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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 622 · 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 all the whole numbers from 1 to 23? (a) 276 (b) 253 (c) 277 (d) 552
  2. 2.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 180 (b) 20 (c) 90 (d) 96
  3. 3.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 10 (b) 12 (c) 8 (d) 9
  4. 4.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 66 (b) 21 (c) 132 (d) 78
  5. 5.What is the 31st term of the AP 11, 20, 29, 38, …? (a) 279 (b) 270 (c) 281 (d) 290
  6. 6.What is the sum of the first 5 terms of the AP 10, 16, 22, …? (a) 34 (b) 220 (c) 125 (d) 110
  7. 7.What is the sum of the first 10 terms of the AP 10, 13, 16, …? (a) 235 (b) 250 (c) 37 (d) 470
  8. 8.What is the sum of all the whole numbers from 1 to 35? (a) 1260 (b) 595 (c) 630 (d) 631
  9. 9.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 90 (b) 75 (c) 150 (d) 27
  10. 10.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 600 (d) 576
  11. 11.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 90 (b) 19 (c) 168 (d) 84
  12. 12.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 30 (c) 15 (d) 9
  13. 13.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 144 (c) 78 (d) 156
  14. 14.What is the sum of the first 8 terms of the AP 5, 6, 7, …? (a) 136 (b) 72 (c) 68 (d) 12
  15. 15.What is the 12th term of the AP 12, 18, 24, 30, …? (a) 72 (b) 84 (c) 66 (d) 78
  16. 16.Which term of the AP 3, 6, 9, 12, … is 75? (a) 24th (b) 27th (c) 26th (d) 25th
  17. 17.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 1432 (c) 1431 (d) 2862
  18. 18.What is the missing term in the AP 16, 19, ?, 25, 28? (a) 23 (b) 21 (c) 22 (d) 25
  19. 19.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 17 (b) 216 (c) 112 (d) 108
  20. 20.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 53 (c) 378 (d) 756
  21. 21.What is the missing term in the AP 13, ?, 25, 31, 37? (a) 20 (b) 18 (c) 25 (d) 19
  22. 22.What is the missing term in the AP 20, 25, ?, 35, 40? (a) 31 (b) 35 (c) 30 (d) 29
  23. 23.What is the missing term in the AP 2, ?, 14, 20, 26? (a) 7 (b) 9 (c) 14 (d) 8
  24. 24.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 351 (c) 51 (d) 676
  25. 25.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 165 (b) 330 (c) 176 (d) 25
  26. 26.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 36 (c) 64 (d) 15
  27. 27.What is the sum of the first 11 terms of the AP 7, 10, 13, …? (a) 242 (b) 484 (c) 245 (d) 37
  28. 28.What is the 16th term of the AP 14, 22, 30, 38, …? (a) 142 (b) 134 (c) 120 (d) 128
  29. 29.What is the missing term in the AP 7, 16, ?, 34, 43? (a) 26 (b) 25 (c) 34 (d) 24
  30. 30.What is the missing term in the AP 12, 15, 18, ?, 24? (a) 21 (b) 20 (c) 24 (d) 22
  31. 31.What is the missing term in the AP 18, ?, 34, 42, 50? (a) 27 (b) 26 (c) 34 (d) 25
  32. 32.What is the 12th term of the AP 13, 21, 29, 37, …? (a) 101 (b) 96 (c) 109 (d) 88
  33. 33.What is the 11th term of the AP 14, 17, 20, 23, …? (a) 44 (b) 33 (c) 30 (d) 47
  34. 34.What is the 11th term of the AP 4, 10, 16, 22, …? (a) 66 (b) 70 (c) 64 (d) 60
  35. 35.What is the sum of the first 11 terms of the AP 3, 7, 11, …? (a) 275 (b) 506 (c) 43 (d) 253
  36. 36.What is the 13th term of the AP 14, 18, 22, 26, …? (a) 52 (b) 66 (c) 48 (d) 62
  37. 37.Which term of the AP 20, 27, 34, 41, … is 69? (a) 7th (b) 9th (c) 10th (d) 8th
  38. 38.Which term of the AP 3, 9, 15, 21, … is 93? (a) 16th (b) 18th (c) 17th (d) 15th
  39. 39.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 120 (b) 138 (c) 35 (d) 240
  40. 40.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 231 (c) 253 (d) 506

Answer key

  1. 276
  2. 90
  3. 9
  4. 66
  5. 281
  6. 110
  7. 235
  8. 630
  9. 75
  10. 576
  11. 84
  12. 25
  13. 144
  14. 68
  15. 78
  16. 25th
  17. 1431
  18. 22
  19. 108
  20. 729
  21. 19
  22. 30
  23. 8
  24. 676
  25. 165
  26. 64
  27. 242
  28. 134
  29. 25
  30. 21
  31. 26
  32. 101
  33. 44
  34. 64
  35. 253
  36. 62
  37. 8th
  38. 16th
  39. 120
  40. 253

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