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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 548 · 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 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 66 (d) 132
  2. 2.What is the missing term in the AP 12, ?, 22, 27, 32? (a) 16 (b) 18 (c) 17 (d) 22
  3. 3.Which term of the AP 2, 4, 6, 8, … is 28? (a) 14th (b) 13th (c) 15th (d) 16th
  4. 4.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 41 (c) 231 (d) 441
  5. 5.What is the 12th term of the AP 15, 19, 23, 27, …? (a) 44 (b) 59 (c) 63 (d) 48
  6. 6.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 33 (c) 289 (d) 153
  7. 7.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 45 (b) 384 (c) 216 (d) 192
  8. 8.What is the missing term in the AP 11, ?, 19, 23, 27? (a) 14 (b) 16 (c) 19 (d) 15
  9. 9.What is the sum of the first 11 terms of the AP 1, 5, 9, …? (a) 41 (b) 253 (c) 462 (d) 231
  10. 10.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 28 (b) 408 (c) 216 (d) 204
  11. 11.What is the 36th term of the AP 20, 24, 28, 32, …? (a) 144 (b) 160 (c) 140 (d) 164
  12. 12.Which term of the AP 11, 15, 19, 23, … is 139? (a) 32nd (b) 35th (c) 33rd (d) 34th
  13. 13.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 20 (b) 18 (c) 21 (d) 19
  14. 14.Which term of the AP 1, 7, 13, 19, … is 61? (a) 12th (b) 10th (c) 13th (d) 11th
  15. 15.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 11 (c) 36 (d) 42
  16. 16.What is the 17th term of the AP 11, 18, 25, 32, …? (a) 119 (b) 112 (c) 123 (d) 130
  17. 17.Which term of the AP 18, 22, 26, 30, … is 138? (a) 31st (b) 30th (c) 32nd (d) 33rd
  18. 18.Which term of the AP 11, 14, 17, 20, … is 92? (a) 29th (b) 30th (c) 27th (d) 28th
  19. 19.What is the 32nd term of the AP 7, 11, 15, 19, …? (a) 131 (b) 124 (c) 128 (d) 135
  20. 20.What is the 31st term of the AP 7, 13, 19, 25, …? (a) 186 (b) 187 (c) 180 (d) 193
  21. 21.What is the 26th term of the AP 11, 20, 29, 38, …? (a) 236 (b) 225 (c) 245 (d) 234
  22. 22.What is the 23rd term of the AP 6, 15, 24, 33, …? (a) 204 (b) 207 (c) 198 (d) 213
  23. 23.What is the 29th term of the AP 3, 10, 17, 24, …? (a) 199 (b) 203 (c) 196 (d) 206
  24. 24.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 90 (b) 11 (c) 45 (d) 46
  25. 25.What is the sum of the first 9 terms of the AP 9, 12, 15, …? (a) 192 (b) 378 (c) 33 (d) 189
  26. 26.What is the sum of the first 8 terms of the AP 7, 13, 19, …? (a) 224 (b) 448 (c) 248 (d) 49
  27. 27.What is the sum of the first 5 terms of the AP 8, 13, 18, …? (a) 28 (b) 180 (c) 95 (d) 90
  28. 28.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 37 (b) 150 (c) 264 (d) 132
  29. 29.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 126 (b) 252 (c) 27 (d) 129
  30. 30.What is the 17th term of the AP 2, 11, 20, 29, …? (a) 155 (b) 144 (c) 153 (d) 146
  31. 31.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 11 (b) 130 (c) 70 (d) 65
  32. 32.What is the 25th term of the AP 4, 10, 16, 22, …? (a) 150 (b) 148 (c) 144 (d) 154
  33. 33.What is the sum of all the whole numbers from 1 to 13? (a) 91 (b) 78 (c) 92 (d) 182
  34. 34.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 154 (b) 80 (c) 77 (d) 20
  35. 35.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 26 (b) 24 (c) 22 (d) 23
  36. 36.What is the 28th term of the AP 1, 3, 5, 7, …? (a) 54 (b) 56 (c) 57 (d) 55
  37. 37.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 62 (b) 414 (c) 444 (d) 828
  38. 38.Which term of the AP 6, 15, 24, 33, … is 276? (a) 31st (b) 32nd (c) 33rd (d) 30th
  39. 39.What is the 11th term of the AP 8, 10, 12, 14, …? (a) 22 (b) 20 (c) 28 (d) 30
  40. 40.Which term of the AP 2, 9, 16, 23, … is 79? (a) 11th (b) 12th (c) 13th (d) 14th

Answer key

  1. 121
  2. 17
  3. 14th
  4. 441
  5. 59
  6. 289
  7. 192
  8. 15
  9. 231
  10. 204
  11. 160
  12. 33rd
  13. 19
  14. 11th
  15. 36
  16. 123
  17. 31st
  18. 28th
  19. 131
  20. 187
  21. 236
  22. 204
  23. 199
  24. 45
  25. 189
  26. 224
  27. 90
  28. 132
  29. 126
  30. 146
  31. 65
  32. 148
  33. 91
  34. 77
  35. 23
  36. 55
  37. 414
  38. 31st
  39. 28
  40. 12th

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