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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 9 · 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 6 terms of the AP 1, 5, 9, …? (a) 132 (b) 66 (c) 21 (d) 78
  2. 2.What is the sum of the first 8 terms of the AP 5, 8, 11, …? (a) 248 (b) 26 (c) 136 (d) 124
  3. 3.What is the 37th term of the AP 7, 15, 23, 31, …? (a) 288 (b) 303 (c) 296 (d) 295
  4. 4.Which term of the AP 16, 20, 24, 28, … is 52? (a) 10th (b) 9th (c) 11th (d) 13th
  5. 5.What is the 16th term of the AP 18, 25, 32, 39, …? (a) 112 (b) 123 (c) 130 (d) 105
  6. 6.What is the 17th term of the AP 16, 18, 20, 22, …? (a) 34 (b) 32 (c) 50 (d) 48
  7. 7.What is the 15th term of the AP 8, 12, 16, 20, …? (a) 64 (b) 56 (c) 60 (d) 68
  8. 8.What is the sum of all the whole numbers from 1 to 69? (a) 2415 (b) 2416 (c) 4830 (d) 2346
  9. 9.What is the sum of the first 8 terms of the AP 9, 12, 15, …? (a) 156 (b) 168 (c) 312 (d) 30
  10. 10.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 198 (b) 374 (c) 187 (d) 27
  11. 11.Which term of the AP 20, 23, 26, 29, … is 74? (a) 18th (b) 20th (c) 19th (d) 21st
  12. 12.What is the sum of all the whole numbers from 1 to 20? (a) 200 (b) 420 (c) 210 (d) 190
  13. 13.What is the 25th term of the AP 3, 11, 19, 27, …? (a) 200 (b) 203 (c) 195 (d) 192
  14. 14.What is the sum of the first 8 terms of the AP 9, 14, 19, …? (a) 232 (b) 424 (c) 212 (d) 44
  15. 15.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 29 (b) 136 (c) 240 (d) 120
  16. 16.What is the 33rd term of the AP 10, 13, 16, 19, …? (a) 109 (b) 96 (c) 106 (d) 99
  17. 17.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 210 (c) 105 (d) 27
  18. 18.What is the sum of the first 12 terms of the AP 10, 16, 22, …? (a) 1032 (b) 552 (c) 76 (d) 516
  19. 19.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 784 (d) 406
  20. 20.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 154 (b) 14 (c) 78 (d) 77
  21. 21.What is the 19th term of the AP 3, 5, 7, 9, …? (a) 36 (b) 38 (c) 41 (d) 39
  22. 22.Which term of the AP 10, 14, 18, 22, … is 150? (a) 35th (b) 36th (c) 37th (d) 38th
  23. 23.What is the missing term in the AP 4, 10, 16, ?, 28? (a) 22 (b) 21 (c) 23 (d) 28
  24. 24.What is the 34th term of the AP 10, 18, 26, 34, …? (a) 264 (b) 272 (c) 282 (d) 274
  25. 25.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 81 (b) 13 (c) 82 (d) 162
  26. 26.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 92 (c) 91 (d) 78
  27. 27.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 110 (c) 55 (d) 19
  28. 28.What is the 17th term of the AP 5, 13, 21, 29, …? (a) 136 (b) 141 (c) 128 (d) 133
  29. 29.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 168 (b) 184 (c) 336 (d) 35
  30. 30.What is the 15th term of the AP 8, 15, 22, 29, …? (a) 98 (b) 105 (c) 106 (d) 113
  31. 31.What is the sum of all the whole numbers from 1 to 60? (a) 1800 (b) 1830 (c) 1770 (d) 3660
  32. 32.What is the 18th term of the AP 14, 20, 26, 32, …? (a) 122 (b) 116 (c) 108 (d) 102
  33. 33.What is the 30th term of the AP 13, 18, 23, 28, …? (a) 163 (b) 145 (c) 150 (d) 158
  34. 34.What is the sum of the first 11 terms of the AP 8, 10, 12, …? (a) 28 (b) 209 (c) 396 (d) 198
  35. 35.What is the sum of all the whole numbers from 1 to 36? (a) 630 (b) 648 (c) 666 (d) 1332
  36. 36.What is the missing term in the AP 6, 9, ?, 15, 18? (a) 11 (b) 12 (c) 15 (d) 13
  37. 37.What is the 35th term of the AP 5, 11, 17, 23, …? (a) 204 (b) 215 (c) 209 (d) 210
  38. 38.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 60 (b) 11 (c) 64 (d) 120
  39. 39.What is the missing term in the AP 17, 24, ?, 38, 45? (a) 31 (b) 32 (c) 30 (d) 38
  40. 40.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 144 (d) 156

Answer key

  1. 66
  2. 124
  3. 295
  4. 10th
  5. 123
  6. 48
  7. 64
  8. 2415
  9. 156
  10. 187
  11. 19th
  12. 210
  13. 195
  14. 212
  15. 120
  16. 106
  17. 196
  18. 516
  19. 784
  20. 77
  21. 39
  22. 36th
  23. 22
  24. 274
  25. 81
  26. 91
  27. 100
  28. 133
  29. 168
  30. 106
  31. 1830
  32. 116
  33. 158
  34. 198
  35. 666
  36. 12
  37. 209
  38. 60
  39. 31
  40. 144

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