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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 533 · 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 37th term of the AP 15, 19, 23, 27, …? (a) 148 (b) 144 (c) 163 (d) 159
  2. 2.What is the missing term in the AP 16, 24, 32, ?, 48? (a) 48 (b) 40 (c) 39 (d) 41
  3. 3.What is the sum of all the whole numbers from 1 to 30? (a) 435 (b) 930 (c) 450 (d) 465
  4. 4.What is the sum of the first 12 terms of the AP 5, 7, 9, …? (a) 384 (b) 27 (c) 192 (d) 204
  5. 5.What is the sum of the first 9 terms of the AP 9, 15, 21, …? (a) 57 (b) 324 (c) 297 (d) 594
  6. 6.What is the missing term in the AP 12, ?, 28, 36, 44? (a) 21 (b) 19 (c) 20 (d) 28
  7. 7.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 256 (b) 128 (c) 30 (d) 144
  8. 8.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 225 (d) 240
  9. 9.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 30 (b) 162 (c) 165 (d) 324
  10. 10.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 6162 (c) 3003 (d) 3081
  11. 11.Which term of the AP 18, 23, 28, 33, … is 93? (a) 18th (b) 17th (c) 15th (d) 16th
  12. 12.Which term of the AP 12, 17, 22, 27, … is 167? (a) 34th (b) 31st (c) 33rd (d) 32nd
  13. 13.What is the sum of all the whole numbers from 1 to 88? (a) 3828 (b) 3916 (c) 7832 (d) 3872
  14. 14.What is the missing term in the AP 14, 17, ?, 23, 26? (a) 21 (b) 23 (c) 19 (d) 20
  15. 15.What is the 22nd term of the AP 12, 17, 22, 27, …? (a) 122 (b) 105 (c) 117 (d) 110
  16. 16.What is the 20th term of the AP 17, 19, 21, 23, …? (a) 55 (b) 57 (c) 38 (d) 40
  17. 17.What is the missing term in the AP 17, 25, ?, 41, 49? (a) 32 (b) 33 (c) 41 (d) 34
  18. 18.What is the 39th term of the AP 19, 27, 35, 43, …? (a) 312 (b) 331 (c) 304 (d) 323
  19. 19.What is the missing term in the AP 14, ?, 22, 26, 30? (a) 18 (b) 17 (c) 22 (d) 19
  20. 20.What is the 22nd term of the AP 18, 20, 22, 24, …? (a) 42 (b) 62 (c) 44 (d) 60
  21. 21.Which term of the AP 1, 4, 7, 10, … is 31? (a) 13th (b) 11th (c) 10th (d) 12th
  22. 22.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 132 (d) 66
  23. 23.What is the 11th term of the AP 7, 15, 23, 31, …? (a) 95 (b) 88 (c) 80 (d) 87
  24. 24.What is the 17th term of the AP 11, 13, 15, 17, …? (a) 34 (b) 43 (c) 32 (d) 45
  25. 25.What is the sum of all the whole numbers from 1 to 72? (a) 2592 (b) 5256 (c) 2628 (d) 2556
  26. 26.What is the sum of all the whole numbers from 1 to 63? (a) 2017 (b) 4032 (c) 2016 (d) 1953
  27. 27.What is the 34th term of the AP 1, 3, 5, 7, …? (a) 68 (b) 67 (c) 66 (d) 69
  28. 28.What is the 11th term of the AP 12, 21, 30, 39, …? (a) 90 (b) 111 (c) 99 (d) 102
  29. 29.Which term of the AP 10, 12, 14, 16, … is 76? (a) 33rd (b) 35th (c) 34th (d) 38th
  30. 30.Which term of the AP 12, 15, 18, 21, … is 42? (a) 12th (b) 14th (c) 11th (d) 10th
  31. 31.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 232 (c) 462 (d) 231
  32. 32.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 276 (c) 529 (d) 45
  33. 33.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 140 (b) 73 (c) 20 (d) 70
  34. 34.What is the 28th term of the AP 6, 10, 14, 18, …? (a) 114 (b) 108 (c) 118 (d) 112
  35. 35.What is the 27th term of the AP 2, 7, 12, 17, …? (a) 130 (b) 137 (c) 132 (d) 135
  36. 36.Which term of the AP 1, 4, 7, 10, … is 73? (a) 24th (b) 25th (c) 27th (d) 26th
  37. 37.Which term of the AP 5, 10, 15, 20, … is 125? (a) 24th (b) 25th (c) 27th (d) 26th
  38. 38.What is the missing term in the AP 5, 13, ?, 29, 37? (a) 20 (b) 21 (c) 22 (d) 29
  39. 39.What is the 28th term of the AP 9, 13, 17, 21, …? (a) 108 (b) 117 (c) 121 (d) 112
  40. 40.Which term of the AP 4, 9, 14, 19, … is 104? (a) 21st (b) 23rd (c) 22nd (d) 20th

Answer key

  1. 159
  2. 40
  3. 465
  4. 192
  5. 297
  6. 20
  7. 128
  8. 225
  9. 162
  10. 3081
  11. 16th
  12. 32nd
  13. 3916
  14. 20
  15. 117
  16. 55
  17. 33
  18. 323
  19. 18
  20. 60
  21. 11th
  22. 121
  23. 87
  24. 43
  25. 2628
  26. 2016
  27. 67
  28. 102
  29. 34th
  30. 11th
  31. 231
  32. 529
  33. 70
  34. 114
  35. 132
  36. 25th
  37. 25th
  38. 21
  39. 117
  40. 21st

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