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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 780 · 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 missing term in the AP 6, ?, 10, 12, 14? (a) 8 (b) 9 (c) 10 (d) 7
  2. 2.Which term of the AP 17, 20, 23, 26, … is 41? (a) 10th (b) 8th (c) 11th (d) 9th
  3. 3.What is the 14th term of the AP 10, 16, 22, 28, …? (a) 78 (b) 84 (c) 94 (d) 88
  4. 4.What is the sum of all the whole numbers from 1 to 100? (a) 5050 (b) 10100 (c) 5000 (d) 4950
  5. 5.What is the sum of the first 6 terms of the AP 3, 6, 9, …? (a) 18 (b) 63 (c) 126 (d) 72
  6. 6.What is the 15th term of the AP 17, 20, 23, 26, …? (a) 62 (b) 42 (c) 59 (d) 45
  7. 7.What is the sum of all the whole numbers from 1 to 32? (a) 496 (b) 1056 (c) 528 (d) 512
  8. 8.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 13 (b) 55 (c) 110 (d) 56
  9. 9.What is the missing term in the AP 18, ?, 32, 39, 46? (a) 32 (b) 25 (c) 24 (d) 26
  10. 10.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 72 (c) 78 (d) 156
  11. 11.What is the sum of the first 7 terms of the AP 4, 9, 14, …? (a) 34 (b) 133 (c) 266 (d) 138
  12. 12.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2278 (c) 2346 (d) 2312
  13. 13.What is the 24th term of the AP 5, 14, 23, 32, …? (a) 216 (b) 221 (c) 207 (d) 212
  14. 14.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 552 (d) 529
  15. 15.What is the missing term in the AP 4, 8, 12, ?, 20? (a) 15 (b) 17 (c) 20 (d) 16
  16. 16.What is the 22nd term of the AP 7, 10, 13, 16, …? (a) 70 (b) 73 (c) 66 (d) 63
  17. 17.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 147 (b) 168 (c) 39 (d) 294
  18. 18.What is the missing term in the AP 8, 17, ?, 35, 44? (a) 26 (b) 25 (c) 27 (d) 35
  19. 19.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 3240 (c) 3200 (d) 6480
  20. 20.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 91 (c) 25 (d) 182
  21. 21.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 12 (b) 42 (c) 48 (d) 84
  22. 22.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 225 (d) 240
  23. 23.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 21 (b) 224 (c) 120 (d) 112
  24. 24.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 56 (b) 341 (c) 682 (d) 346
  25. 25.What is the 32nd term of the AP 16, 19, 22, 25, …? (a) 112 (b) 93 (c) 96 (d) 109
  26. 26.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 378 (b) 210 (c) 45 (d) 189
  27. 27.What is the missing term in the AP 14, 16, 18, ?, 22? (a) 20 (b) 21 (c) 22 (d) 19
  28. 28.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 870 (c) 841 (d) 57
  29. 29.What is the 40th term of the AP 19, 21, 23, 25, …? (a) 78 (b) 97 (c) 99 (d) 80
  30. 30.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 440 (b) 30 (c) 220 (d) 231
  31. 31.What is the 17th term of the AP 1, 9, 17, 25, …? (a) 128 (b) 129 (c) 136 (d) 137
  32. 32.Which term of the AP 4, 6, 8, 10, … is 24? (a) 11th (b) 10th (c) 12th (d) 13th
  33. 33.Which term of the AP 9, 17, 25, 33, … is 289? (a) 38th (b) 36th (c) 37th (d) 35th
  34. 34.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 540 (b) 288 (c) 270 (d) 39
  35. 35.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 171 (c) 35 (d) 324
  36. 36.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 154 (b) 77 (c) 84 (d) 17
  37. 37.What is the missing term in the AP 18, ?, 26, 30, 34? (a) 26 (b) 21 (c) 22 (d) 23
  38. 38.What is the sum of the first 12 terms of the AP 2, 4, 6, …? (a) 156 (b) 168 (c) 312 (d) 24
  39. 39.What is the 21st term of the AP 3, 10, 17, 24, …? (a) 150 (b) 140 (c) 147 (d) 143
  40. 40.What is the 32nd term of the AP 15, 19, 23, 27, …? (a) 143 (b) 128 (c) 139 (d) 124

Answer key

  1. 8
  2. 9th
  3. 88
  4. 5050
  5. 63
  6. 59
  7. 528
  8. 55
  9. 25
  10. 78
  11. 133
  12. 2346
  13. 212
  14. 529
  15. 16
  16. 70
  17. 147
  18. 26
  19. 3240
  20. 169
  21. 42
  22. 225
  23. 112
  24. 341
  25. 109
  26. 189
  27. 20
  28. 841
  29. 97
  30. 220
  31. 129
  32. 11th
  33. 36th
  34. 270
  35. 324
  36. 77
  37. 22
  38. 156
  39. 143
  40. 139

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