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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 890 · 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 8, ?, 20, 26, 32? (a) 15 (b) 14 (c) 13 (d) 20
  2. 2.What is the missing term in the AP 7, 12, 17, ?, 27? (a) 23 (b) 22 (c) 27 (d) 21
  3. 3.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 96 (b) 84 (c) 168 (d) 24
  4. 4.What is the missing term in the AP 14, ?, 22, 26, 30? (a) 22 (b) 17 (c) 19 (d) 18
  5. 5.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 289 (d) 306
  6. 6.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 96 (b) 92 (c) 15 (d) 184
  7. 7.Which term of the AP 10, 12, 14, 16, … is 88? (a) 44th (b) 39th (c) 41st (d) 40th
  8. 8.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 90 (d) 81
  9. 9.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 182 (b) 92 (c) 16 (d) 91
  10. 10.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 72 (c) 156 (d) 78
  11. 11.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 50 (c) 110 (d) 55
  12. 12.What is the missing term in the AP 12, 18, ?, 30, 36? (a) 24 (b) 30 (c) 23 (d) 25
  13. 13.Which term of the AP 9, 15, 21, 27, … is 135? (a) 24th (b) 21st (c) 23rd (d) 22nd
  14. 14.What is the 24th term of the AP 6, 13, 20, 27, …? (a) 168 (b) 174 (c) 167 (d) 161
  15. 15.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 65 (b) 60 (c) 22 (d) 120
  16. 16.What is the sum of all the whole numbers from 1 to 69? (a) 2415 (b) 2346 (c) 4830 (d) 2416
  17. 17.What is the missing term in the AP 4, 9, ?, 19, 24? (a) 14 (b) 19 (c) 15 (d) 13
  18. 18.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 1482 (c) 741 (d) 703
  19. 19.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1378 (c) 1326 (d) 1352
  20. 20.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 266 (b) 28 (c) 133 (d) 136
  21. 21.What is the missing term in the AP 7, 14, ?, 28, 35? (a) 20 (b) 28 (c) 22 (d) 21
  22. 22.Which term of the AP 4, 7, 10, 13, … is 73? (a) 24th (b) 25th (c) 26th (d) 23rd
  23. 23.What is the 37th term of the AP 20, 29, 38, 47, …? (a) 353 (b) 324 (c) 344 (d) 333
  24. 24.What is the 17th term of the AP 8, 11, 14, 17, …? (a) 59 (b) 56 (c) 48 (d) 51
  25. 25.What is the sum of the first 10 terms of the AP 5, 11, 17, …? (a) 59 (b) 320 (c) 350 (d) 640
  26. 26.What is the sum of the first 11 terms of the AP 8, 12, 16, …? (a) 330 (b) 308 (c) 616 (d) 48
  27. 27.What is the missing term in the AP 17, 21, ?, 29, 33? (a) 26 (b) 29 (c) 24 (d) 25
  28. 28.What is the 20th term of the AP 1, 4, 7, 10, …? (a) 60 (b) 61 (c) 58 (d) 57
  29. 29.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 396 (b) 66 (c) 429 (d) 792
  30. 30.What is the 33rd term of the AP 11, 18, 25, 32, …? (a) 242 (b) 224 (c) 231 (d) 235
  31. 31.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 990 (c) 1035 (d) 2070
  32. 32.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 33 (b) 36 (c) 8 (d) 66
  33. 33.What is the missing term in the AP 10, 18, 26, ?, 42? (a) 33 (b) 42 (c) 35 (d) 34
  34. 34.Which term of the AP 18, 25, 32, 39, … is 277? (a) 37th (b) 39th (c) 38th (d) 40th
  35. 35.What is the 14th term of the AP 1, 3, 5, 7, …? (a) 26 (b) 27 (c) 28 (d) 29
  36. 36.What is the 16th term of the AP 6, 15, 24, 33, …? (a) 150 (b) 144 (c) 135 (d) 141
  37. 37.What is the 11th term of the AP 3, 6, 9, 12, …? (a) 33 (b) 36 (c) 30 (d) 34
  38. 38.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 156 (b) 176 (c) 37 (d) 312
  39. 39.Which term of the AP 3, 10, 17, 24, … is 262? (a) 39th (b) 37th (c) 40th (d) 38th
  40. 40.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 36 (d) 21

Answer key

  1. 14
  2. 22
  3. 84
  4. 18
  5. 289
  6. 92
  7. 40th
  8. 81
  9. 91
  10. 78
  11. 55
  12. 24
  13. 22nd
  14. 167
  15. 60
  16. 2415
  17. 14
  18. 741
  19. 1378
  20. 133
  21. 21
  22. 24th
  23. 344
  24. 56
  25. 320
  26. 308
  27. 25
  28. 58
  29. 396
  30. 235
  31. 1035
  32. 33
  33. 34
  34. 38th
  35. 27
  36. 141
  37. 33
  38. 156
  39. 38th
  40. 36

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