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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 565 · 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 24th term of the AP 15, 22, 29, 36, …? (a) 183 (b) 161 (c) 168 (d) 176
  2. 2.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 341 (b) 638 (c) 49 (d) 319
  3. 3.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 2279 (c) 2278 (d) 4556
  4. 4.Which term of the AP 11, 15, 19, 23, … is 107? (a) 26th (b) 27th (c) 24th (d) 25th
  5. 5.What is the missing term in the AP 11, 14, 17, ?, 23? (a) 20 (b) 19 (c) 21 (d) 23
  6. 6.What is the missing term in the AP 11, 18, ?, 32, 39? (a) 32 (b) 25 (c) 26 (d) 24
  7. 7.What is the 14th term of the AP 19, 21, 23, 25, …? (a) 26 (b) 28 (c) 45 (d) 47
  8. 8.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 708 (b) 57 (c) 384 (d) 354
  9. 9.What is the 14th term of the AP 1, 7, 13, 19, …? (a) 79 (b) 84 (c) 78 (d) 85
  10. 10.Which term of the AP 9, 17, 25, 33, … is 257? (a) 34th (b) 33rd (c) 31st (d) 32nd
  11. 11.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 625 (d) 650
  12. 12.What is the sum of the first 11 terms of the AP 9, 12, 15, …? (a) 39 (b) 528 (c) 264 (d) 267
  13. 13.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 22 (b) 143 (c) 264 (d) 132
  14. 14.Which term of the AP 1, 6, 11, 16, … is 76? (a) 15th (b) 17th (c) 16th (d) 18th
  15. 15.What is the missing term in the AP 1, 8, ?, 22, 29? (a) 16 (b) 15 (c) 22 (d) 14
  16. 16.What is the missing term in the AP 17, 25, ?, 41, 49? (a) 33 (b) 32 (c) 41 (d) 34
  17. 17.What is the sum of the first 11 terms of the AP 7, 10, 13, …? (a) 37 (b) 484 (c) 245 (d) 242
  18. 18.What is the sum of all the whole numbers from 1 to 57? (a) 1596 (b) 1653 (c) 1654 (d) 3306
  19. 19.Which term of the AP 3, 12, 21, 30, … is 129? (a) 17th (b) 16th (c) 15th (d) 14th
  20. 20.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 131 (b) 33 (c) 126 (d) 252
  21. 21.What is the missing term in the AP 16, ?, 32, 40, 48? (a) 24 (b) 32 (c) 23 (d) 25
  22. 22.Which term of the AP 3, 8, 13, 18, … is 143? (a) 29th (b) 28th (c) 30th (d) 31st
  23. 23.What is the 35th term of the AP 7, 9, 11, 13, …? (a) 68 (b) 70 (c) 75 (d) 77
  24. 24.Which term of the AP 9, 17, 25, 33, … is 321? (a) 39th (b) 41st (c) 40th (d) 42nd
  25. 25.What is the missing term in the AP 7, 15, 23, ?, 39? (a) 30 (b) 32 (c) 39 (d) 31
  26. 26.What is the 12th term of the AP 15, 18, 21, 24, …? (a) 48 (b) 36 (c) 33 (d) 51
  27. 27.What is the missing term in the AP 4, 11, ?, 25, 32? (a) 19 (b) 17 (c) 25 (d) 18
  28. 28.Which term of the AP 20, 25, 30, 35, … is 165? (a) 30th (b) 31st (c) 29th (d) 33rd
  29. 29.Which term of the AP 20, 24, 28, 32, … is 128? (a) 29th (b) 27th (c) 32nd (d) 28th
  30. 30.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 90 (b) 23 (c) 156 (d) 78
  31. 31.What is the 36th term of the AP 7, 9, 11, 13, …? (a) 72 (b) 77 (c) 70 (d) 79
  32. 32.What is the 40th term of the AP 1, 8, 15, 22, …? (a) 273 (b) 281 (c) 274 (d) 280
  33. 33.Which term of the AP 12, 21, 30, 39, … is 237? (a) 25th (b) 27th (c) 26th (d) 28th
  34. 34.What is the 15th term of the AP 11, 15, 19, 23, …? (a) 71 (b) 60 (c) 67 (d) 56
  35. 35.What is the sum of all the whole numbers from 1 to 60? (a) 1830 (b) 1770 (c) 1800 (d) 3660
  36. 36.What is the 36th term of the AP 18, 20, 22, 24, …? (a) 90 (b) 70 (c) 88 (d) 72
  37. 37.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 1122 (c) 562 (d) 528
  38. 38.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 25 (b) 50 (c) 30 (d) 9
  39. 39.What is the 15th term of the AP 9, 14, 19, 24, …? (a) 79 (b) 70 (c) 84 (d) 75
  40. 40.What is the 13th term of the AP 15, 23, 31, 39, …? (a) 119 (b) 111 (c) 104 (d) 96

Answer key

  1. 176
  2. 319
  3. 2278
  4. 25th
  5. 20
  6. 25
  7. 45
  8. 354
  9. 79
  10. 32nd
  11. 625
  12. 264
  13. 132
  14. 16th
  15. 15
  16. 33
  17. 242
  18. 1653
  19. 15th
  20. 126
  21. 24
  22. 29th
  23. 75
  24. 40th
  25. 31
  26. 48
  27. 18
  28. 30th
  29. 28th
  30. 78
  31. 77
  32. 274
  33. 26th
  34. 67
  35. 1830
  36. 88
  37. 561
  38. 25
  39. 79
  40. 111

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