missing term in the AP 17, 24, ?, 38, 45? (a) 30 (b) 38 (c) 32 (d) 31
  2. 2.What is the 21st term of the AP 4, 11, 18, 25, …? (a) 140 (b) 147 (c) 144 (d) 151
  3. 3.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 18 (b) 270 (c) 140 (d) 135
  4. 4.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 190 (b) 187 (c) 374 (d) 32
  5. 5.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 41 (b) 80 (c) 40 (d) 10
  6. 6.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 182 (b) 41 (c) 161 (d) 322
  7. 7.What is the missing term in the AP 11, 15, ?, 23, 27? (a) 23 (b) 19 (c) 20 (d) 18
  8. 8.What is the missing term in the AP 2, ?, 14, 20, 26? (a) 9 (b) 14 (c) 7 (d) 8
  9. 9.Which term of the AP 16, 20, 24, 28, … is 124? (a) 29th (b) 31st (c) 28th (d) 27th
  10. 10.What is the 38th term of the AP 18, 27, 36, 45, …? (a) 360 (b) 342 (c) 351 (d) 333
  11. 11.What is the 23rd term of the AP 8, 10, 12, 14, …? (a) 46 (b) 44 (c) 54 (d) 52
  12. 12.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 480 (b) 31 (c) 240 (d) 252
  13. 13.What is the 30th term of the AP 5, 8, 11, 14, …? (a) 87 (b) 90 (c) 95 (d) 92
  14. 14.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 190 (c) 380 (d) 37
  15. 15.What is the missing term in the AP 2, 7, 12, ?, 22? (a) 16 (b) 18 (c) 22 (d) 17
  16. 16.What is the sum of all the whole numbers from 1 to 61? (a) 1830 (b) 1891 (c) 3782 (d) 1892
  17. 17.Which term of the AP 18, 20, 22, 24, … is 34? (a) 8th (b) 10th (c) 17th (d) 9th
  18. 18.What is the missing term in the AP 4, 12, 20, ?, 36? (a) 27 (b) 36 (c) 29 (d) 28
  19. 19.What is the missing term in the AP 5, ?, 13, 17, 21? (a) 10 (b) 9 (c) 8 (d) 13
  20. 20.What is the 32nd term of the AP 15, 17, 19, 21, …? (a) 79 (b) 77 (c) 62 (d) 64
  21. 21.What is the 36th term of the AP 6, 13, 20, 27, …? (a) 252 (b) 245 (c) 251 (d) 258
  22. 22.What is the missing term in the AP 1, 4, 7, ?, 13? (a) 13 (b) 11 (c) 10 (d) 9
  23. 23.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 133 (b) 266 (c) 31 (d) 147
  24. 24.What is the sum of the first 11 terms of the AP 10, 15, 20, …? (a) 390 (b) 385 (c) 770 (d) 60
  25. 25.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 171 (c) 342 (d) 324
  26. 26.What is the sum of all the whole numbers from 1 to 41? (a) 861 (b) 862 (c) 820 (d) 1722
  27. 27.What is the 15th term of the AP 16, 23, 30, 37, …? (a) 121 (b) 105 (c) 98 (d) 114
  28. 28.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 702 (c) 51 (d) 351
  29. 29.What is the 13th term of the AP 8, 17, 26, 35, …? (a) 108 (b) 125 (c) 117 (d) 116
  30. 30.What is the missing term in the AP 1, ?, 9, 13, 17? (a) 6 (b) 4 (c) 9 (d) 5
  31. 31.What is the 31st term of the AP 2, 8, 14, 20, …? (a) 188 (b) 182 (c) 180 (d) 186
  32. 32.Which term of the AP 4, 9, 14, 19, … is 154? (a) 30th (b) 33rd (c) 32nd (d) 31st
  33. 33.What is the 18th term of the AP 10, 13, 16, 19, …? (a) 51 (b) 54 (c) 64 (d) 61
  34. 34.What is the 18th term of the AP 9, 15, 21, 27, …? (a) 117 (b) 102 (c) 108 (d) 111
  35. 35.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 70 (b) 140 (c) 75 (d) 18
  36. 36.What is the 36th term of the AP 9, 13, 17, 21, …? (a) 149 (b) 144 (c) 153 (d) 140
  37. 37.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 49 (d) 28
  38. 38.What is the sum of all the whole numbers from 1 to 59? (a) 1771 (b) 3540 (c) 1770 (d) 1711
  39. 39.What is the 14th term of the AP 15, 17, 19, 21, …? (a) 43 (b) 28 (c) 26 (d) 41
  40. 40.What is the sum of all the whole numbers from 1 to 79? (a) 3160 (b) 3081 (c) 6320 (d) 3161

Answer key

  1. 31
  2. 144
  3. 135
  4. 187
  5. 40
  6. 161
  7. 19
  8. 8
  9. 28th
  10. 351
  11. 52
  12. 240
  13. 92
  14. 361
  15. 17
  16. 1891
  17. 9th
  18. 28
  19. 9
  20. 77
  21. 251
  22. 10
  23. 133
  24. 385
  25. 324
  26. 861
  27. 114
  28. 676
  29. 116
  30. 5
  31. 182
  32. 31st
  33. 61
  34. 111
  35. 70
  36. 149
  37. 49
  38. 1770
  39. 41
  40. 3160

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