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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 799 · 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 30th term of the AP 8, 16, 24, 32, …? (a) 240 (b) 248 (c) 232 (d) 241
  2. 2.What is the missing term in the AP 14, ?, 26, 32, 38? (a) 26 (b) 19 (c) 20 (d) 21
  3. 3.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 41 (c) 441 (d) 231
  4. 4.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 144 (b) 16 (c) 80 (d) 72
  5. 5.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 144 (d) 23
  6. 6.Which term of the AP 6, 14, 22, 30, … is 110? (a) 13th (b) 15th (c) 16th (d) 14th
  7. 7.What is the 37th term of the AP 10, 14, 18, 22, …? (a) 144 (b) 158 (c) 148 (d) 154
  8. 8.What is the missing term in the AP 4, ?, 12, 16, 20? (a) 12 (b) 8 (c) 9 (d) 7
  9. 9.What is the sum of the first 5 terms of the AP 8, 13, 18, …? (a) 28 (b) 95 (c) 180 (d) 90
  10. 10.What is the sum of the first 12 terms of the AP 3, 9, 15, …? (a) 432 (b) 864 (c) 69 (d) 468
  11. 11.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 300 (c) 576 (d) 47
  12. 12.What is the 13th term of the AP 16, 22, 28, 34, …? (a) 94 (b) 88 (c) 72 (d) 78
  13. 13.What is the 19th term of the AP 13, 20, 27, 34, …? (a) 146 (b) 126 (c) 139 (d) 133
  14. 14.What is the 37th term of the AP 2, 5, 8, 11, …? (a) 108 (b) 111 (c) 113 (d) 110
  15. 15.What is the sum of the first 12 terms of the AP 8, 12, 16, …? (a) 720 (b) 360 (c) 384 (d) 52
  16. 16.What is the missing term in the AP 13, 20, 27, ?, 41? (a) 41 (b) 33 (c) 34 (d) 35
  17. 17.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 150 (b) 15 (c) 78 (d) 75
  18. 18.What is the 19th term of the AP 14, 21, 28, 35, …? (a) 133 (b) 147 (c) 126 (d) 140
  19. 19.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 19 (c) 110 (d) 100
  20. 20.Which term of the AP 13, 15, 17, 19, … is 31? (a) 11th (b) 12th (c) 9th (d) 10th
  21. 21.What is the 16th term of the AP 5, 14, 23, 32, …? (a) 135 (b) 149 (c) 144 (d) 140
  22. 22.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 400 (c) 210 (d) 39
  23. 23.Which term of the AP 19, 26, 33, 40, … is 173? (a) 24th (b) 23rd (c) 22nd (d) 25th
  24. 24.What is the 14th term of the AP 1, 8, 15, 22, …? (a) 99 (b) 91 (c) 98 (d) 92
  25. 25.What is the missing term in the AP 7, 11, 15, ?, 23? (a) 20 (b) 19 (c) 18 (d) 23
  26. 26.Which term of the AP 17, 23, 29, 35, … is 197? (a) 31st (b) 33rd (c) 32nd (d) 30th
  27. 27.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 56 (b) 49 (c) 13 (d) 98
  28. 28.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 396 (b) 203 (c) 198 (d) 42
  29. 29.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 184 (b) 22 (c) 92 (d) 104
  30. 30.What is the 37th term of the AP 1, 9, 17, 25, …? (a) 289 (b) 296 (c) 297 (d) 288
  31. 31.What is the 31st term of the AP 14, 21, 28, 35, …? (a) 231 (b) 217 (c) 210 (d) 224
  32. 32.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 240 (b) 260 (c) 480 (d) 42
  33. 33.What is the missing term in the AP 19, 26, 33, ?, 47? (a) 39 (b) 40 (c) 47 (d) 41
  34. 34.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 612 (b) 333 (c) 58 (d) 306
  35. 35.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 66 (c) 78 (d) 156
  36. 36.What is the sum of the first 12 terms of the AP 5, 8, 11, …? (a) 258 (b) 276 (c) 38 (d) 516
  37. 37.What is the sum of the first 7 terms of the AP 4, 9, 14, …? (a) 138 (b) 133 (c) 34 (d) 266
  38. 38.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 435 (c) 870 (d) 841
  39. 39.What is the sum of all the whole numbers from 1 to 20? (a) 420 (b) 190 (c) 210 (d) 200
  40. 40.What is the 39th term of the AP 8, 10, 12, 14, …? (a) 78 (b) 86 (c) 76 (d) 84

Answer key

  1. 240
  2. 20
  3. 441
  4. 72
  5. 144
  6. 14th
  7. 154
  8. 8
  9. 90
  10. 432
  11. 576
  12. 88
  13. 139
  14. 110
  15. 360
  16. 34
  17. 75
  18. 140
  19. 100
  20. 10th
  21. 140
  22. 400
  23. 23rd
  24. 92
  25. 19
  26. 31st
  27. 49
  28. 198
  29. 92
  30. 289
  31. 224
  32. 240
  33. 40
  34. 306
  35. 78
  36. 258
  37. 133
  38. 841
  39. 210
  40. 84

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