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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 504 · 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 3, 8, ?, 18, 23? (a) 12 (b) 13 (c) 18 (d) 14
  2. 2.What is the missing term in the AP 12, 21, 30, ?, 48? (a) 38 (b) 48 (c) 39 (d) 40
  3. 3.What is the 26th term of the AP 10, 12, 14, 16, …? (a) 50 (b) 60 (c) 62 (d) 52
  4. 4.What is the missing term in the AP 2, 9, ?, 23, 30? (a) 15 (b) 23 (c) 16 (d) 17
  5. 5.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 306 (c) 33 (d) 289
  6. 6.What is the 14th term of the AP 10, 14, 18, 22, …? (a) 66 (b) 52 (c) 62 (d) 56
  7. 7.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 351 (c) 702 (d) 338
  8. 8.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 26 (b) 176 (c) 352 (d) 187
  9. 9.What is the 19th term of the AP 13, 17, 21, 25, …? (a) 85 (b) 76 (c) 72 (d) 89
  10. 10.What is the 12th term of the AP 1, 4, 7, 10, …? (a) 37 (b) 33 (c) 36 (d) 34
  11. 11.Which term of the AP 13, 15, 17, 19, … is 31? (a) 12th (b) 10th (c) 9th (d) 11th
  12. 12.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 54 (b) 108 (c) 10 (d) 55
  13. 13.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 19 (c) 100 (d) 110
  14. 14.What is the 16th term of the AP 11, 20, 29, 38, …? (a) 155 (b) 146 (c) 135 (d) 144
  15. 15.What is the sum of all the whole numbers from 1 to 91? (a) 8372 (b) 4186 (c) 4095 (d) 4187
  16. 16.What is the 23rd term of the AP 17, 23, 29, 35, …? (a) 132 (b) 149 (c) 138 (d) 155
  17. 17.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 198 (b) 24 (c) 108 (d) 99
  18. 18.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 28 (b) 160 (c) 145 (d) 290
  19. 19.What is the missing term in the AP 8, ?, 24, 32, 40? (a) 15 (b) 17 (c) 16 (d) 24
  20. 20.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 28 (d) 49
  21. 21.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 729 (c) 53 (d) 378
  22. 22.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 156 (b) 150 (c) 18 (d) 300
  23. 23.What is the missing term in the AP 17, 21, ?, 29, 33? (a) 29 (b) 24 (c) 25 (d) 26
  24. 24.What is the sum of all the whole numbers from 1 to 96? (a) 4656 (b) 4560 (c) 4608 (d) 9312
  25. 25.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 42 (b) 84 (c) 43 (d) 9
  26. 26.What is the 17th term of the AP 1, 9, 17, 25, …? (a) 136 (b) 137 (c) 129 (d) 128
  27. 27.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 184 (b) 92 (c) 15 (d) 96
  28. 28.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 60 (b) 55 (c) 110 (d) 15
  29. 29.What is the sum of all the whole numbers from 1 to 67? (a) 2279 (b) 4556 (c) 2278 (d) 2211
  30. 30.What is the missing term in the AP 3, 12, ?, 30, 39? (a) 22 (b) 30 (c) 21 (d) 20
  31. 31.Which term of the AP 8, 11, 14, 17, … is 32? (a) 11th (b) 9th (c) 8th (d) 10th
  32. 32.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 154 (b) 77 (c) 78 (d) 12
  33. 33.Which term of the AP 1, 8, 15, 22, … is 190? (a) 30th (b) 29th (c) 28th (d) 27th
  34. 34.What is the 16th term of the AP 14, 23, 32, 41, …? (a) 158 (b) 135 (c) 149 (d) 144
  35. 35.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 43 (c) 253 (d) 506
  36. 36.What is the 21st term of the AP 5, 11, 17, 23, …? (a) 125 (b) 120 (c) 126 (d) 131
  37. 37.What is the missing term in the AP 18, 25, 32, ?, 46? (a) 40 (b) 38 (c) 46 (d) 39
  38. 38.What is the missing term in the AP 14, ?, 30, 38, 46? (a) 22 (b) 23 (c) 21 (d) 30
  39. 39.What is the sum of all the whole numbers from 1 to 40? (a) 1640 (b) 820 (c) 800 (d) 780
  40. 40.What is the 11th term of the AP 10, 13, 16, 19, …? (a) 40 (b) 33 (c) 30 (d) 43

Answer key

  1. 13
  2. 39
  3. 60
  4. 16
  5. 289
  6. 62
  7. 351
  8. 176
  9. 85
  10. 34
  11. 10th
  12. 54
  13. 100
  14. 146
  15. 4186
  16. 149
  17. 99
  18. 145
  19. 16
  20. 49
  21. 729
  22. 150
  23. 25
  24. 4656
  25. 42
  26. 129
  27. 92
  28. 55
  29. 2278
  30. 21
  31. 9th
  32. 77
  33. 28th
  34. 149
  35. 484
  36. 125
  37. 39
  38. 22
  39. 820
  40. 40

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