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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 768 · 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 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 306 (c) 153 (d) 33
  2. 2.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 55 (d) 100
  3. 3.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3828 (c) 7832 (d) 3916
  4. 4.What is the 22nd term of the AP 5, 9, 13, 17, …? (a) 88 (b) 93 (c) 84 (d) 89
  5. 5.What is the 13th term of the AP 11, 18, 25, 32, …? (a) 102 (b) 84 (c) 91 (d) 95
  6. 6.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 122 (b) 242 (c) 121 (d) 16
  7. 7.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 22 (b) 104 (c) 184 (d) 92
  8. 8.What is the 38th term of the AP 3, 12, 21, 30, …? (a) 342 (b) 336 (c) 345 (d) 333
  9. 9.Which term of the AP 2, 5, 8, 11, … is 80? (a) 28th (b) 29th (c) 26th (d) 27th
  10. 10.What is the missing term in the AP 2, 7, 12, ?, 22? (a) 16 (b) 18 (c) 17 (d) 22
  11. 11.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 16 (b) 182 (c) 92 (d) 91
  12. 12.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 408 (b) 378 (c) 59 (d) 756
  13. 13.What is the 11th term of the AP 12, 15, 18, 21, …? (a) 45 (b) 33 (c) 30 (d) 42
  14. 14.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 55 (d) 784
  15. 15.What is the missing term in the AP 3, 5, ?, 9, 11? (a) 7 (b) 6 (c) 8 (d) 9
  16. 16.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 161 (b) 322 (c) 38 (d) 166
  17. 17.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 112 (b) 14 (c) 63 (d) 56
  18. 18.Which term of the AP 6, 13, 20, 27, … is 55? (a) 9th (b) 8th (c) 7th (d) 10th
  19. 19.What is the 35th term of the AP 4, 6, 8, 10, …? (a) 68 (b) 74 (c) 72 (d) 70
  20. 20.What is the missing term in the AP 7, ?, 11, 13, 15? (a) 9 (b) 10 (c) 11 (d) 8
  21. 21.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 78 (c) 156 (d) 66
  22. 22.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 870 (d) 841
  23. 23.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 28 (b) 120 (c) 108 (d) 216
  24. 24.What is the 19th term of the AP 9, 12, 15, 18, …? (a) 57 (b) 66 (c) 63 (d) 54
  25. 25.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 62 (b) 380 (c) 700 (d) 350
  26. 26.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 35 (b) 215 (c) 230 (d) 430
  27. 27.What is the missing term in the AP 14, 17, ?, 23, 26? (a) 20 (b) 21 (c) 23 (d) 19
  28. 28.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 184 (b) 38 (c) 328 (d) 164
  29. 29.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 600 (c) 300 (d) 47
  30. 30.What is the sum of all the whole numbers from 1 to 63? (a) 2016 (b) 2017 (c) 1953 (d) 4032
  31. 31.What is the missing term in the AP 3, ?, 19, 27, 35? (a) 12 (b) 10 (c) 19 (d) 11
  32. 32.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 169 (c) 182 (d) 91
  33. 33.What is the 36th term of the AP 7, 15, 23, 31, …? (a) 287 (b) 295 (c) 288 (d) 280
  34. 34.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 119 (b) 112 (c) 22 (d) 224
  35. 35.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 69 (b) 429 (c) 858 (d) 462
  36. 36.What is the 37th term of the AP 13, 17, 21, 25, …? (a) 148 (b) 144 (c) 157 (d) 161
  37. 37.What is the sum of the first 7 terms of the AP 1, 4, 7, …? (a) 73 (b) 140 (c) 19 (d) 70
  38. 38.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 198 (b) 187 (c) 374 (d) 27
  39. 39.What is the 30th term of the AP 4, 9, 14, 19, …? (a) 154 (b) 149 (c) 150 (d) 145
  40. 40.What is the 26th term of the AP 5, 11, 17, 23, …? (a) 150 (b) 156 (c) 155 (d) 161

Answer key

  1. 289
  2. 100
  3. 3916
  4. 89
  5. 95
  6. 121
  7. 92
  8. 336
  9. 27th
  10. 17
  11. 91
  12. 378
  13. 42
  14. 784
  15. 7
  16. 161
  17. 56
  18. 8th
  19. 72
  20. 9
  21. 78
  22. 841
  23. 108
  24. 63
  25. 350
  26. 215
  27. 20
  28. 164
  29. 576
  30. 2016
  31. 11
  32. 169
  33. 287
  34. 112
  35. 429
  36. 157
  37. 70
  38. 187
  39. 149
  40. 155

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