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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 581 · 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 25th term of the AP 18, 21, 24, 27, …? (a) 72 (b) 90 (c) 75 (d) 93
  2. 2.What is the 16th term of the AP 6, 14, 22, 30, …? (a) 126 (b) 134 (c) 128 (d) 120
  3. 3.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 67 (b) 408 (c) 816 (d) 444
  4. 4.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 28 (b) 108 (c) 120 (d) 216
  5. 5.Which term of the AP 5, 10, 15, 20, … is 170? (a) 36th (b) 34th (c) 33rd (d) 35th
  6. 6.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 352 (b) 176 (c) 26 (d) 187
  7. 7.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 121 (d) 66
  8. 8.Which term of the AP 7, 15, 23, 31, … is 303? (a) 40th (b) 38th (c) 39th (d) 37th
  9. 9.Which term of the AP 13, 21, 29, 37, … is 85? (a) 10th (b) 12th (c) 11th (d) 9th
  10. 10.What is the 22nd term of the AP 2, 7, 12, 17, …? (a) 105 (b) 107 (c) 112 (d) 110
  11. 11.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 253 (c) 506 (d) 484
  12. 12.What is the 12th term of the AP 3, 11, 19, 27, …? (a) 88 (b) 99 (c) 96 (d) 91
  13. 13.What is the missing term in the AP 8, ?, 26, 35, 44? (a) 26 (b) 18 (c) 17 (d) 16
  14. 14.What is the 13th term of the AP 8, 15, 22, 29, …? (a) 92 (b) 91 (c) 99 (d) 84
  15. 15.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 180 (b) 25 (c) 102 (d) 90
  16. 16.What is the sum of the first 8 terms of the AP 9, 12, 15, …? (a) 30 (b) 312 (c) 156 (d) 168
  17. 17.What is the 11th term of the AP 18, 20, 22, 24, …? (a) 40 (b) 38 (c) 20 (d) 22
  18. 18.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 275 (b) 253 (c) 43 (d) 506
  19. 19.Which term of the AP 9, 16, 23, 30, … is 205? (a) 31st (b) 28th (c) 30th (d) 29th
  20. 20.What is the 30th term of the AP 14, 18, 22, 26, …? (a) 120 (b) 130 (c) 134 (d) 116
  21. 21.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 156 (c) 78 (d) 23
  22. 22.What is the 12th term of the AP 15, 23, 31, 39, …? (a) 88 (b) 96 (c) 111 (d) 103
  23. 23.Which term of the AP 6, 9, 12, 15, … is 48? (a) 17th (b) 14th (c) 15th (d) 16th
  24. 24.What is the 23rd term of the AP 4, 13, 22, 31, …? (a) 198 (b) 202 (c) 211 (d) 207
  25. 25.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 650 (d) 625
  26. 26.What is the 33rd term of the AP 9, 15, 21, 27, …? (a) 198 (b) 201 (c) 207 (d) 192
  27. 27.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 10 (b) 13 (c) 12 (d) 11
  28. 28.What is the sum of all the whole numbers from 1 to 82? (a) 3403 (b) 3362 (c) 3321 (d) 6806
  29. 29.What is the 18th term of the AP 10, 14, 18, 22, …? (a) 68 (b) 72 (c) 82 (d) 78
  30. 30.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 286 (b) 23 (c) 154 (d) 143
  31. 31.Which term of the AP 5, 11, 17, 23, … is 239? (a) 42nd (b) 41st (c) 39th (d) 40th
  32. 32.What is the sum of the first 12 terms of the AP 3, 8, 13, …? (a) 58 (b) 396 (c) 732 (d) 366
  33. 33.What is the 23rd term of the AP 10, 19, 28, 37, …? (a) 217 (b) 207 (c) 198 (d) 208
  34. 34.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 69 (b) 858 (c) 429 (d) 462
  35. 35.What is the 30th term of the AP 17, 20, 23, 26, …? (a) 90 (b) 104 (c) 87 (d) 107
  36. 36.What is the 15th term of the AP 6, 13, 20, 27, …? (a) 104 (b) 105 (c) 111 (d) 98
  37. 37.What is the missing term in the AP 3, 12, ?, 30, 39? (a) 20 (b) 22 (c) 30 (d) 21
  38. 38.What is the 13th term of the AP 15, 22, 29, 36, …? (a) 91 (b) 106 (c) 99 (d) 84
  39. 39.What is the 22nd term of the AP 6, 11, 16, 21, …? (a) 110 (b) 111 (c) 116 (d) 105
  40. 40.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 36 (c) 64 (d) 15

Answer key

  1. 90
  2. 126
  3. 408
  4. 108
  5. 34th
  6. 176
  7. 121
  8. 38th
  9. 10th
  10. 107
  11. 484
  12. 91
  13. 17
  14. 92
  15. 90
  16. 156
  17. 38
  18. 253
  19. 29th
  20. 130
  21. 144
  22. 103
  23. 15th
  24. 202
  25. 625
  26. 201
  27. 11
  28. 3403
  29. 78
  30. 143
  31. 40th
  32. 366
  33. 208
  34. 429
  35. 104
  36. 104
  37. 21
  38. 99
  39. 111
  40. 64

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