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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 221 · 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 13th term of the AP 20, 26, 32, 38, …? (a) 78 (b) 92 (c) 72 (d) 98
  2. 2.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 37 (b) 189 (c) 207 (d) 378
  3. 3.What is the 17th term of the AP 19, 25, 31, 37, …? (a) 96 (b) 115 (c) 121 (d) 102
  4. 4.What is the 14th term of the AP 12, 18, 24, 30, …? (a) 84 (b) 96 (c) 90 (d) 78
  5. 5.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 276 (c) 552 (d) 529
  6. 6.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 24 (b) 21 (c) 6 (d) 42
  7. 7.Which term of the AP 4, 12, 20, 28, … is 300? (a) 40th (b) 39th (c) 38th (d) 37th
  8. 8.What is the 11th term of the AP 11, 17, 23, 29, …? (a) 60 (b) 77 (c) 71 (d) 66
  9. 9.What is the 24th term of the AP 1, 4, 7, 10, …? (a) 70 (b) 72 (c) 69 (d) 73
  10. 10.What is the 18th term of the AP 7, 9, 11, 13, …? (a) 34 (b) 43 (c) 41 (d) 36
  11. 11.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 6 (b) 7 (c) 10 (d) 5
  12. 12.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 56 (c) 13 (d) 28
  13. 13.What is the 29th term of the AP 15, 17, 19, 21, …? (a) 73 (b) 56 (c) 71 (d) 58
  14. 14.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 684 (b) 56 (c) 372 (d) 342
  15. 15.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 88 (b) 17 (c) 160 (d) 80
  16. 16.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 756 (c) 378 (d) 351
  17. 17.What is the missing term in the AP 1, 9, 17, ?, 33? (a) 26 (b) 25 (c) 24 (d) 33
  18. 18.What is the sum of all the whole numbers from 1 to 85? (a) 3655 (b) 3656 (c) 3570 (d) 7310
  19. 19.Which term of the AP 19, 22, 25, 28, … is 136? (a) 40th (b) 39th (c) 41st (d) 42nd
  20. 20.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 4950 (c) 9900 (d) 4851
  21. 21.What is the 23rd term of the AP 15, 18, 21, 24, …? (a) 81 (b) 66 (c) 69 (d) 84
  22. 22.What is the missing term in the AP 18, 21, ?, 27, 30? (a) 27 (b) 25 (c) 23 (d) 24
  23. 23.What is the 10th term of the AP 8, 16, 24, 32, …? (a) 88 (b) 81 (c) 72 (d) 80
  24. 24.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 812 (d) 784
  25. 25.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 75 (b) 24 (c) 140 (d) 70
  26. 26.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 121 (d) 21
  27. 27.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1225 (c) 1176 (d) 1226
  28. 28.What is the sum of the first 5 terms of the AP 1, 6, 11, …? (a) 21 (b) 55 (c) 110 (d) 60
  29. 29.What is the sum of all the whole numbers from 1 to 65? (a) 2146 (b) 2145 (c) 2080 (d) 4290
  30. 30.What is the 17th term of the AP 12, 14, 16, 18, …? (a) 46 (b) 44 (c) 34 (d) 32
  31. 31.What is the sum of all the whole numbers from 1 to 42? (a) 1806 (b) 861 (c) 903 (d) 882
  32. 32.What is the 11th term of the AP 16, 23, 30, 37, …? (a) 86 (b) 77 (c) 70 (d) 93
  33. 33.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 39 (b) 144 (c) 162 (d) 288
  34. 34.What is the sum of all the whole numbers from 1 to 12? (a) 156 (b) 78 (c) 66 (d) 72
  35. 35.Which term of the AP 15, 17, 19, 21, … is 41? (a) 15th (b) 16th (c) 14th (d) 13th
  36. 36.What is the missing term in the AP 1, 10, 19, ?, 37? (a) 29 (b) 27 (c) 37 (d) 28
  37. 37.What is the 34th term of the AP 5, 14, 23, 32, …? (a) 306 (b) 311 (c) 297 (d) 302
  38. 38.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 95 (b) 160 (c) 28 (d) 80
  39. 39.What is the 16th term of the AP 19, 26, 33, 40, …? (a) 105 (b) 124 (c) 131 (d) 112
  40. 40.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 25 (d) 30

Answer key

  1. 92
  2. 189
  3. 115
  4. 90
  5. 529
  6. 21
  7. 38th
  8. 71
  9. 70
  10. 41
  11. 6
  12. 49
  13. 71
  14. 342
  15. 80
  16. 378
  17. 25
  18. 3655
  19. 40th
  20. 4950
  21. 81
  22. 24
  23. 80
  24. 784
  25. 70
  26. 121
  27. 1225
  28. 55
  29. 2145
  30. 44
  31. 903
  32. 86
  33. 144
  34. 78
  35. 14th
  36. 28
  37. 302
  38. 80
  39. 124
  40. 25

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