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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 463 · 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 sum of the first 10 terms of the AP 5, 9, 13, …? (a) 230 (b) 250 (c) 460 (d) 41
  2. 2.What is the 34th term of the AP 1, 5, 9, 13, …? (a) 132 (b) 137 (c) 133 (d) 136
  3. 3.What is the 32nd term of the AP 15, 19, 23, 27, …? (a) 124 (b) 139 (c) 143 (d) 128
  4. 4.What is the missing term in the AP 1, ?, 11, 16, 21? (a) 5 (b) 11 (c) 7 (d) 6
  5. 5.Which term of the AP 4, 6, 8, 10, … is 54? (a) 25th (b) 27th (c) 28th (d) 26th
  6. 6.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 552 (d) 529
  7. 7.What is the 30th term of the AP 15, 20, 25, 30, …? (a) 145 (b) 160 (c) 150 (d) 165
  8. 8.What is the sum of all the whole numbers from 1 to 58? (a) 1682 (b) 3422 (c) 1653 (d) 1711
  9. 9.Which term of the AP 1, 7, 13, 19, … is 181? (a) 30th (b) 31st (c) 32nd (d) 33rd
  10. 10.What is the missing term in the AP 13, 19, 25, ?, 37? (a) 37 (b) 31 (c) 32 (d) 30
  11. 11.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 102 (b) 11 (c) 51 (d) 54
  12. 12.What is the missing term in the AP 3, 5, ?, 9, 11? (a) 7 (b) 6 (c) 9 (d) 8
  13. 13.What is the sum of the first 10 terms of the AP 8, 9, 10, …? (a) 250 (b) 130 (c) 17 (d) 125
  14. 14.What is the 21st term of the AP 15, 20, 25, 30, …? (a) 105 (b) 120 (c) 100 (d) 115
  15. 15.What is the sum of all the whole numbers from 1 to 63? (a) 2017 (b) 4032 (c) 2016 (d) 1953
  16. 16.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 91 (c) 169 (d) 25
  17. 17.What is the 17th term of the AP 6, 9, 12, 15, …? (a) 51 (b) 54 (c) 57 (d) 48
  18. 18.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 406 (c) 812 (d) 378
  19. 19.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 21 (b) 6 (c) 42 (d) 24
  20. 20.What is the missing term in the AP 6, 10, 14, ?, 22? (a) 22 (b) 17 (c) 18 (d) 19
  21. 21.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 10 (b) 80 (c) 41 (d) 40
  22. 22.What is the missing term in the AP 16, ?, 24, 28, 32? (a) 21 (b) 19 (c) 20 (d) 24
  23. 23.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 741 (c) 1482 (d) 703
  24. 24.What is the 36th term of the AP 13, 19, 25, 31, …? (a) 216 (b) 223 (c) 210 (d) 229
  25. 25.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 625 (d) 650
  26. 26.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 66 (b) 8 (c) 36 (d) 33
  27. 27.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 114 (b) 27 (c) 204 (d) 102
  28. 28.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 26 (b) 25 (c) 27 (d) 33
  29. 29.Which term of the AP 19, 26, 33, 40, … is 271? (a) 39th (b) 37th (c) 36th (d) 38th
  30. 30.What is the sum of all the whole numbers from 1 to 81? (a) 6642 (b) 3322 (c) 3240 (d) 3321
  31. 31.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 25 (b) 30 (c) 50 (d) 9
  32. 32.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 302 (b) 52 (c) 594 (d) 297
  33. 33.What is the missing term in the AP 20, 26, 32, ?, 44? (a) 44 (b) 37 (c) 38 (d) 39
  34. 34.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 51 (c) 702 (d) 351
  35. 35.Which term of the AP 8, 13, 18, 23, … is 68? (a) 12th (b) 14th (c) 15th (d) 13th
  36. 36.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 161 (b) 147 (c) 33 (d) 294
  37. 37.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 10 (b) 30 (c) 60 (d) 35
  38. 38.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 156 (c) 144 (d) 78
  39. 39.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 30 (d) 25
  40. 40.What is the 20th term of the AP 11, 20, 29, 38, …? (a) 180 (b) 182 (c) 191 (d) 171

Answer key

  1. 230
  2. 133
  3. 139
  4. 6
  5. 26th
  6. 529
  7. 160
  8. 1711
  9. 31st
  10. 31
  11. 51
  12. 7
  13. 125
  14. 115
  15. 2016
  16. 169
  17. 54
  18. 406
  19. 21
  20. 18
  21. 40
  22. 20
  23. 741
  24. 223
  25. 625
  26. 33
  27. 102
  28. 26
  29. 37th
  30. 3321
  31. 25
  32. 297
  33. 38
  34. 676
  35. 13th
  36. 147
  37. 30
  38. 144
  39. 25
  40. 182

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