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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 809 · 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 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 72 (c) 64 (d) 15
  2. 2.What is the missing term in the AP 1, ?, 9, 13, 17? (a) 6 (b) 4 (c) 5 (d) 9
  3. 3.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 171 (c) 162 (d) 342
  4. 4.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 182 (c) 169 (d) 91
  5. 5.What is the 21st term of the AP 12, 14, 16, 18, …? (a) 52 (b) 40 (c) 54 (d) 42
  6. 6.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 992 (c) 496 (d) 497
  7. 7.What is the 28th term of the AP 15, 19, 23, 27, …? (a) 108 (b) 127 (c) 123 (d) 112
  8. 8.What is the 39th term of the AP 12, 16, 20, 24, …? (a) 168 (b) 164 (c) 156 (d) 152
  9. 9.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 216 (b) 109 (c) 16 (d) 108
  10. 10.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 96 (b) 26 (c) 108 (d) 192
  11. 11.Which term of the AP 18, 21, 24, 27, … is 111? (a) 33rd (b) 31st (c) 37th (d) 32nd
  12. 12.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 60 (b) 22 (c) 120 (d) 65
  13. 13.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 192 (b) 352 (c) 36 (d) 176
  14. 14.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 37 (c) 380 (d) 190
  15. 15.Which term of the AP 18, 22, 26, 30, … is 150? (a) 36th (b) 33rd (c) 34th (d) 35th
  16. 16.What is the missing term in the AP 2, 4, 6, ?, 10? (a) 8 (b) 7 (c) 9 (d) 10
  17. 17.Which term of the AP 1, 10, 19, 28, … is 109? (a) 13th (b) 14th (c) 15th (d) 12th
  18. 18.What is the missing term in the AP 7, ?, 15, 19, 23? (a) 12 (b) 15 (c) 10 (d) 11
  19. 19.What is the missing term in the AP 9, 17, ?, 33, 41? (a) 24 (b) 33 (c) 26 (d) 25
  20. 20.What is the sum of all the whole numbers from 1 to 98? (a) 4851 (b) 4802 (c) 4753 (d) 9702
  21. 21.What is the missing term in the AP 9, 17, 25, ?, 41? (a) 32 (b) 33 (c) 41 (d) 34
  22. 22.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 43 (b) 270 (c) 250 (d) 500
  23. 23.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 37 (b) 378 (c) 189 (d) 207
  24. 24.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 595 (c) 630 (d) 1260
  25. 25.What is the sum of all the whole numbers from 1 to 13? (a) 91 (b) 92 (c) 182 (d) 78
  26. 26.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 8 (b) 6 (c) 7 (d) 9
  27. 27.What is the 10th term of the AP 6, 9, 12, 15, …? (a) 30 (b) 27 (c) 33 (d) 36
  28. 28.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 31 (b) 192 (c) 114 (d) 96
  29. 29.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 294 (b) 161 (c) 33 (d) 147
  30. 30.What is the 13th term of the AP 6, 8, 10, 12, …? (a) 24 (b) 32 (c) 26 (d) 30
  31. 31.What is the missing term in the AP 20, 26, 32, ?, 44? (a) 39 (b) 37 (c) 44 (d) 38
  32. 32.What is the 25th term of the AP 10, 14, 18, 22, …? (a) 96 (b) 100 (c) 106 (d) 110
  33. 33.Which term of the AP 9, 12, 15, 18, … is 111? (a) 37th (b) 34th (c) 35th (d) 36th
  34. 34.What is the 34th term of the AP 6, 11, 16, 21, …? (a) 170 (b) 171 (c) 165 (d) 176
  35. 35.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 15 (b) 12 (c) 13 (d) 11
  36. 36.What is the sum of the first 9 terms of the AP 1, 4, 7, …? (a) 234 (b) 25 (c) 117 (d) 120
  37. 37.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 53 (c) 378 (d) 756
  38. 38.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 19 (d) 55
  39. 39.Which term of the AP 4, 8, 12, 16, … is 40? (a) 11th (b) 12th (c) 9th (d) 10th
  40. 40.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 25 (b) 210 (c) 114 (d) 105

Answer key

  1. 64
  2. 5
  3. 171
  4. 169
  5. 52
  6. 496
  7. 123
  8. 164
  9. 108
  10. 96
  11. 32nd
  12. 60
  13. 176
  14. 361
  15. 34th
  16. 8
  17. 13th
  18. 11
  19. 25
  20. 4851
  21. 33
  22. 250
  23. 189
  24. 630
  25. 91
  26. 7
  27. 33
  28. 96
  29. 147
  30. 30
  31. 38
  32. 106
  33. 35th
  34. 171
  35. 12
  36. 117
  37. 729
  38. 100
  39. 10th
  40. 105

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