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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 63 · 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 38th term of the AP 13, 19, 25, 31, …? (a) 228 (b) 235 (c) 222 (d) 241
  2. 2.Which term of the AP 13, 20, 27, 34, … is 132? (a) 20th (b) 19th (c) 18th (d) 17th
  3. 3.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 70 (b) 35 (c) 11 (d) 40
  4. 4.What is the sum of all the whole numbers from 1 to 65? (a) 2080 (b) 2145 (c) 2146 (d) 4290
  5. 5.Which term of the AP 8, 16, 24, 32, … is 216? (a) 29th (b) 28th (c) 26th (d) 27th
  6. 6.What is the missing term in the AP 5, ?, 23, 32, 41? (a) 14 (b) 23 (c) 15 (d) 13
  7. 7.What is the 14th term of the AP 11, 18, 25, 32, …? (a) 109 (b) 102 (c) 91 (d) 98
  8. 8.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 75 (b) 15 (c) 150 (d) 78
  9. 9.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 91 (c) 25 (d) 169
  10. 10.What is the 29th term of the AP 20, 23, 26, 29, …? (a) 87 (b) 107 (c) 84 (d) 104
  11. 11.Which term of the AP 20, 23, 26, 29, … is 125? (a) 35th (b) 36th (c) 37th (d) 38th
  12. 12.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 57 (b) 60 (c) 114 (d) 12
  13. 13.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 176 (b) 187 (c) 26 (d) 352
  14. 14.What is the missing term in the AP 1, 5, ?, 13, 17? (a) 8 (b) 13 (c) 10 (d) 9
  15. 15.What is the sum of the first 10 terms of the AP 10, 14, 18, …? (a) 280 (b) 560 (c) 300 (d) 46
  16. 16.What is the 23rd term of the AP 13, 21, 29, 37, …? (a) 197 (b) 189 (c) 176 (d) 184
  17. 17.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 870 (c) 57 (d) 435
  18. 18.What is the missing term in the AP 11, ?, 27, 35, 43? (a) 27 (b) 19 (c) 20 (d) 18
  19. 19.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 78 (b) 138 (c) 19 (d) 69
  20. 20.What is the 24th term of the AP 15, 19, 23, 27, …? (a) 111 (b) 107 (c) 96 (d) 92
  21. 21.What is the 27th term of the AP 15, 21, 27, 33, …? (a) 162 (b) 156 (c) 171 (d) 177
  22. 22.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 726 (b) 63 (c) 396 (d) 363
  23. 23.What is the missing term in the AP 15, ?, 27, 33, 39? (a) 20 (b) 27 (c) 21 (d) 22
  24. 24.What is the 28th term of the AP 15, 21, 27, 33, …? (a) 177 (b) 162 (c) 168 (d) 183
  25. 25.What is the missing term in the AP 12, ?, 20, 24, 28? (a) 17 (b) 20 (c) 16 (d) 15
  26. 26.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 196 (c) 27 (d) 105
  27. 27.What is the missing term in the AP 12, 14, ?, 18, 20? (a) 18 (b) 15 (c) 17 (d) 16
  28. 28.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 13 (c) 28 (d) 56
  29. 29.What is the 37th term of the AP 17, 23, 29, 35, …? (a) 216 (b) 239 (c) 233 (d) 222
  30. 30.What is the 11th term of the AP 11, 20, 29, 38, …? (a) 99 (b) 101 (c) 90 (d) 110
  31. 31.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 330 (b) 176 (c) 165 (d) 25
  32. 32.What is the missing term in the AP 12, 20, ?, 36, 44? (a) 29 (b) 36 (c) 28 (d) 27
  33. 33.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 126 (b) 66 (c) 13 (d) 63
  34. 34.What is the 22nd term of the AP 12, 18, 24, 30, …? (a) 144 (b) 138 (c) 126 (d) 132
  35. 35.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 60 (b) 15 (c) 110 (d) 55
  36. 36.What is the 21st term of the AP 12, 14, 16, 18, …? (a) 54 (b) 42 (c) 52 (d) 40
  37. 37.What is the 19th term of the AP 19, 22, 25, 28, …? (a) 57 (b) 73 (c) 76 (d) 54
  38. 38.What is the missing term in the AP 3, 9, 15, ?, 27? (a) 27 (b) 21 (c) 20 (d) 22
  39. 39.Which term of the AP 4, 7, 10, 13, … is 46? (a) 17th (b) 16th (c) 15th (d) 14th
  40. 40.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 15 (b) 168 (c) 84 (d) 85

Answer key

  1. 235
  2. 18th
  3. 35
  4. 2145
  5. 27th
  6. 14
  7. 102
  8. 75
  9. 169
  10. 104
  11. 36th
  12. 57
  13. 176
  14. 9
  15. 280
  16. 189
  17. 841
  18. 19
  19. 69
  20. 107
  21. 171
  22. 363
  23. 21
  24. 177
  25. 16
  26. 196
  27. 16
  28. 49
  29. 233
  30. 101
  31. 165
  32. 28
  33. 63
  34. 138
  35. 55
  36. 52
  37. 73
  38. 21
  39. 15th
  40. 84

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