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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 291 · 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 7 terms of the AP 5, 7, 9, …? (a) 154 (b) 84 (c) 17 (d) 77
  2. 2.What is the sum of all the whole numbers from 1 to 38? (a) 1482 (b) 703 (c) 741 (d) 722
  3. 3.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 96 (b) 18 (c) 176 (d) 88
  4. 4.What is the 36th term of the AP 20, 26, 32, 38, …? (a) 210 (b) 216 (c) 230 (d) 236
  5. 5.What is the sum of all the whole numbers from 1 to 59? (a) 3540 (b) 1771 (c) 1711 (d) 1770
  6. 6.What is the 29th term of the AP 14, 16, 18, 20, …? (a) 56 (b) 70 (c) 58 (d) 72
  7. 7.What is the missing term in the AP 9, 17, ?, 33, 41? (a) 25 (b) 33 (c) 24 (d) 26
  8. 8.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 70 (b) 17 (c) 65 (d) 130
  9. 9.Which term of the AP 3, 5, 7, 9, … is 73? (a) 37th (b) 38th (c) 35th (d) 36th
  10. 10.What is the 35th term of the AP 1, 8, 15, 22, …? (a) 245 (b) 239 (c) 238 (d) 246
  11. 11.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 90 (b) 13 (c) 85 (d) 170
  12. 12.What is the missing term in the AP 8, ?, 16, 20, 24? (a) 13 (b) 11 (c) 16 (d) 12
  13. 13.What is the sum of the first 7 terms of the AP 4, 8, 12, …? (a) 224 (b) 112 (c) 126 (d) 28
  14. 14.What is the sum of the first 8 terms of the AP 6, 9, 12, …? (a) 132 (b) 144 (c) 27 (d) 264
  15. 15.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 11 (b) 51 (c) 54 (d) 102
  16. 16.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 10 (b) 15 (c) 12 (d) 11
  17. 17.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 228 (b) 29 (c) 126 (d) 114
  18. 18.What is the sum of all the whole numbers from 1 to 10? (a) 55 (b) 50 (c) 110 (d) 45
  19. 19.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 67 (c) 66 (d) 55
  20. 20.What is the 37th term of the AP 8, 14, 20, 26, …? (a) 230 (b) 222 (c) 216 (d) 224
  21. 21.What is the 13th term of the AP 1, 9, 17, 25, …? (a) 97 (b) 96 (c) 104 (d) 105
  22. 22.What is the 11th term of the AP 13, 19, 25, 31, …? (a) 60 (b) 73 (c) 66 (d) 79
  23. 23.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 45 (c) 81 (d) 90
  24. 24.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 380 (b) 190 (c) 200 (d) 28
  25. 25.What is the 14th term of the AP 17, 25, 33, 41, …? (a) 104 (b) 112 (c) 121 (d) 129
  26. 26.Which term of the AP 12, 14, 16, 18, … is 36? (a) 13th (b) 18th (c) 14th (d) 12th
  27. 27.What is the 29th term of the AP 8, 10, 12, 14, …? (a) 64 (b) 56 (c) 58 (d) 66
  28. 28.What is the 29th term of the AP 7, 14, 21, 28, …? (a) 196 (b) 204 (c) 203 (d) 210
  29. 29.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 100 (d) 110
  30. 30.What is the 22nd term of the AP 2, 4, 6, 8, …? (a) 42 (b) 45 (c) 44 (d) 46
  31. 31.What is the 35th term of the AP 9, 12, 15, 18, …? (a) 102 (b) 105 (c) 111 (d) 114
  32. 32.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 78 (b) 138 (c) 19 (d) 69
  33. 33.What is the 15th term of the AP 17, 19, 21, 23, …? (a) 45 (b) 47 (c) 28 (d) 30
  34. 34.Which term of the AP 5, 14, 23, 32, … is 203? (a) 22nd (b) 25th (c) 24th (d) 23rd
  35. 35.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 85 (b) 168 (c) 84 (d) 15
  36. 36.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 156 (c) 78 (d) 66
  37. 37.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 25 (b) 105 (c) 114 (d) 210
  38. 38.What is the 22nd term of the AP 18, 20, 22, 24, …? (a) 44 (b) 42 (c) 60 (d) 62
  39. 39.What is the missing term in the AP 3, ?, 15, 21, 27? (a) 10 (b) 8 (c) 9 (d) 15
  40. 40.Which term of the AP 8, 14, 20, 26, … is 74? (a) 13th (b) 12th (c) 14th (d) 11th

Answer key

  1. 77
  2. 741
  3. 88
  4. 230
  5. 1770
  6. 70
  7. 25
  8. 65
  9. 36th
  10. 239
  11. 85
  12. 12
  13. 112
  14. 132
  15. 51
  16. 11
  17. 114
  18. 55
  19. 66
  20. 224
  21. 97
  22. 73
  23. 81
  24. 190
  25. 121
  26. 13th
  27. 64
  28. 203
  29. 100
  30. 44
  31. 111
  32. 69
  33. 45
  34. 23rd
  35. 84
  36. 78
  37. 105
  38. 60
  39. 9
  40. 12th

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