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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 320 · 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 36th term of the AP 15, 19, 23, 27, …? (a) 155 (b) 159 (c) 140 (d) 144
  2. 2.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 104 (b) 96 (c) 192 (d) 19
  3. 3.What is the 37th term of the AP 1, 9, 17, 25, …? (a) 296 (b) 297 (c) 288 (d) 289
  4. 4.What is the missing term in the AP 6, 8, 10, ?, 14? (a) 11 (b) 14 (c) 12 (d) 13
  5. 5.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 435 (c) 57 (d) 841
  6. 6.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 529 (c) 552 (d) 276
  7. 7.What is the 29th term of the AP 11, 14, 17, 20, …? (a) 98 (b) 84 (c) 87 (d) 95
  8. 8.What is the sum of the first 11 terms of the AP 4, 10, 16, …? (a) 748 (b) 64 (c) 374 (d) 407
  9. 9.What is the missing term in the AP 8, ?, 20, 26, 32? (a) 20 (b) 14 (c) 13 (d) 15
  10. 10.What is the 11th term of the AP 2, 9, 16, 23, …? (a) 79 (b) 70 (c) 72 (d) 77
  11. 11.What is the 32nd term of the AP 17, 26, 35, 44, …? (a) 296 (b) 305 (c) 279 (d) 288
  12. 12.Which term of the AP 12, 21, 30, 39, … is 210? (a) 24th (b) 25th (c) 22nd (d) 23rd
  13. 13.What is the sum of all the whole numbers from 1 to 38? (a) 703 (b) 741 (c) 1482 (d) 722
  14. 14.What is the missing term in the AP 14, ?, 22, 26, 30? (a) 17 (b) 19 (c) 22 (d) 18
  15. 15.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 90 (b) 180 (c) 105 (d) 30
  16. 16.What is the sum of all the whole numbers from 1 to 92? (a) 4278 (b) 4232 (c) 4186 (d) 8556
  17. 17.What is the sum of all the whole numbers from 1 to 37? (a) 703 (b) 666 (c) 704 (d) 1406
  18. 18.What is the sum of the first 9 terms of the AP 2, 8, 14, …? (a) 50 (b) 468 (c) 234 (d) 261
  19. 19.What is the 24th term of the AP 11, 16, 21, 26, …? (a) 131 (b) 126 (c) 120 (d) 115
  20. 20.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 198 (b) 100 (c) 14 (d) 99
  21. 21.What is the 16th term of the AP 12, 16, 20, 24, …? (a) 60 (b) 72 (c) 64 (d) 76
  22. 22.What is the 24th term of the AP 5, 9, 13, 17, …? (a) 92 (b) 96 (c) 101 (d) 97
  23. 23.What is the 11th term of the AP 6, 13, 20, 27, …? (a) 77 (b) 70 (c) 76 (d) 83
  24. 24.Which term of the AP 15, 18, 21, 24, … is 132? (a) 39th (b) 44th (c) 40th (d) 41st
  25. 25.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 120 (b) 138 (c) 35 (d) 240
  26. 26.What is the missing term in the AP 17, 19, ?, 23, 25? (a) 22 (b) 20 (c) 21 (d) 23
  27. 27.What is the sum of the first 7 terms of the AP 8, 12, 16, …? (a) 140 (b) 154 (c) 32 (d) 280
  28. 28.What is the 10th term of the AP 19, 25, 31, 37, …? (a) 79 (b) 60 (c) 73 (d) 54
  29. 29.What is the missing term in the AP 16, ?, 28, 34, 40? (a) 28 (b) 23 (c) 22 (d) 21
  30. 30.What is the sum of the first 6 terms of the AP 8, 11, 14, …? (a) 93 (b) 23 (c) 102 (d) 186
  31. 31.What is the sum of all the whole numbers from 1 to 60? (a) 1800 (b) 1830 (c) 1770 (d) 3660
  32. 32.What is the missing term in the AP 17, ?, 33, 41, 49? (a) 33 (b) 25 (c) 24 (d) 26
  33. 33.What is the 17th term of the AP 3, 5, 7, 9, …? (a) 32 (b) 35 (c) 37 (d) 34
  34. 34.What is the sum of the first 7 terms of the AP 6, 8, 10, …? (a) 84 (b) 18 (c) 168 (d) 91
  35. 35.What is the 15th term of the AP 2, 6, 10, 14, …? (a) 56 (b) 58 (c) 62 (d) 60
  36. 36.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 380 (c) 37 (d) 361
  37. 37.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 170 (b) 180 (c) 26 (d) 340
  38. 38.What is the 22nd term of the AP 11, 14, 17, 20, …? (a) 77 (b) 63 (c) 74 (d) 66
  39. 39.What is the 21st term of the AP 8, 16, 24, 32, …? (a) 168 (b) 169 (c) 160 (d) 176
  40. 40.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 84 (b) 9 (c) 42 (d) 43

Answer key

  1. 155
  2. 96
  3. 289
  4. 12
  5. 841
  6. 529
  7. 95
  8. 374
  9. 14
  10. 72
  11. 296
  12. 23rd
  13. 741
  14. 18
  15. 90
  16. 4278
  17. 703
  18. 234
  19. 126
  20. 99
  21. 72
  22. 97
  23. 76
  24. 40th
  25. 120
  26. 21
  27. 140
  28. 73
  29. 22
  30. 93
  31. 1830
  32. 25
  33. 35
  34. 84
  35. 58
  36. 361
  37. 170
  38. 74
  39. 168
  40. 42

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