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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 777 · 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 68? (a) 2346 (b) 4692 (c) 2312 (d) 2278
  2. 2.What is the 32nd term of the AP 16, 21, 26, 31, …? (a) 155 (b) 171 (c) 160 (d) 176
  3. 3.What is the sum of the first 10 terms of the AP 2, 5, 8, …? (a) 310 (b) 155 (c) 170 (d) 29
  4. 4.What is the 17th term of the AP 1, 9, 17, 25, …? (a) 128 (b) 129 (c) 136 (d) 137
  5. 5.What is the missing term in the AP 11, ?, 25, 32, 39? (a) 17 (b) 25 (c) 18 (d) 19
  6. 6.What is the missing term in the AP 1, ?, 15, 22, 29? (a) 7 (b) 9 (c) 8 (d) 15
  7. 7.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 784 (d) 55
  8. 8.What is the 17th term of the AP 16, 19, 22, 25, …? (a) 48 (b) 51 (c) 67 (d) 64
  9. 9.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 650 (c) 49 (d) 625
  10. 10.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 440 (b) 40 (c) 220 (d) 240
  11. 11.What is the 14th term of the AP 3, 9, 15, 21, …? (a) 84 (b) 87 (c) 81 (d) 78
  12. 12.What is the 18th term of the AP 13, 15, 17, 19, …? (a) 49 (b) 47 (c) 36 (d) 34
  13. 13.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 324 (d) 35
  14. 14.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 90 (b) 180 (c) 25 (d) 102
  15. 15.What is the 31st term of the AP 18, 24, 30, 36, …? (a) 180 (b) 198 (c) 204 (d) 186
  16. 16.What is the 31st term of the AP 14, 19, 24, 29, …? (a) 169 (b) 150 (c) 155 (d) 164
  17. 17.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 30 (b) 162 (c) 324 (d) 165
  18. 18.What is the sum of all the whole numbers from 1 to 33? (a) 562 (b) 528 (c) 1122 (d) 561
  19. 19.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 143 (b) 18 (c) 286 (d) 144
  20. 20.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 171 (c) 342 (d) 153
  21. 21.What is the sum of the first 11 terms of the AP 6, 9, 12, …? (a) 234 (b) 462 (c) 231 (d) 36
  22. 22.What is the missing term in the AP 6, 9, ?, 15, 18? (a) 15 (b) 11 (c) 13 (d) 12
  23. 23.What is the sum of the first 7 terms of the AP 5, 8, 11, …? (a) 98 (b) 101 (c) 196 (d) 23
  24. 24.What is the 13th term of the AP 9, 11, 13, 15, …? (a) 26 (b) 33 (c) 35 (d) 24
  25. 25.What is the 11th term of the AP 2, 7, 12, 17, …? (a) 52 (b) 57 (c) 55 (d) 50
  26. 26.What is the 34th term of the AP 4, 11, 18, 25, …? (a) 231 (b) 235 (c) 238 (d) 242
  27. 27.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 14 (b) 18 (c) 16 (d) 15
  28. 28.What is the 19th term of the AP 16, 19, 22, 25, …? (a) 73 (b) 54 (c) 57 (d) 70
  29. 29.What is the 39th term of the AP 4, 6, 8, 10, …? (a) 76 (b) 80 (c) 82 (d) 78
  30. 30.What is the 28th term of the AP 6, 8, 10, 12, …? (a) 62 (b) 60 (c) 54 (d) 56
  31. 31.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 168 (b) 90 (c) 84 (d) 19
  32. 32.What is the missing term in the AP 15, 24, ?, 42, 51? (a) 33 (b) 42 (c) 32 (d) 34
  33. 33.What is the sum of all the whole numbers from 1 to 78? (a) 3081 (b) 3003 (c) 6162 (d) 3042
  34. 34.What is the 18th term of the AP 5, 13, 21, 29, …? (a) 149 (b) 144 (c) 136 (d) 141
  35. 35.What is the 35th term of the AP 11, 16, 21, 26, …? (a) 170 (b) 181 (c) 186 (d) 175
  36. 36.What is the 40th term of the AP 8, 12, 16, 20, …? (a) 164 (b) 156 (c) 160 (d) 168
  37. 37.What is the 23rd term of the AP 3, 10, 17, 24, …? (a) 154 (b) 164 (c) 157 (d) 161
  38. 38.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 75 (b) 504 (c) 1008 (d) 540
  39. 39.What is the missing term in the AP 10, ?, 24, 31, 38? (a) 24 (b) 16 (c) 17 (d) 18
  40. 40.What is the 14th term of the AP 18, 26, 34, 42, …? (a) 104 (b) 122 (c) 130 (d) 112

Answer key

  1. 2346
  2. 171
  3. 155
  4. 129
  5. 18
  6. 8
  7. 784
  8. 64
  9. 625
  10. 220
  11. 81
  12. 47
  13. 324
  14. 90
  15. 198
  16. 164
  17. 162
  18. 561
  19. 143
  20. 171
  21. 231
  22. 12
  23. 98
  24. 33
  25. 52
  26. 235
  27. 15
  28. 70
  29. 80
  30. 60
  31. 84
  32. 33
  33. 3081
  34. 141
  35. 181
  36. 164
  37. 157
  38. 504
  39. 17
  40. 122

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