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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 748 · 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 9 terms of the AP 7, 10, 13, …? (a) 31 (b) 174 (c) 342 (d) 171
  2. 2.What is the 14th term of the AP 4, 8, 12, 16, …? (a) 56 (b) 52 (c) 60 (d) 57
  3. 3.Which term of the AP 1, 7, 13, 19, … is 169? (a) 30th (b) 29th (c) 28th (d) 31st
  4. 4.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 784 (c) 812 (d) 55
  5. 5.What is the 30th term of the AP 3, 9, 15, 21, …? (a) 183 (b) 174 (c) 177 (d) 180
  6. 6.Which term of the AP 20, 26, 32, 38, … is 92? (a) 13th (b) 14th (c) 15th (d) 12th
  7. 7.Which term of the AP 12, 21, 30, 39, … is 246? (a) 27th (b) 29th (c) 26th (d) 28th
  8. 8.What is the 33rd term of the AP 2, 4, 6, 8, …? (a) 64 (b) 67 (c) 68 (d) 66
  9. 9.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 133 (b) 29 (c) 119 (d) 238
  10. 10.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 189 (b) 171 (c) 342 (d) 35
  11. 11.What is the 26th term of the AP 1, 5, 9, 13, …? (a) 100 (b) 105 (c) 101 (d) 104
  12. 12.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 470 (b) 260 (c) 46 (d) 235
  13. 13.What is the missing term in the AP 6, 15, ?, 33, 42? (a) 33 (b) 25 (c) 23 (d) 24
  14. 14.Which term of the AP 8, 17, 26, 35, … is 134? (a) 14th (b) 17th (c) 16th (d) 15th
  15. 15.What is the 36th term of the AP 13, 22, 31, 40, …? (a) 315 (b) 337 (c) 324 (d) 328
  16. 16.What is the 18th term of the AP 5, 14, 23, 32, …? (a) 167 (b) 158 (c) 153 (d) 162
  17. 17.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 225 (d) 240
  18. 18.What is the 33rd term of the AP 17, 22, 27, 32, …? (a) 182 (b) 160 (c) 165 (d) 177
  19. 19.What is the sum of the first 12 terms of the AP 10, 13, 16, …? (a) 43 (b) 336 (c) 636 (d) 318
  20. 20.What is the missing term in the AP 13, 20, ?, 34, 41? (a) 27 (b) 26 (c) 34 (d) 28
  21. 21.Which term of the AP 16, 18, 20, 22, … is 94? (a) 47th (b) 41st (c) 40th (d) 39th
  22. 22.What is the missing term in the AP 1, 10, ?, 28, 37? (a) 20 (b) 18 (c) 19 (d) 28
  23. 23.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 55 (d) 19
  24. 24.Which term of the AP 8, 14, 20, 26, … is 224? (a) 36th (b) 39th (c) 37th (d) 38th
  25. 25.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 39 (b) 172 (c) 344 (d) 192
  26. 26.What is the 38th term of the AP 12, 16, 20, 24, …? (a) 152 (b) 148 (c) 164 (d) 160
  27. 27.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 26 (b) 140 (c) 85 (d) 70
  28. 28.What is the sum of all the whole numbers from 1 to 77? (a) 3004 (b) 6006 (c) 3003 (d) 2926
  29. 29.What is the 28th term of the AP 6, 12, 18, 24, …? (a) 162 (b) 169 (c) 174 (d) 168
  30. 30.What is the missing term in the AP 17, ?, 25, 29, 33? (a) 22 (b) 25 (c) 20 (d) 21
  31. 31.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 224 (b) 112 (c) 31 (d) 117
  32. 32.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 240 (b) 138 (c) 120 (d) 35
  33. 33.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 132 (c) 66 (d) 21
  34. 34.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 95 (b) 25 (c) 170 (d) 85
  35. 35.What is the missing term in the AP 19, ?, 37, 46, 55? (a) 37 (b) 27 (c) 28 (d) 29
  36. 36.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 408 (b) 216 (c) 28 (d) 204
  37. 37.What is the 12th term of the AP 11, 19, 27, 35, …? (a) 99 (b) 107 (c) 96 (d) 88
  38. 38.What is the 20th term of the AP 9, 13, 17, 21, …? (a) 76 (b) 89 (c) 80 (d) 85
  39. 39.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 64 (c) 72 (d) 15
  40. 40.What is the 14th term of the AP 3, 12, 21, 30, …? (a) 129 (b) 117 (c) 126 (d) 120

Answer key

  1. 171
  2. 56
  3. 29th
  4. 784
  5. 177
  6. 13th
  7. 27th
  8. 66
  9. 119
  10. 171
  11. 101
  12. 235
  13. 24
  14. 15th
  15. 328
  16. 158
  17. 225
  18. 177
  19. 318
  20. 27
  21. 40th
  22. 19
  23. 100
  24. 37th
  25. 172
  26. 160
  27. 70
  28. 3003
  29. 168
  30. 21
  31. 112
  32. 120
  33. 121
  34. 85
  35. 28
  36. 204
  37. 99
  38. 85
  39. 64
  40. 120

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