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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 530 · 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 17th term of the AP 6, 9, 12, 15, …? (a) 48 (b) 57 (c) 51 (d) 54
  2. 2.What is the 12th term of the AP 6, 9, 12, 15, …? (a) 36 (b) 42 (c) 39 (d) 33
  3. 3.What is the sum of all the whole numbers from 1 to 41? (a) 1722 (b) 861 (c) 862 (d) 820
  4. 4.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 380 (c) 190 (d) 361
  5. 5.Which term of the AP 14, 16, 18, 20, … is 52? (a) 26th (b) 19th (c) 21st (d) 20th
  6. 6.What is the 17th term of the AP 1, 3, 5, 7, …? (a) 32 (b) 35 (c) 34 (d) 33
  7. 7.What is the 33rd term of the AP 12, 16, 20, 24, …? (a) 132 (b) 140 (c) 144 (d) 128
  8. 8.What is the 32nd term of the AP 4, 11, 18, 25, …? (a) 228 (b) 217 (c) 224 (d) 221
  9. 9.What is the 34th term of the AP 19, 24, 29, 34, …? (a) 170 (b) 184 (c) 165 (d) 189
  10. 10.What is the 28th term of the AP 14, 22, 30, 38, …? (a) 224 (b) 216 (c) 238 (d) 230
  11. 11.What is the sum of the first 5 terms of the AP 4, 8, 12, …? (a) 120 (b) 60 (c) 70 (d) 20
  12. 12.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 4753 (c) 9506 (d) 4656
  13. 13.What is the 36th term of the AP 2, 6, 10, 14, …? (a) 140 (b) 144 (c) 146 (d) 142
  14. 14.Which term of the AP 7, 10, 13, 16, … is 124? (a) 40th (b) 39th (c) 41st (d) 42nd
  15. 15.What is the sum of all the whole numbers from 1 to 21? (a) 231 (b) 210 (c) 462 (d) 232
  16. 16.What is the 25th term of the AP 18, 24, 30, 36, …? (a) 162 (b) 144 (c) 168 (d) 150
  17. 17.What is the 31st term of the AP 19, 27, 35, 43, …? (a) 267 (b) 240 (c) 248 (d) 259
  18. 18.What is the sum of all the whole numbers from 1 to 60? (a) 3660 (b) 1770 (c) 1830 (d) 1800
  19. 19.What is the sum of all the whole numbers from 1 to 57? (a) 3306 (b) 1596 (c) 1653 (d) 1654
  20. 20.What is the 38th term of the AP 8, 10, 12, 14, …? (a) 82 (b) 74 (c) 84 (d) 76
  21. 21.What is the 17th term of the AP 9, 12, 15, 18, …? (a) 51 (b) 57 (c) 48 (d) 60
  22. 22.What is the missing term in the AP 7, 13, ?, 25, 31? (a) 25 (b) 20 (c) 19 (d) 18
  23. 23.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 676 (c) 51 (d) 702
  24. 24.What is the sum of the first 5 terms of the AP 8, 13, 18, …? (a) 95 (b) 180 (c) 90 (d) 28
  25. 25.Which term of the AP 10, 15, 20, 25, … is 195? (a) 37th (b) 40th (c) 39th (d) 38th
  26. 26.What is the missing term in the AP 11, ?, 19, 23, 27? (a) 16 (b) 19 (c) 15 (d) 14
  27. 27.Which term of the AP 13, 18, 23, 28, … is 63? (a) 10th (b) 13th (c) 11th (d) 12th
  28. 28.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 55 (b) 108 (c) 10 (d) 54
  29. 29.What is the 17th term of the AP 8, 10, 12, 14, …? (a) 34 (b) 42 (c) 32 (d) 40
  30. 30.What is the 20th term of the AP 15, 22, 29, 36, …? (a) 148 (b) 155 (c) 133 (d) 140
  31. 31.What is the 15th term of the AP 8, 14, 20, 26, …? (a) 90 (b) 98 (c) 84 (d) 92
  32. 32.What is the 15th term of the AP 14, 16, 18, 20, …? (a) 44 (b) 42 (c) 28 (d) 30
  33. 33.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 88 (b) 48 (c) 9 (d) 44
  34. 34.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 66 (b) 8 (c) 36 (d) 33
  35. 35.What is the sum of all the whole numbers from 1 to 65? (a) 2145 (b) 2146 (c) 2080 (d) 4290
  36. 36.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 42 (b) 6 (c) 24 (d) 21
  37. 37.What is the missing term in the AP 18, 20, 22, ?, 26? (a) 25 (b) 23 (c) 26 (d) 24
  38. 38.What is the sum of the first 5 terms of the AP 10, 14, 18, …? (a) 26 (b) 90 (c) 180 (d) 100
  39. 39.Which term of the AP 16, 18, 20, 22, … is 64? (a) 26th (b) 32nd (c) 24th (d) 25th
  40. 40.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 306 (b) 612 (c) 42 (d) 324

Answer key

  1. 54
  2. 39
  3. 861
  4. 361
  5. 20th
  6. 33
  7. 140
  8. 221
  9. 184
  10. 230
  11. 60
  12. 4753
  13. 142
  14. 40th
  15. 231
  16. 162
  17. 259
  18. 1830
  19. 1653
  20. 82
  21. 57
  22. 19
  23. 676
  24. 90
  25. 38th
  26. 15
  27. 11th
  28. 54
  29. 40
  30. 148
  31. 92
  32. 42
  33. 44
  34. 33
  35. 2145
  36. 21
  37. 24
  38. 90
  39. 25th
  40. 306

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