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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 93 · 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 12th term of the AP 4, 10, 16, 22, …? (a) 66 (b) 72 (c) 70 (d) 76
  2. 2.What is the 16th term of the AP 1, 9, 17, 25, …? (a) 120 (b) 129 (c) 128 (d) 121
  3. 3.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 306 (c) 289 (d) 153
  4. 4.Which term of the AP 17, 22, 27, 32, … is 147? (a) 26th (b) 27th (c) 29th (d) 28th
  5. 5.What is the 23rd term of the AP 2, 6, 10, 14, …? (a) 94 (b) 90 (c) 88 (d) 92
  6. 6.What is the 20th term of the AP 14, 21, 28, 35, …? (a) 133 (b) 154 (c) 147 (d) 140
  7. 7.What is the 36th term of the AP 18, 27, 36, 45, …? (a) 333 (b) 315 (c) 324 (d) 342
  8. 8.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 3 (b) 5 (c) 4 (d) 6
  9. 9.What is the missing term in the AP 7, 9, 11, ?, 15? (a) 12 (b) 13 (c) 15 (d) 14
  10. 10.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 42 (d) 21
  11. 11.What is the missing term in the AP 10, 12, ?, 16, 18? (a) 13 (b) 15 (c) 14 (d) 16
  12. 12.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 272 (d) 31
  13. 13.What is the 14th term of the AP 13, 15, 17, 19, …? (a) 41 (b) 28 (c) 26 (d) 39
  14. 14.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 351 (c) 676 (d) 51
  15. 15.What is the missing term in the AP 17, ?, 29, 35, 41? (a) 29 (b) 22 (c) 23 (d) 24
  16. 16.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 47 (c) 576 (d) 300
  17. 17.What is the 31st term of the AP 17, 19, 21, 23, …? (a) 62 (b) 79 (c) 60 (d) 77
  18. 18.Which term of the AP 7, 15, 23, 31, … is 127? (a) 17th (b) 16th (c) 18th (d) 15th
  19. 19.What is the sum of all the whole numbers from 1 to 31? (a) 497 (b) 496 (c) 465 (d) 992
  20. 20.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 90 (b) 17 (c) 81 (d) 162
  21. 21.What is the sum of the first 12 terms of the AP 9, 11, 13, …? (a) 252 (b) 240 (c) 480 (d) 31
  22. 22.Which term of the AP 18, 21, 24, 27, … is 60? (a) 14th (b) 16th (c) 20th (d) 15th
  23. 23.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 168 (b) 84 (c) 88 (d) 14
  24. 24.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 484 (c) 43 (d) 253
  25. 25.What is the sum of all the whole numbers from 1 to 35? (a) 595 (b) 1260 (c) 631 (d) 630
  26. 26.What is the missing term in the AP 9, 18, 27, ?, 45? (a) 35 (b) 36 (c) 37 (d) 45
  27. 27.What is the sum of all the whole numbers from 1 to 42? (a) 861 (b) 882 (c) 903 (d) 1806
  28. 28.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 240 (c) 120 (d) 225
  29. 29.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 56 (b) 684 (c) 372 (d) 342
  30. 30.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 374 (b) 198 (c) 187 (d) 27
  31. 31.Which term of the AP 15, 18, 21, 24, … is 75? (a) 20th (b) 22nd (c) 25th (d) 21st
  32. 32.What is the sum of all the whole numbers from 1 to 24? (a) 276 (b) 300 (c) 288 (d) 600
  33. 33.What is the missing term in the AP 18, ?, 34, 42, 50? (a) 27 (b) 34 (c) 26 (d) 25
  34. 34.What is the sum of the first 11 terms of the AP 4, 9, 14, …? (a) 638 (b) 324 (c) 319 (d) 54
  35. 35.What is the missing term in the AP 19, 24, 29, ?, 39? (a) 33 (b) 35 (c) 34 (d) 39
  36. 36.What is the 14th term of the AP 11, 14, 17, 20, …? (a) 53 (b) 50 (c) 39 (d) 42
  37. 37.Which term of the AP 4, 9, 14, 19, … is 104? (a) 20th (b) 22nd (c) 21st (d) 23rd
  38. 38.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 164 (b) 328 (c) 38 (d) 184
  39. 39.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 25 (d) 30
  40. 40.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 81 (c) 45 (d) 90

Answer key

  1. 70
  2. 121
  3. 289
  4. 27th
  5. 90
  6. 147
  7. 333
  8. 4
  9. 13
  10. 36
  11. 14
  12. 256
  13. 39
  14. 676
  15. 23
  16. 576
  17. 77
  18. 16th
  19. 496
  20. 81
  21. 240
  22. 15th
  23. 84
  24. 484
  25. 630
  26. 36
  27. 903
  28. 225
  29. 342
  30. 187
  31. 21st
  32. 300
  33. 26
  34. 319
  35. 34
  36. 50
  37. 21st
  38. 164
  39. 25
  40. 81

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