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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 691 · 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 11th term of the AP 20, 29, 38, 47, …? (a) 119 (b) 99 (c) 110 (d) 90
  2. 2.What is the sum of the first 12 terms of the AP 1, 5, 9, …? (a) 276 (b) 45 (c) 300 (d) 552
  3. 3.What is the sum of the first 6 terms of the AP 10, 16, 22, …? (a) 168 (b) 150 (c) 300 (d) 40
  4. 4.What is the 30th term of the AP 9, 11, 13, 15, …? (a) 58 (b) 60 (c) 69 (d) 67
  5. 5.Which term of the AP 5, 8, 11, 14, … is 119? (a) 38th (b) 41st (c) 40th (d) 39th
  6. 6.What is the 23rd term of the AP 18, 22, 26, 30, …? (a) 92 (b) 88 (c) 110 (d) 106
  7. 7.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 192 (b) 372 (c) 186 (d) 21
  8. 8.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 114 (b) 12 (c) 60 (d) 57
  9. 9.What is the sum of all the whole numbers from 1 to 11? (a) 55 (b) 66 (c) 132 (d) 67
  10. 10.What is the 13th term of the AP 7, 14, 21, 28, …? (a) 84 (b) 92 (c) 91 (d) 98
  11. 11.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 190 (d) 37
  12. 12.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 7832 (c) 3828 (d) 3916
  13. 13.What is the sum of the first 10 terms of the AP 9, 13, 17, …? (a) 290 (b) 270 (c) 45 (d) 540
  14. 14.Which term of the AP 12, 21, 30, 39, … is 228? (a) 26th (b) 25th (c) 27th (d) 24th
  15. 15.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 812 (d) 784
  16. 16.What is the 39th term of the AP 16, 18, 20, 22, …? (a) 76 (b) 78 (c) 94 (d) 92
  17. 17.What is the missing term in the AP 10, 14, 18, ?, 26? (a) 22 (b) 23 (c) 21 (d) 26
  18. 18.What is the 24th term of the AP 11, 16, 21, 26, …? (a) 120 (b) 126 (c) 115 (d) 131
  19. 19.What is the 30th term of the AP 11, 19, 27, 35, …? (a) 232 (b) 251 (c) 243 (d) 240
  20. 20.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 2888 (c) 2926 (d) 5852
  21. 21.What is the 19th term of the AP 19, 24, 29, 34, …? (a) 90 (b) 114 (c) 95 (d) 109
  22. 22.What is the sum of the first 9 terms of the AP 7, 12, 17, …? (a) 486 (b) 248 (c) 243 (d) 47
  23. 23.What is the missing term in the AP 8, 11, 14, ?, 20? (a) 20 (b) 16 (c) 17 (d) 18
  24. 24.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 900 (c) 59 (d) 465
  25. 25.What is the 10th term of the AP 5, 11, 17, 23, …? (a) 65 (b) 54 (c) 59 (d) 60
  26. 26.What is the 40th term of the AP 5, 8, 11, 14, …? (a) 122 (b) 117 (c) 125 (d) 120
  27. 27.What is the sum of all the whole numbers from 1 to 46? (a) 1035 (b) 1081 (c) 1058 (d) 2162
  28. 28.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 522 (b) 261 (c) 49 (d) 266
  29. 29.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 22 (b) 140 (c) 70 (d) 80
  30. 30.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 36 (c) 72 (d) 15
  31. 31.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 190 (c) 420 (d) 200
  32. 32.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 444 (b) 414 (c) 62 (d) 828
  33. 33.What is the sum of all the whole numbers from 1 to 64? (a) 2016 (b) 2048 (c) 4160 (d) 2080
  34. 34.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 43 (c) 506 (d) 484
  35. 35.What is the sum of the first 12 terms of the AP 4, 5, 6, …? (a) 114 (b) 228 (c) 120 (d) 15
  36. 36.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 126 (b) 252 (c) 127 (d) 18
  37. 37.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 169 (c) 91 (d) 182
  38. 38.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 180 (b) 91 (c) 14 (d) 90
  39. 39.Which term of the AP 15, 23, 31, 39, … is 95? (a) 10th (b) 12th (c) 13th (d) 11th
  40. 40.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 650 (c) 325 (d) 300

Answer key

  1. 110
  2. 276
  3. 150
  4. 67
  5. 39th
  6. 106
  7. 186
  8. 57
  9. 66
  10. 91
  11. 361
  12. 3916
  13. 270
  14. 25th
  15. 784
  16. 92
  17. 22
  18. 126
  19. 243
  20. 2926
  21. 109
  22. 243
  23. 17
  24. 900
  25. 59
  26. 122
  27. 1081
  28. 261
  29. 70
  30. 64
  31. 210
  32. 414
  33. 2080
  34. 484
  35. 114
  36. 126
  37. 169
  38. 90
  39. 11th
  40. 325

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