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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 709 · 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 sum of the first 10 terms of the AP 6, 9, 12, …? (a) 33 (b) 210 (c) 195 (d) 390
  2. 2.What is the sum of all the whole numbers from 1 to 31? (a) 497 (b) 465 (c) 992 (d) 496
  3. 3.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 870 (c) 841 (d) 57
  4. 4.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 154 (b) 77 (c) 84 (d) 17
  5. 5.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 66 (b) 114 (c) 57 (d) 17
  6. 6.What is the 14th term of the AP 3, 7, 11, 15, …? (a) 56 (b) 55 (c) 59 (d) 52
  7. 7.Which term of the AP 2, 5, 8, 11, … is 74? (a) 26th (b) 24th (c) 25th (d) 27th
  8. 8.What is the sum of the first 7 terms of the AP 6, 8, 10, …? (a) 84 (b) 91 (c) 18 (d) 168
  9. 9.Which term of the AP 11, 13, 15, 17, … is 75? (a) 32nd (b) 33rd (c) 34th (d) 35th
  10. 10.What is the 30th term of the AP 1, 8, 15, 22, …? (a) 203 (b) 211 (c) 210 (d) 204
  11. 11.What is the 18th term of the AP 8, 15, 22, 29, …? (a) 119 (b) 134 (c) 126 (d) 127
  12. 12.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 1431 (c) 2862 (d) 1432
  13. 13.What is the sum of the first 10 terms of the AP 9, 15, 21, …? (a) 720 (b) 63 (c) 390 (d) 360
  14. 14.What is the sum of all the whole numbers from 1 to 96? (a) 4656 (b) 4608 (c) 9312 (d) 4560
  15. 15.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 288 (b) 576 (c) 46 (d) 312
  16. 16.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 324 (b) 300 (c) 600 (d) 47
  17. 17.What is the sum of all the whole numbers from 1 to 98? (a) 4802 (b) 4753 (c) 4851 (d) 9702
  18. 18.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 756 (c) 378 (d) 351
  19. 19.Which term of the AP 9, 15, 21, 27, … is 195? (a) 33rd (b) 32nd (c) 34th (d) 31st
  20. 20.What is the 20th term of the AP 19, 24, 29, 34, …? (a) 119 (b) 95 (c) 114 (d) 100
  21. 21.What is the 17th term of the AP 15, 20, 25, 30, …? (a) 95 (b) 85 (c) 80 (d) 100
  22. 22.Which term of the AP 18, 23, 28, 33, … is 98? (a) 18th (b) 17th (c) 19th (d) 16th
  23. 23.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 108 (b) 24 (c) 105 (d) 210
  24. 24.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 650 (c) 49 (d) 625
  25. 25.What is the missing term in the AP 6, ?, 20, 27, 34? (a) 13 (b) 12 (c) 14 (d) 20
  26. 26.What is the 13th term of the AP 12, 20, 28, 36, …? (a) 104 (b) 96 (c) 108 (d) 116
  27. 27.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 43 (c) 484 (d) 506
  28. 28.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1176 (c) 1225 (d) 1226
  29. 29.What is the sum of the first 9 terms of the AP 2, 8, 14, …? (a) 50 (b) 261 (c) 468 (d) 234
  30. 30.What is the 25th term of the AP 4, 9, 14, 19, …? (a) 124 (b) 120 (c) 125 (d) 129
  31. 31.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 6 (b) 3 (c) 5 (d) 4
  32. 32.What is the 14th term of the AP 18, 24, 30, 36, …? (a) 102 (b) 78 (c) 96 (d) 84
  33. 33.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 576 (c) 600 (d) 300
  34. 34.What is the missing term in the AP 17, 20, 23, ?, 29? (a) 25 (b) 26 (c) 27 (d) 29
  35. 35.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 30 (d) 25
  36. 36.What is the 13th term of the AP 3, 6, 9, 12, …? (a) 36 (b) 40 (c) 42 (d) 39
  37. 37.What is the 17th term of the AP 2, 5, 8, 11, …? (a) 48 (b) 50 (c) 51 (d) 53
  38. 38.What is the 25th term of the AP 8, 11, 14, 17, …? (a) 72 (b) 80 (c) 83 (d) 75
  39. 39.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 15 (b) 100 (c) 198 (d) 99
  40. 40.What is the sum of all the whole numbers from 1 to 66? (a) 2211 (b) 2145 (c) 2178 (d) 4422

Answer key

  1. 195
  2. 496
  3. 841
  4. 77
  5. 57
  6. 55
  7. 25th
  8. 84
  9. 33rd
  10. 204
  11. 127
  12. 1431
  13. 360
  14. 4656
  15. 288
  16. 300
  17. 4851
  18. 378
  19. 32nd
  20. 114
  21. 95
  22. 17th
  23. 105
  24. 625
  25. 13
  26. 108
  27. 484
  28. 1225
  29. 234
  30. 124
  31. 4
  32. 96
  33. 576
  34. 26
  35. 25
  36. 39
  37. 50
  38. 80
  39. 99
  40. 2211

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