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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 787 · 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 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 25 (c) 30 (d) 9
  2. 2.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 222 (b) 444 (c) 35 (d) 240
  3. 3.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 85 (b) 25 (c) 95 (d) 170
  4. 4.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 100 (c) 55 (d) 110
  5. 5.What is the 40th term of the AP 5, 9, 13, 17, …? (a) 161 (b) 165 (c) 160 (d) 156
  6. 6.What is the sum of the first 8 terms of the AP 3, 7, 11, …? (a) 152 (b) 31 (c) 136 (d) 272
  7. 7.What is the 30th term of the AP 3, 5, 7, 9, …? (a) 58 (b) 61 (c) 60 (d) 63
  8. 8.What is the 17th term of the AP 7, 11, 15, 19, …? (a) 75 (b) 68 (c) 64 (d) 71
  9. 9.What is the sum of all the whole numbers from 1 to 11? (a) 55 (b) 67 (c) 132 (d) 66
  10. 10.What is the missing term in the AP 6, ?, 14, 18, 22? (a) 9 (b) 14 (c) 11 (d) 10
  11. 11.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 21 (c) 36 (d) 42
  12. 12.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 361 (c) 190 (d) 380
  13. 13.Which term of the AP 19, 21, 23, 25, … is 73? (a) 30th (b) 28th (c) 27th (d) 29th
  14. 14.Which term of the AP 17, 25, 33, 41, … is 145? (a) 19th (b) 17th (c) 18th (d) 16th
  15. 15.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 108 (b) 28 (c) 186 (d) 93
  16. 16.What is the 17th term of the AP 7, 9, 11, 13, …? (a) 41 (b) 32 (c) 34 (d) 39
  17. 17.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 14 (b) 168 (c) 84 (d) 88
  18. 18.What is the sum of all the whole numbers from 1 to 88? (a) 3828 (b) 3872 (c) 3916 (d) 7832
  19. 19.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 560 (b) 280 (c) 310 (d) 55
  20. 20.What is the 24th term of the AP 10, 16, 22, 28, …? (a) 138 (b) 154 (c) 148 (d) 144
  21. 21.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 781 (c) 1560 (d) 780
  22. 22.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 552 (c) 45 (d) 276
  23. 23.What is the 23rd term of the AP 9, 12, 15, 18, …? (a) 78 (b) 66 (c) 75 (d) 69
  24. 24.What is the sum of the first 7 terms of the AP 10, 15, 20, …? (a) 180 (b) 40 (c) 175 (d) 350
  25. 25.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 408 (b) 216 (c) 28 (d) 204
  26. 26.What is the 34th term of the AP 7, 9, 11, 13, …? (a) 68 (b) 66 (c) 75 (d) 73
  27. 27.What is the 11th term of the AP 12, 17, 22, 27, …? (a) 67 (b) 55 (c) 50 (d) 62
  28. 28.Which term of the AP 1, 7, 13, 19, … is 85? (a) 17th (b) 14th (c) 16th (d) 15th
  29. 29.What is the missing term in the AP 11, ?, 29, 38, 47? (a) 29 (b) 21 (c) 20 (d) 19
  30. 30.Which term of the AP 12, 19, 26, 33, … is 208? (a) 31st (b) 30th (c) 28th (d) 29th
  31. 31.What is the sum of all the whole numbers from 1 to 77? (a) 3003 (b) 6006 (c) 3004 (d) 2926
  32. 32.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 324 (d) 342
  33. 33.What is the 40th term of the AP 5, 7, 9, 11, …? (a) 78 (b) 85 (c) 80 (d) 83
  34. 34.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 351 (c) 51 (d) 702
  35. 35.Which term of the AP 2, 8, 14, 20, … is 128? (a) 24th (b) 21st (c) 22nd (d) 23rd
  36. 36.What is the sum of all the whole numbers from 1 to 92? (a) 4232 (b) 4186 (c) 4278 (d) 8556
  37. 37.What is the missing term in the AP 9, 14, ?, 24, 29? (a) 20 (b) 24 (c) 18 (d) 19
  38. 38.What is the 13th term of the AP 11, 20, 29, 38, …? (a) 128 (b) 108 (c) 119 (d) 117
  39. 39.Which term of the AP 10, 18, 26, 34, … is 130? (a) 18th (b) 15th (c) 17th (d) 16th
  40. 40.Which term of the AP 3, 6, 9, 12, … is 63? (a) 23rd (b) 22nd (c) 21st (d) 20th

Answer key

  1. 25
  2. 222
  3. 85
  4. 100
  5. 161
  6. 136
  7. 61
  8. 71
  9. 66
  10. 10
  11. 36
  12. 361
  13. 28th
  14. 17th
  15. 93
  16. 39
  17. 84
  18. 3916
  19. 280
  20. 148
  21. 780
  22. 529
  23. 75
  24. 175
  25. 204
  26. 73
  27. 62
  28. 15th
  29. 20
  30. 29th
  31. 3003
  32. 324
  33. 83
  34. 676
  35. 22nd
  36. 4278
  37. 19
  38. 119
  39. 16th
  40. 21st

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