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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 57 · 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 34th term of the AP 7, 12, 17, 22, …? (a) 170 (b) 165 (c) 172 (d) 177
  2. 2.Which term of the AP 9, 18, 27, 36, … is 153? (a) 17th (b) 18th (c) 19th (d) 16th
  3. 3.What is the 10th term of the AP 4, 6, 8, 10, …? (a) 20 (b) 22 (c) 18 (d) 24
  4. 4.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 600 (c) 47 (d) 576
  5. 5.What is the 15th term of the AP 15, 24, 33, 42, …? (a) 126 (b) 150 (c) 141 (d) 135
  6. 6.What is the 29th term of the AP 10, 19, 28, 37, …? (a) 252 (b) 271 (c) 261 (d) 262
  7. 7.Which term of the AP 4, 12, 20, 28, … is 180? (a) 25th (b) 23rd (c) 24th (d) 22nd
  8. 8.What is the missing term in the AP 15, 23, 31, ?, 47? (a) 38 (b) 40 (c) 47 (d) 39
  9. 9.What is the missing term in the AP 12, ?, 22, 27, 32? (a) 22 (b) 17 (c) 18 (d) 16
  10. 10.What is the 11th term of the AP 3, 5, 7, 9, …? (a) 25 (b) 20 (c) 22 (d) 23
  11. 11.What is the 14th term of the AP 15, 22, 29, 36, …? (a) 113 (b) 91 (c) 106 (d) 98
  12. 12.What is the missing term in the AP 8, ?, 18, 23, 28? (a) 14 (b) 12 (c) 13 (d) 18
  13. 13.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 174 (b) 20 (c) 180 (d) 348
  14. 14.What is the missing term in the AP 8, 16, 24, ?, 40? (a) 40 (b) 31 (c) 33 (d) 32
  15. 15.What is the missing term in the AP 3, 7, 11, ?, 19? (a) 15 (b) 14 (c) 16 (d) 19
  16. 16.What is the 12th term of the AP 6, 11, 16, 21, …? (a) 66 (b) 60 (c) 55 (d) 61
  17. 17.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 29 (c) 120 (d) 225
  18. 18.What is the sum of all the whole numbers from 1 to 56? (a) 1568 (b) 1596 (c) 3192 (d) 1540
  19. 19.What is the 27th term of the AP 6, 12, 18, 24, …? (a) 156 (b) 168 (c) 163 (d) 162
  20. 20.Which term of the AP 19, 22, 25, 28, … is 64? (a) 18th (b) 15th (c) 16th (d) 17th
  21. 21.What is the sum of all the whole numbers from 1 to 53? (a) 1378 (b) 2862 (c) 1432 (d) 1431
  22. 22.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 88 (b) 160 (c) 80 (d) 17
  23. 23.What is the sum of the first 8 terms of the AP 5, 8, 11, …? (a) 248 (b) 136 (c) 26 (d) 124
  24. 24.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 25 (b) 176 (c) 165 (d) 330
  25. 25.What is the missing term in the AP 12, ?, 26, 33, 40? (a) 26 (b) 19 (c) 18 (d) 20
  26. 26.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 20 (b) 96 (c) 90 (d) 180
  27. 27.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 66 (c) 21 (d) 121
  28. 28.What is the 31st term of the AP 20, 23, 26, 29, …? (a) 90 (b) 110 (c) 113 (d) 93
  29. 29.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 18 (b) 20 (c) 19 (d) 21
  30. 30.What is the 22nd term of the AP 15, 24, 33, 42, …? (a) 189 (b) 204 (c) 198 (d) 213
  31. 31.What is the 10th term of the AP 19, 26, 33, 40, …? (a) 70 (b) 82 (c) 89 (d) 63
  32. 32.Which term of the AP 17, 26, 35, 44, … is 197? (a) 22nd (b) 21st (c) 23rd (d) 20th
  33. 33.What is the 16th term of the AP 4, 13, 22, 31, …? (a) 148 (b) 139 (c) 135 (d) 144
  34. 34.What is the 28th term of the AP 4, 12, 20, 28, …? (a) 224 (b) 220 (c) 216 (d) 228
  35. 35.What is the sum of all the whole numbers from 1 to 86? (a) 3741 (b) 7482 (c) 3698 (d) 3655
  36. 36.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 133 (b) 119 (c) 29 (d) 238
  37. 37.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 253 (c) 277 (d) 276
  38. 38.What is the 20th term of the AP 3, 6, 9, 12, …? (a) 57 (b) 63 (c) 61 (d) 60
  39. 39.What is the 15th term of the AP 6, 12, 18, 24, …? (a) 90 (b) 84 (c) 96 (d) 91
  40. 40.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 80 (b) 25 (c) 65 (d) 130

Answer key

  1. 172
  2. 17th
  3. 22
  4. 576
  5. 141
  6. 262
  7. 23rd
  8. 39
  9. 17
  10. 23
  11. 106
  12. 13
  13. 174
  14. 32
  15. 15
  16. 61
  17. 225
  18. 1596
  19. 162
  20. 16th
  21. 1431
  22. 80
  23. 124
  24. 165
  25. 19
  26. 90
  27. 121
  28. 110
  29. 19
  30. 204
  31. 82
  32. 21st
  33. 139
  34. 220
  35. 3741
  36. 119
  37. 276
  38. 60
  39. 90
  40. 65

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