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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 156 · 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 65? (a) 2145 (b) 4290 (c) 2146 (d) 2080
  2. 2.What is the missing term in the AP 13, 20, 27, ?, 41? (a) 35 (b) 33 (c) 34 (d) 41
  3. 3.What is the sum of the first 9 terms of the AP 1, 4, 7, …? (a) 25 (b) 234 (c) 120 (d) 117
  4. 4.What is the 13th term of the AP 5, 13, 21, 29, …? (a) 109 (b) 96 (c) 104 (d) 101
  5. 5.What is the sum of all the whole numbers from 1 to 35? (a) 595 (b) 1260 (c) 631 (d) 630
  6. 6.What is the 19th term of the AP 4, 13, 22, 31, …? (a) 166 (b) 171 (c) 162 (d) 175
  7. 7.What is the missing term in the AP 19, ?, 29, 34, 39? (a) 25 (b) 24 (c) 23 (d) 29
  8. 8.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 168 (b) 96 (c) 24 (d) 84
  9. 9.What is the 37th term of the AP 14, 19, 24, 29, …? (a) 194 (b) 185 (c) 180 (d) 199
  10. 10.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 5 (b) 15 (c) 30 (d) 16
  11. 11.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 30 (b) 105 (c) 120 (d) 210
  12. 12.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 380 (d) 361
  13. 13.What is the 21st term of the AP 8, 16, 24, 32, …? (a) 169 (b) 176 (c) 160 (d) 168
  14. 14.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 91 (c) 182 (d) 169
  15. 15.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 16 (b) 108 (c) 109 (d) 216
  16. 16.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 180 (b) 18 (c) 90 (d) 99
  17. 17.What is the sum of the first 12 terms of the AP 10, 16, 22, …? (a) 516 (b) 76 (c) 1032 (d) 552
  18. 18.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 102 (b) 87 (c) 174 (d) 27
  19. 19.What is the 11th term of the AP 6, 12, 18, 24, …? (a) 66 (b) 72 (c) 67 (d) 60
  20. 20.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 78 (c) 66 (d) 156
  21. 21.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 108 (b) 28 (c) 186 (d) 93
  22. 22.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 57 (b) 11 (c) 112 (d) 56
  23. 23.Which term of the AP 3, 10, 17, 24, … is 262? (a) 37th (b) 39th (c) 40th (d) 38th
  24. 24.What is the 12th term of the AP 7, 15, 23, 31, …? (a) 103 (b) 95 (c) 88 (d) 96
  25. 25.What is the sum of the first 10 terms of the AP 6, 7, 8, …? (a) 210 (b) 15 (c) 105 (d) 110
  26. 26.What is the sum of the first 12 terms of the AP 5, 6, 7, …? (a) 16 (b) 126 (c) 132 (d) 252
  27. 27.What is the 32nd term of the AP 13, 21, 29, 37, …? (a) 269 (b) 248 (c) 261 (d) 256
  28. 28.What is the 14th term of the AP 12, 21, 30, 39, …? (a) 126 (b) 138 (c) 117 (d) 129
  29. 29.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 396 (b) 726 (c) 63 (d) 363
  30. 30.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 462 (c) 41 (d) 231
  31. 31.What is the sum of the first 10 terms of the AP 10, 13, 16, …? (a) 250 (b) 37 (c) 235 (d) 470
  32. 32.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 272 (c) 256 (d) 31
  33. 33.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 276 (c) 552 (d) 529
  34. 34.What is the sum of all the whole numbers from 1 to 92? (a) 8556 (b) 4278 (c) 4232 (d) 4186
  35. 35.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 342 (b) 189 (c) 35 (d) 171
  36. 36.Which term of the AP 5, 9, 13, 17, … is 65? (a) 18th (b) 16th (c) 17th (d) 15th
  37. 37.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 28 (c) 13 (d) 49
  38. 38.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 14 (b) 198 (c) 100 (d) 99
  39. 39.What is the sum of the first 10 terms of the AP 7, 10, 13, …? (a) 34 (b) 410 (c) 220 (d) 205
  40. 40.What is the sum of all the whole numbers from 1 to 11? (a) 67 (b) 55 (c) 66 (d) 132

Answer key

  1. 2145
  2. 34
  3. 117
  4. 101
  5. 630
  6. 166
  7. 24
  8. 84
  9. 194
  10. 15
  11. 105
  12. 361
  13. 168
  14. 169
  15. 108
  16. 90
  17. 516
  18. 87
  19. 66
  20. 78
  21. 93
  22. 56
  23. 38th
  24. 95
  25. 105
  26. 126
  27. 261
  28. 129
  29. 363
  30. 441
  31. 235
  32. 256
  33. 529
  34. 4278
  35. 171
  36. 16th
  37. 49
  38. 99
  39. 205
  40. 66

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