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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 844 · 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 33rd term of the AP 4, 13, 22, 31, …? (a) 292 (b) 288 (c) 301 (d) 297
  2. 2.What is the 39th term of the AP 6, 10, 14, 18, …? (a) 158 (b) 156 (c) 152 (d) 162
  3. 3.What is the 19th term of the AP 12, 14, 16, 18, …? (a) 36 (b) 50 (c) 38 (d) 48
  4. 4.What is the missing term in the AP 18, ?, 30, 36, 42? (a) 24 (b) 23 (c) 25 (d) 30
  5. 5.What is the sum of all the whole numbers from 1 to 91? (a) 4186 (b) 4187 (c) 4095 (d) 8372
  6. 6.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 70 (b) 140 (c) 18 (d) 75
  7. 7.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 324 (b) 162 (c) 171 (d) 26
  8. 8.What is the missing term in the AP 16, 21, 26, ?, 36? (a) 30 (b) 32 (c) 31 (d) 36
  9. 9.What is the missing term in the AP 5, 10, 15, ?, 25? (a) 25 (b) 19 (c) 21 (d) 20
  10. 10.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 108 (b) 17 (c) 216 (d) 112
  11. 11.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 168 (b) 14 (c) 88 (d) 84
  12. 12.What is the 31st term of the AP 3, 9, 15, 21, …? (a) 180 (b) 189 (c) 186 (d) 183
  13. 13.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 184 (b) 368 (c) 44 (d) 208
  14. 14.Which term of the AP 20, 24, 28, 32, … is 92? (a) 19th (b) 23rd (c) 18th (d) 20th
  15. 15.Which term of the AP 14, 23, 32, 41, … is 131? (a) 14th (b) 16th (c) 13th (d) 15th
  16. 16.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 330 (b) 600 (c) 300 (d) 57
  17. 17.What is the missing term in the AP 5, 7, ?, 11, 13? (a) 9 (b) 8 (c) 10 (d) 11
  18. 18.What is the sum of all the whole numbers from 1 to 78? (a) 6162 (b) 3003 (c) 3042 (d) 3081
  19. 19.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 756 (c) 53 (d) 378
  20. 20.What is the missing term in the AP 12, 16, ?, 24, 28? (a) 19 (b) 21 (c) 20 (d) 24
  21. 21.Which term of the AP 18, 26, 34, 42, … is 146? (a) 16th (b) 18th (c) 17th (d) 19th
  22. 22.What is the 34th term of the AP 6, 9, 12, 15, …? (a) 99 (b) 108 (c) 102 (d) 105
  23. 23.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 228 (b) 34 (c) 420 (d) 210
  24. 24.What is the 40th term of the AP 10, 16, 22, 28, …? (a) 250 (b) 240 (c) 244 (d) 234
  25. 25.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 122 (b) 26 (c) 119 (d) 238
  26. 26.What is the 39th term of the AP 3, 5, 7, 9, …? (a) 79 (b) 76 (c) 81 (d) 78
  27. 27.Which term of the AP 8, 10, 12, 14, … is 34? (a) 17th (b) 13th (c) 14th (d) 15th
  28. 28.What is the 40th term of the AP 1, 6, 11, 16, …? (a) 200 (b) 196 (c) 195 (d) 201
  29. 29.What is the 24th term of the AP 13, 16, 19, 22, …? (a) 82 (b) 72 (c) 69 (d) 85
  30. 30.What is the sum of the first 7 terms of the AP 7, 9, 11, …? (a) 19 (b) 98 (c) 182 (d) 91
  31. 31.What is the 33rd term of the AP 13, 20, 27, 34, …? (a) 231 (b) 244 (c) 237 (d) 224
  32. 32.What is the sum of all the whole numbers from 1 to 92? (a) 4186 (b) 8556 (c) 4232 (d) 4278
  33. 33.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 17 (b) 57 (c) 66 (d) 114
  34. 34.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 132 (b) 11 (c) 66 (d) 67
  35. 35.What is the 19th term of the AP 2, 8, 14, 20, …? (a) 108 (b) 110 (c) 116 (d) 114
  36. 36.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 552 (c) 277 (d) 276
  37. 37.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 66 (c) 21 (d) 121
  38. 38.What is the 16th term of the AP 8, 16, 24, 32, …? (a) 129 (b) 120 (c) 128 (d) 136
  39. 39.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 441 (d) 231
  40. 40.What is the 37th term of the AP 14, 19, 24, 29, …? (a) 180 (b) 199 (c) 185 (d) 194

Answer key

  1. 292
  2. 158
  3. 48
  4. 24
  5. 4186
  6. 70
  7. 162
  8. 31
  9. 20
  10. 108
  11. 84
  12. 183
  13. 184
  14. 19th
  15. 14th
  16. 300
  17. 9
  18. 3081
  19. 729
  20. 20
  21. 17th
  22. 105
  23. 210
  24. 244
  25. 119
  26. 79
  27. 14th
  28. 196
  29. 82
  30. 91
  31. 237
  32. 4278
  33. 57
  34. 66
  35. 110
  36. 276
  37. 121
  38. 128
  39. 441
  40. 194

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