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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 764 · 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 5, ?, 15, 20, 25? (a) 11 (b) 10 (c) 9 (d) 15
  2. 2.What is the 17th term of the AP 14, 18, 22, 26, …? (a) 82 (b) 68 (c) 64 (d) 78
  3. 3.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 36 (c) 21 (d) 11
  4. 4.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 18 (b) 286 (c) 143 (d) 144
  5. 5.What is the missing term in the AP 5, 7, ?, 11, 13? (a) 8 (b) 11 (c) 10 (d) 9
  6. 6.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 120 (b) 210 (c) 105 (d) 30
  7. 7.What is the 34th term of the AP 3, 8, 13, 18, …? (a) 168 (b) 165 (c) 173 (d) 170
  8. 8.What is the 33rd term of the AP 12, 16, 20, 24, …? (a) 128 (b) 140 (c) 144 (d) 132
  9. 9.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 110 (b) 60 (c) 55 (d) 10
  10. 10.What is the missing term in the AP 15, 23, 31, ?, 47? (a) 38 (b) 47 (c) 39 (d) 40
  11. 11.What is the missing term in the AP 1, 9, ?, 25, 33? (a) 25 (b) 18 (c) 17 (d) 16
  12. 12.What is the missing term in the AP 3, 11, ?, 27, 35? (a) 18 (b) 20 (c) 19 (d) 27
  13. 13.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 35 (c) 342 (d) 171
  14. 14.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 26 (b) 119 (c) 122 (d) 238
  15. 15.What is the sum of the first 11 terms of the AP 8, 14, 20, …? (a) 68 (b) 418 (c) 836 (d) 451
  16. 16.What is the sum of all the whole numbers from 1 to 50? (a) 1275 (b) 2550 (c) 1225 (d) 1250
  17. 17.What is the 37th term of the AP 4, 6, 8, 10, …? (a) 76 (b) 74 (c) 78 (d) 72
  18. 18.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 29 (b) 114 (c) 198 (d) 99
  19. 19.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 368 (b) 37 (c) 200 (d) 184
  20. 20.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 49 (c) 650 (d) 325
  21. 21.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 51 (c) 351 (d) 702
  22. 22.Which term of the AP 4, 13, 22, 31, … is 337? (a) 40th (b) 39th (c) 38th (d) 37th
  23. 23.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 930 (d) 900
  24. 24.What is the 12th term of the AP 15, 19, 23, 27, …? (a) 63 (b) 44 (c) 48 (d) 59
  25. 25.What is the sum of the first 7 terms of the AP 6, 8, 10, …? (a) 168 (b) 84 (c) 91 (d) 18
  26. 26.What is the 29th term of the AP 5, 11, 17, 23, …? (a) 168 (b) 174 (c) 179 (d) 173
  27. 27.What is the missing term in the AP 6, 13, 20, ?, 34? (a) 27 (b) 26 (c) 34 (d) 28
  28. 28.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 253 (c) 506 (d) 231
  29. 29.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 27 (c) 105 (d) 210
  30. 30.What is the sum of all the whole numbers from 1 to 42? (a) 861 (b) 1806 (c) 903 (d) 882
  31. 31.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 184 (b) 15 (c) 92 (d) 96
  32. 32.Which term of the AP 1, 5, 9, 13, … is 65? (a) 16th (b) 18th (c) 17th (d) 19th
  33. 33.What is the missing term in the AP 3, ?, 17, 24, 31? (a) 10 (b) 11 (c) 9 (d) 17
  34. 34.What is the sum of all the whole numbers from 1 to 59? (a) 3540 (b) 1771 (c) 1770 (d) 1711
  35. 35.Which term of the AP 1, 3, 5, 7, … is 29? (a) 14th (b) 15th (c) 16th (d) 17th
  36. 36.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 169 (c) 182 (d) 25
  37. 37.What is the 24th term of the AP 15, 24, 33, 42, …? (a) 222 (b) 207 (c) 216 (d) 231
  38. 38.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 5 (b) 16 (c) 30 (d) 15
  39. 39.What is the 18th term of the AP 3, 11, 19, 27, …? (a) 136 (b) 147 (c) 139 (d) 144
  40. 40.What is the 15th term of the AP 16, 20, 24, 28, …? (a) 56 (b) 72 (c) 60 (d) 76

Answer key

  1. 10
  2. 78
  3. 36
  4. 143
  5. 9
  6. 105
  7. 168
  8. 140
  9. 55
  10. 39
  11. 17
  12. 19
  13. 324
  14. 119
  15. 418
  16. 1275
  17. 76
  18. 99
  19. 184
  20. 625
  21. 676
  22. 38th
  23. 900
  24. 59
  25. 84
  26. 173
  27. 27
  28. 253
  29. 196
  30. 903
  31. 92
  32. 17th
  33. 10
  34. 1770
  35. 15th
  36. 169
  37. 222
  38. 15
  39. 139
  40. 72

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