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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 404 · 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 missing term in the AP 4, ?, 18, 25, 32? (a) 10 (b) 18 (c) 12 (d) 11
  2. 2.Which term of the AP 8, 10, 12, 14, … is 80? (a) 36th (b) 38th (c) 37th (d) 40th
  3. 3.What is the 30th term of the AP 3, 9, 15, 21, …? (a) 183 (b) 180 (c) 177 (d) 174
  4. 4.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 19 (b) 162 (c) 324 (d) 168
  5. 5.What is the 28th term of the AP 2, 7, 12, 17, …? (a) 142 (b) 135 (c) 140 (d) 137
  6. 6.What is the 24th term of the AP 7, 16, 25, 34, …? (a) 223 (b) 214 (c) 207 (d) 216
  7. 7.What is the missing term in the AP 18, 26, 34, ?, 50? (a) 41 (b) 43 (c) 42 (d) 50
  8. 8.What is the missing term in the AP 19, 21, 23, ?, 27? (a) 27 (b) 26 (c) 25 (d) 24
  9. 9.What is the sum of the first 12 terms of the AP 5, 8, 11, …? (a) 258 (b) 516 (c) 276 (d) 38
  10. 10.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 37 (b) 312 (c) 176 (d) 156
  11. 11.What is the 14th term of the AP 6, 15, 24, 33, …? (a) 126 (b) 132 (c) 117 (d) 123
  12. 12.What is the 38th term of the AP 2, 10, 18, 26, …? (a) 296 (b) 306 (c) 304 (d) 298
  13. 13.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 49 (d) 28
  14. 14.What is the 35th term of the AP 5, 7, 9, 11, …? (a) 70 (b) 75 (c) 73 (d) 68
  15. 15.What is the 35th term of the AP 5, 12, 19, 26, …? (a) 250 (b) 238 (c) 243 (d) 245
  16. 16.What is the 31st term of the AP 5, 9, 13, 17, …? (a) 124 (b) 120 (c) 125 (d) 129
  17. 17.What is the sum of all the whole numbers from 1 to 94? (a) 8930 (b) 4465 (c) 4371 (d) 4418
  18. 18.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 12 (b) 14 (c) 13 (d) 16
  19. 19.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 15 (c) 25 (d) 30
  20. 20.What is the sum of all the whole numbers from 1 to 29? (a) 436 (b) 406 (c) 870 (d) 435
  21. 21.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 190 (b) 374 (c) 187 (d) 32
  22. 22.What is the sum of the first 9 terms of the AP 4, 6, 8, …? (a) 20 (b) 117 (c) 108 (d) 216
  23. 23.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 169 (c) 182 (d) 25
  24. 24.What is the missing term in the AP 17, 20, 23, ?, 29? (a) 26 (b) 25 (c) 29 (d) 27
  25. 25.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 23 (b) 78 (c) 90 (d) 156
  26. 26.Which term of the AP 11, 16, 21, 26, … is 46? (a) 9th (b) 7th (c) 10th (d) 8th
  27. 27.What is the sum of all the whole numbers from 1 to 91? (a) 4186 (b) 8372 (c) 4187 (d) 4095
  28. 28.What is the sum of all the whole numbers from 1 to 63? (a) 2016 (b) 1953 (c) 2017 (d) 4032
  29. 29.What is the sum of all the whole numbers from 1 to 41? (a) 862 (b) 861 (c) 820 (d) 1722
  30. 30.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 8 (b) 10 (c) 6 (d) 7
  31. 31.What is the 15th term of the AP 18, 27, 36, 45, …? (a) 153 (b) 144 (c) 126 (d) 135
  32. 32.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 112 (b) 63 (c) 14 (d) 56
  33. 33.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 55 (b) 110 (c) 58 (d) 17
  34. 34.What is the missing term in the AP 14, ?, 28, 35, 42? (a) 22 (b) 28 (c) 21 (d) 20
  35. 35.What is the missing term in the AP 2, 4, 6, ?, 10? (a) 8 (b) 7 (c) 10 (d) 9
  36. 36.What is the 33rd term of the AP 9, 13, 17, 21, …? (a) 141 (b) 128 (c) 132 (d) 137
  37. 37.What is the 34th term of the AP 11, 18, 25, 32, …? (a) 249 (b) 242 (c) 231 (d) 238
  38. 38.What is the 23rd term of the AP 14, 18, 22, 26, …? (a) 88 (b) 106 (c) 92 (d) 102
  39. 39.What is the sum of the first 7 terms of the AP 3, 5, 7, …? (a) 126 (b) 70 (c) 15 (d) 63
  40. 40.What is the 10th term of the AP 4, 8, 12, 16, …? (a) 40 (b) 36 (c) 41 (d) 44

Answer key

  1. 11
  2. 37th
  3. 177
  4. 162
  5. 137
  6. 214
  7. 42
  8. 25
  9. 258
  10. 156
  11. 123
  12. 298
  13. 49
  14. 73
  15. 243
  16. 125
  17. 4465
  18. 13
  19. 25
  20. 435
  21. 187
  22. 108
  23. 169
  24. 26
  25. 78
  26. 8th
  27. 4186
  28. 2016
  29. 861
  30. 7
  31. 144
  32. 56
  33. 55
  34. 21
  35. 8
  36. 137
  37. 242
  38. 102
  39. 63
  40. 40

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