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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 771 · 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 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 465 (c) 59 (d) 900
  2. 2.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 60 (b) 10 (c) 30 (d) 35
  3. 3.Which term of the AP 15, 24, 33, 42, … is 231? (a) 27th (b) 25th (c) 26th (d) 24th
  4. 4.What is the missing term in the AP 12, ?, 24, 30, 36? (a) 19 (b) 18 (c) 24 (d) 17
  5. 5.What is the sum of the first 11 terms of the AP 8, 12, 16, …? (a) 616 (b) 330 (c) 308 (d) 48
  6. 6.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 429 (b) 858 (c) 462 (d) 69
  7. 7.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 792 (b) 429 (c) 396 (d) 66
  8. 8.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 9 (b) 70 (c) 35 (d) 36
  9. 9.What is the 27th term of the AP 3, 9, 15, 21, …? (a) 156 (b) 162 (c) 159 (d) 165
  10. 10.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 306 (c) 289 (d) 33
  11. 11.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 66 (c) 21 (d) 121
  12. 12.What is the missing term in the AP 17, 20, 23, ?, 29? (a) 29 (b) 27 (c) 26 (d) 25
  13. 13.What is the 30th term of the AP 14, 19, 24, 29, …? (a) 145 (b) 164 (c) 159 (d) 150
  14. 14.What is the 18th term of the AP 13, 17, 21, 25, …? (a) 72 (b) 85 (c) 68 (d) 81
  15. 15.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 80 (b) 14 (c) 43 (d) 40
  16. 16.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 225 (b) 414 (c) 39 (d) 207
  17. 17.What is the missing term in the AP 12, ?, 20, 24, 28? (a) 20 (b) 16 (c) 17 (d) 15
  18. 18.What is the 13th term of the AP 9, 18, 27, 36, …? (a) 118 (b) 126 (c) 108 (d) 117
  19. 19.What is the 16th term of the AP 20, 24, 28, 32, …? (a) 60 (b) 80 (c) 84 (d) 64
  20. 20.What is the 34th term of the AP 12, 14, 16, 18, …? (a) 66 (b) 80 (c) 68 (d) 78
  21. 21.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 81 (d) 90
  22. 22.What is the missing term in the AP 8, 11, 14, ?, 20? (a) 18 (b) 16 (c) 17 (d) 20
  23. 23.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 30 (b) 60 (c) 31 (d) 8
  24. 24.What is the sum of the first 6 terms of the AP 10, 15, 20, …? (a) 270 (b) 135 (c) 35 (d) 150
  25. 25.What is the 21st term of the AP 14, 22, 30, 38, …? (a) 168 (b) 160 (c) 182 (d) 174
  26. 26.What is the 28th term of the AP 16, 24, 32, 40, …? (a) 240 (b) 232 (c) 216 (d) 224
  27. 27.Which term of the AP 7, 10, 13, 16, … is 55? (a) 16th (b) 17th (c) 19th (d) 18th
  28. 28.What is the sum of all the whole numbers from 1 to 39? (a) 780 (b) 741 (c) 1560 (d) 781
  29. 29.What is the missing term in the AP 4, 11, ?, 25, 32? (a) 25 (b) 19 (c) 17 (d) 18
  30. 30.What is the sum of all the whole numbers from 1 to 42? (a) 861 (b) 1806 (c) 882 (d) 903
  31. 31.What is the 11th term of the AP 16, 22, 28, 34, …? (a) 82 (b) 60 (c) 76 (d) 66
  32. 32.What is the 25th term of the AP 5, 11, 17, 23, …? (a) 144 (b) 150 (c) 155 (d) 149
  33. 33.What is the 24th term of the AP 12, 16, 20, 24, …? (a) 104 (b) 92 (c) 108 (d) 96
  34. 34.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 496 (c) 528 (d) 512
  35. 35.What is the missing term in the AP 9, ?, 25, 33, 41? (a) 25 (b) 16 (c) 17 (d) 18
  36. 36.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 162 (b) 165 (c) 30 (d) 324
  37. 37.What is the sum of all the whole numbers from 1 to 100? (a) 10100 (b) 5000 (c) 5050 (d) 4950
  38. 38.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 150 (b) 37 (c) 132 (d) 264
  39. 39.What is the 37th term of the AP 6, 8, 10, 12, …? (a) 72 (b) 78 (c) 80 (d) 74
  40. 40.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 190 (b) 27 (c) 180 (d) 360

Answer key

  1. 900
  2. 30
  3. 25th
  4. 18
  5. 308
  6. 429
  7. 396
  8. 35
  9. 159
  10. 289
  11. 121
  12. 26
  13. 159
  14. 81
  15. 40
  16. 207
  17. 16
  18. 117
  19. 80
  20. 78
  21. 81
  22. 17
  23. 30
  24. 135
  25. 174
  26. 232
  27. 17th
  28. 780
  29. 18
  30. 903
  31. 76
  32. 149
  33. 104
  34. 528
  35. 17
  36. 162
  37. 5050
  38. 132
  39. 78
  40. 180

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