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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 694 · 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 missing term in the AP 10, ?, 20, 25, 30? (a) 14 (b) 20 (c) 15 (d) 16
  2. 2.What is the 24th term of the AP 11, 14, 17, 20, …? (a) 72 (b) 80 (c) 83 (d) 69
  3. 3.What is the 34th term of the AP 12, 21, 30, 39, …? (a) 318 (b) 297 (c) 306 (d) 309
  4. 4.What is the 22nd term of the AP 16, 18, 20, 22, …? (a) 44 (b) 42 (c) 60 (d) 58
  5. 5.What is the sum of the first 7 terms of the AP 7, 9, 11, …? (a) 91 (b) 182 (c) 98 (d) 19
  6. 6.Which term of the AP 17, 23, 29, 35, … is 125? (a) 20th (b) 21st (c) 18th (d) 19th
  7. 7.What is the missing term in the AP 19, ?, 31, 37, 43? (a) 31 (b) 24 (c) 26 (d) 25
  8. 8.What is the sum of all the whole numbers from 1 to 54? (a) 1485 (b) 1431 (c) 1458 (d) 2970
  9. 9.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 192 (b) 19 (c) 104 (d) 96
  10. 10.What is the sum of the first 11 terms of the AP 1, 5, 9, …? (a) 231 (b) 41 (c) 462 (d) 253
  11. 11.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 330 (b) 166 (c) 165 (d) 20
  12. 12.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 80 (b) 95 (c) 160 (d) 28
  13. 13.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 256 (c) 272 (d) 136
  14. 14.What is the missing term in the AP 8, 12, ?, 20, 24? (a) 15 (b) 20 (c) 16 (d) 17
  15. 15.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 240 (c) 225 (d) 29
  16. 16.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 35 (b) 30 (c) 60 (d) 10
  17. 17.What is the 15th term of the AP 18, 23, 28, 33, …? (a) 88 (b) 75 (c) 70 (d) 93
  18. 18.What is the sum of the first 5 terms of the AP 5, 10, 15, …? (a) 80 (b) 150 (c) 25 (d) 75
  19. 19.What is the 14th term of the AP 16, 18, 20, 22, …? (a) 44 (b) 28 (c) 26 (d) 42
  20. 20.What is the 27th term of the AP 2, 4, 6, 8, …? (a) 52 (b) 55 (c) 54 (d) 56
  21. 21.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 73 (b) 70 (c) 20 (d) 140
  22. 22.What is the 37th term of the AP 10, 13, 16, 19, …? (a) 108 (b) 111 (c) 121 (d) 118
  23. 23.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 5852 (c) 2926 (d) 2888
  24. 24.What is the 12th term of the AP 11, 19, 27, 35, …? (a) 107 (b) 99 (c) 96 (d) 88
  25. 25.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 676 (c) 351 (d) 51
  26. 26.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 420 (b) 456 (c) 840 (d) 68
  27. 27.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 126 (b) 70 (c) 15 (d) 63
  28. 28.What is the sum of all the whole numbers from 1 to 74? (a) 2775 (b) 2738 (c) 5550 (d) 2701
  29. 29.What is the 14th term of the AP 1, 4, 7, 10, …? (a) 40 (b) 43 (c) 42 (d) 39
  30. 30.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 45 (d) 90
  31. 31.Which term of the AP 2, 6, 10, 14, … is 134? (a) 34th (b) 35th (c) 33rd (d) 36th
  32. 32.What is the 34th term of the AP 4, 10, 16, 22, …? (a) 198 (b) 202 (c) 208 (d) 204
  33. 33.Which term of the AP 14, 19, 24, 29, … is 59? (a) 10th (b) 11th (c) 12th (d) 9th
  34. 34.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 324 (c) 35 (d) 171
  35. 35.What is the sum of all the whole numbers from 1 to 38? (a) 1482 (b) 741 (c) 703 (d) 722
  36. 36.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 529 (c) 276 (d) 45
  37. 37.What is the missing term in the AP 14, ?, 20, 23, 26? (a) 18 (b) 20 (c) 17 (d) 16
  38. 38.Which term of the AP 16, 23, 30, 37, … is 149? (a) 22nd (b) 19th (c) 20th (d) 21st
  39. 39.Which term of the AP 10, 15, 20, 25, … is 155? (a) 31st (b) 32nd (c) 30th (d) 29th
  40. 40.What is the missing term in the AP 16, ?, 30, 37, 44? (a) 22 (b) 24 (c) 23 (d) 30

Answer key

  1. 15
  2. 80
  3. 309
  4. 58
  5. 91
  6. 19th
  7. 25
  8. 1485
  9. 96
  10. 231
  11. 165
  12. 80
  13. 256
  14. 16
  15. 225
  16. 30
  17. 88
  18. 75
  19. 42
  20. 54
  21. 70
  22. 118
  23. 2926
  24. 99
  25. 676
  26. 420
  27. 63
  28. 2775
  29. 40
  30. 81
  31. 34th
  32. 202
  33. 10th
  34. 324
  35. 741
  36. 529
  37. 17
  38. 20th
  39. 30th
  40. 23

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