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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 200 · 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 12th term of the AP 10, 12, 14, 16, …? (a) 34 (b) 24 (c) 22 (d) 32
  2. 2.What is the 36th term of the AP 13, 19, 25, 31, …? (a) 210 (b) 216 (c) 223 (d) 229
  3. 3.What is the 19th term of the AP 15, 20, 25, 30, …? (a) 90 (b) 105 (c) 95 (d) 110
  4. 4.What is the 39th term of the AP 5, 9, 13, 17, …? (a) 157 (b) 161 (c) 156 (d) 152
  5. 5.What is the sum of all the whole numbers from 1 to 75? (a) 2851 (b) 2850 (c) 5700 (d) 2775
  6. 6.What is the sum of all the whole numbers from 1 to 61? (a) 1892 (b) 1891 (c) 1830 (d) 3782
  7. 7.What is the sum of all the whole numbers from 1 to 24? (a) 288 (b) 276 (c) 300 (d) 600
  8. 8.What is the sum of all the whole numbers from 1 to 30? (a) 435 (b) 465 (c) 450 (d) 930
  9. 9.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 9 (b) 7 (c) 10 (d) 8
  10. 10.What is the 10th term of the AP 15, 18, 21, 24, …? (a) 42 (b) 45 (c) 27 (d) 30
  11. 11.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 7 (b) 54 (c) 30 (d) 27
  12. 12.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 104 (b) 184 (c) 22 (d) 92
  13. 13.What is the sum of all the whole numbers from 1 to 73? (a) 2701 (b) 2628 (c) 2702 (d) 5402
  14. 14.What is the sum of all the whole numbers from 1 to 32? (a) 496 (b) 512 (c) 1056 (d) 528
  15. 15.Which term of the AP 3, 12, 21, 30, … is 264? (a) 31st (b) 30th (c) 32nd (d) 29th
  16. 16.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 45 (b) 378 (c) 189 (d) 210
  17. 17.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 41 (b) 450 (c) 243 (d) 225
  18. 18.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 78 (c) 23 (d) 156
  19. 19.What is the 22nd term of the AP 13, 16, 19, 22, …? (a) 63 (b) 76 (c) 66 (d) 79
  20. 20.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 20 (b) 196 (c) 105 (d) 98
  21. 21.What is the 21st term of the AP 11, 18, 25, 32, …? (a) 140 (b) 147 (c) 158 (d) 151
  22. 22.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 57 (c) 841 (d) 435
  23. 23.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 96 (b) 192 (c) 31 (d) 114
  24. 24.What is the 12th term of the AP 5, 8, 11, 14, …? (a) 36 (b) 41 (c) 38 (d) 33
  25. 25.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 100 (c) 19 (d) 110
  26. 26.What is the 40th term of the AP 1, 8, 15, 22, …? (a) 281 (b) 274 (c) 273 (d) 280
  27. 27.What is the sum of all the whole numbers from 1 to 10? (a) 55 (b) 110 (c) 50 (d) 45
  28. 28.Which term of the AP 6, 11, 16, 21, … is 116? (a) 24th (b) 22nd (c) 25th (d) 23rd
  29. 29.What is the 13th term of the AP 3, 5, 7, 9, …? (a) 29 (b) 26 (c) 27 (d) 24
  30. 30.What is the 25th term of the AP 15, 24, 33, 42, …? (a) 216 (b) 225 (c) 231 (d) 240
  31. 31.What is the 10th term of the AP 16, 24, 32, 40, …? (a) 96 (b) 80 (c) 88 (d) 72
  32. 32.What is the sum of all the whole numbers from 1 to 38? (a) 741 (b) 722 (c) 1482 (d) 703
  33. 33.What is the 12th term of the AP 5, 13, 21, 29, …? (a) 88 (b) 96 (c) 93 (d) 101
  34. 34.What is the 10th term of the AP 19, 25, 31, 37, …? (a) 73 (b) 79 (c) 60 (d) 54
  35. 35.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 46 (b) 312 (c) 576 (d) 288
  36. 36.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 11 (b) 70 (c) 65 (d) 130
  37. 37.Which term of the AP 4, 7, 10, 13, … is 40? (a) 14th (b) 13th (c) 15th (d) 12th
  38. 38.What is the 23rd term of the AP 10, 14, 18, 22, …? (a) 98 (b) 102 (c) 92 (d) 88
  39. 39.What is the sum of all the whole numbers from 1 to 65? (a) 2145 (b) 2080 (c) 2146 (d) 4290
  40. 40.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 144 (b) 72 (c) 12 (d) 73

Answer key

  1. 32
  2. 223
  3. 105
  4. 157
  5. 2850
  6. 1891
  7. 300
  8. 465
  9. 8
  10. 42
  11. 27
  12. 92
  13. 2701
  14. 528
  15. 30th
  16. 189
  17. 225
  18. 144
  19. 76
  20. 98
  21. 151
  22. 841
  23. 96
  24. 38
  25. 100
  26. 274
  27. 55
  28. 23rd
  29. 27
  30. 231
  31. 88
  32. 741
  33. 93
  34. 73
  35. 288
  36. 65
  37. 13th
  38. 98
  39. 2145
  40. 72

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