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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 602 · 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 the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 21 (d) 121
  2. 2.What is the 40th term of the AP 12, 16, 20, 24, …? (a) 156 (b) 160 (c) 172 (d) 168
  3. 3.What is the 31st term of the AP 2, 8, 14, 20, …? (a) 182 (b) 180 (c) 186 (d) 188
  4. 4.What is the 12th term of the AP 7, 11, 15, 19, …? (a) 44 (b) 51 (c) 55 (d) 48
  5. 5.What is the sum of all the whole numbers from 1 to 68? (a) 2278 (b) 4692 (c) 2346 (d) 2312
  6. 6.What is the sum of all the whole numbers from 1 to 77? (a) 2926 (b) 3004 (c) 3003 (d) 6006
  7. 7.What is the 23rd term of the AP 17, 20, 23, 26, …? (a) 69 (b) 66 (c) 86 (d) 83
  8. 8.What is the sum of the first 11 terms of the AP 7, 8, 9, …? (a) 264 (b) 17 (c) 132 (d) 133
  9. 9.What is the 14th term of the AP 2, 5, 8, 11, …? (a) 42 (b) 41 (c) 39 (d) 44
  10. 10.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 441 (c) 462 (d) 231
  11. 11.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 30 (b) 54 (c) 27 (d) 7
  12. 12.What is the sum of all the whole numbers from 1 to 87? (a) 3741 (b) 3829 (c) 7656 (d) 3828
  13. 13.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 33 (b) 126 (c) 216 (d) 108
  14. 14.What is the 17th term of the AP 19, 26, 33, 40, …? (a) 119 (b) 112 (c) 138 (d) 131
  15. 15.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 100 (c) 110 (d) 19
  16. 16.Which term of the AP 4, 6, 8, 10, … is 76? (a) 36th (b) 39th (c) 38th (d) 37th
  17. 17.What is the sum of all the whole numbers from 1 to 76? (a) 5852 (b) 2888 (c) 2850 (d) 2926
  18. 18.What is the missing term in the AP 20, 26, ?, 38, 44? (a) 33 (b) 38 (c) 31 (d) 32
  19. 19.What is the missing term in the AP 20, 29, ?, 47, 56? (a) 39 (b) 37 (c) 38 (d) 47
  20. 20.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 132 (b) 121 (c) 21 (d) 242
  21. 21.What is the 19th term of the AP 15, 17, 19, 21, …? (a) 36 (b) 51 (c) 38 (d) 53
  22. 22.Which term of the AP 2, 7, 12, 17, … is 192? (a) 38th (b) 39th (c) 40th (d) 41st
  23. 23.What is the sum of all the whole numbers from 1 to 18? (a) 171 (b) 162 (c) 342 (d) 153
  24. 24.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 342 (c) 324 (d) 35
  25. 25.What is the 16th term of the AP 10, 16, 22, 28, …? (a) 106 (b) 96 (c) 90 (d) 100
  26. 26.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 304 (b) 168 (c) 33 (d) 152
  27. 27.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 110 (b) 19 (c) 100 (d) 200
  28. 28.What is the 24th term of the AP 5, 12, 19, 26, …? (a) 166 (b) 161 (c) 168 (d) 173
  29. 29.What is the 14th term of the AP 18, 23, 28, 33, …? (a) 70 (b) 65 (c) 83 (d) 88
  30. 30.What is the 31st term of the AP 11, 14, 17, 20, …? (a) 104 (b) 90 (c) 101 (d) 93
  31. 31.Which term of the AP 5, 11, 17, 23, … is 233? (a) 40th (b) 39th (c) 38th (d) 41st
  32. 32.What is the 34th term of the AP 15, 19, 23, 27, …? (a) 151 (b) 132 (c) 136 (d) 147
  33. 33.What is the 40th term of the AP 8, 11, 14, 17, …? (a) 128 (b) 117 (c) 120 (d) 125
  34. 34.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 352 (b) 179 (c) 176 (d) 31
  35. 35.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 58 (b) 726 (c) 363 (d) 368
  36. 36.Which term of the AP 8, 14, 20, 26, … is 134? (a) 23rd (b) 21st (c) 24th (d) 22nd
  37. 37.What is the 25th term of the AP 17, 22, 27, 32, …? (a) 142 (b) 120 (c) 137 (d) 125
  38. 38.What is the missing term in the AP 18, 23, 28, ?, 38? (a) 38 (b) 32 (c) 34 (d) 33
  39. 39.What is the sum of all the whole numbers from 1 to 82? (a) 3403 (b) 6806 (c) 3321 (d) 3362
  40. 40.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 256 (b) 253 (c) 506 (d) 38

Answer key

  1. 121
  2. 168
  3. 182
  4. 51
  5. 2346
  6. 3003
  7. 83
  8. 132
  9. 41
  10. 441
  11. 27
  12. 3828
  13. 108
  14. 131
  15. 100
  16. 37th
  17. 2926
  18. 32
  19. 38
  20. 121
  21. 51
  22. 39th
  23. 171
  24. 324
  25. 100
  26. 152
  27. 100
  28. 166
  29. 83
  30. 101
  31. 39th
  32. 147
  33. 125
  34. 176
  35. 363
  36. 22nd
  37. 137
  38. 33
  39. 3403
  40. 253

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