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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 341 · 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, 14, ?, 30, 38? (a) 22 (b) 30 (c) 21 (d) 23
  2. 2.Which term of the AP 18, 26, 34, 42, … is 114? (a) 13th (b) 12th (c) 14th (d) 15th
  3. 3.What is the 18th term of the AP 5, 8, 11, 14, …? (a) 56 (b) 54 (c) 51 (d) 59
  4. 4.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 35 (c) 342 (d) 171
  5. 5.What is the 30th term of the AP 12, 20, 28, 36, …? (a) 232 (b) 252 (c) 244 (d) 240
  6. 6.What is the 13th term of the AP 11, 18, 25, 32, …? (a) 84 (b) 91 (c) 102 (d) 95
  7. 7.What is the 37th term of the AP 1, 10, 19, 28, …? (a) 333 (b) 324 (c) 325 (d) 334
  8. 8.What is the 38th term of the AP 5, 9, 13, 17, …? (a) 148 (b) 152 (c) 153 (d) 157
  9. 9.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 200 (b) 100 (c) 19 (d) 110
  10. 10.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 63 (b) 56 (c) 112 (d) 14
  11. 11.What is the 10th term of the AP 18, 22, 26, 30, …? (a) 40 (b) 54 (c) 58 (d) 36
  12. 12.What is the sum of the first 6 terms of the AP 8, 11, 14, …? (a) 102 (b) 93 (c) 23 (d) 186
  13. 13.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 210 (c) 105 (d) 196
  14. 14.What is the 13th term of the AP 6, 15, 24, 33, …? (a) 123 (b) 108 (c) 117 (d) 114
  15. 15.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 396 (b) 203 (c) 42 (d) 198
  16. 16.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 45 (b) 192 (c) 384 (d) 216
  17. 17.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 81 (d) 90
  18. 18.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 378 (b) 408 (c) 756 (d) 59
  19. 19.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 13 (b) 56 (c) 110 (d) 55
  20. 20.What is the 16th term of the AP 17, 21, 25, 29, …? (a) 64 (b) 77 (c) 60 (d) 81
  21. 21.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 297 (b) 52 (c) 594 (d) 302
  22. 22.What is the 36th term of the AP 15, 17, 19, 21, …? (a) 72 (b) 85 (c) 70 (d) 87
  23. 23.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 72 (c) 36 (d) 15
  24. 24.Which term of the AP 3, 9, 15, 21, … is 129? (a) 21st (b) 24th (c) 22nd (d) 23rd
  25. 25.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 4753 (c) 4656 (d) 9506
  26. 26.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 128 (b) 136 (c) 23 (d) 256
  27. 27.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 115 (b) 25 (c) 224 (d) 112
  28. 28.What is the 29th term of the AP 6, 13, 20, 27, …? (a) 209 (b) 203 (c) 202 (d) 196
  29. 29.What is the missing term in the AP 8, 13, 18, ?, 28? (a) 23 (b) 22 (c) 24 (d) 28
  30. 30.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 28 (d) 49
  31. 31.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 300 (b) 40 (c) 282 (d) 564
  32. 32.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 650 (c) 625 (d) 325
  33. 33.What is the 29th term of the AP 20, 22, 24, 26, …? (a) 56 (b) 76 (c) 78 (d) 58
  34. 34.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 288 (b) 162 (c) 144 (d) 39
  35. 35.What is the 22nd term of the AP 4, 11, 18, 25, …? (a) 158 (b) 154 (c) 147 (d) 151
  36. 36.What is the 33rd term of the AP 8, 11, 14, 17, …? (a) 107 (b) 99 (c) 96 (d) 104
  37. 37.What is the 17th term of the AP 9, 14, 19, 24, …? (a) 94 (b) 80 (c) 89 (d) 85
  38. 38.What is the 35th term of the AP 4, 12, 20, 28, …? (a) 284 (b) 272 (c) 276 (d) 280
  39. 39.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 682 (b) 346 (c) 341 (d) 56
  40. 40.What is the 12th term of the AP 18, 24, 30, 36, …? (a) 84 (b) 72 (c) 66 (d) 90

Answer key

  1. 22
  2. 13th
  3. 56
  4. 324
  5. 244
  6. 95
  7. 325
  8. 153
  9. 100
  10. 56
  11. 54
  12. 93
  13. 196
  14. 114
  15. 198
  16. 192
  17. 81
  18. 378
  19. 55
  20. 77
  21. 297
  22. 85
  23. 64
  24. 22nd
  25. 4753
  26. 128
  27. 112
  28. 202
  29. 23
  30. 49
  31. 282
  32. 625
  33. 76
  34. 144
  35. 151
  36. 104
  37. 89
  38. 276
  39. 341
  40. 84

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