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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 220 · 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 28th term of the AP 3, 6, 9, 12, …? (a) 87 (b) 81 (c) 84 (d) 85
  2. 2.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 676 (d) 702
  3. 3.What is the 18th term of the AP 10, 18, 26, 34, …? (a) 136 (b) 154 (c) 144 (d) 146
  4. 4.What is the 12th term of the AP 15, 22, 29, 36, …? (a) 77 (b) 84 (c) 92 (d) 99
  5. 5.What is the 30th term of the AP 11, 13, 15, 17, …? (a) 60 (b) 58 (c) 69 (d) 71
  6. 6.What is the 20th term of the AP 1, 7, 13, 19, …? (a) 114 (b) 121 (c) 120 (d) 115
  7. 7.What is the sum of all the whole numbers from 1 to 28? (a) 406 (b) 392 (c) 812 (d) 378
  8. 8.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 289 (c) 33 (d) 153
  9. 9.What is the 37th term of the AP 7, 13, 19, 25, …? (a) 229 (b) 216 (c) 223 (d) 222
  10. 10.Which term of the AP 2, 10, 18, 26, … is 202? (a) 28th (b) 26th (c) 25th (d) 27th
  11. 11.What is the 38th term of the AP 5, 10, 15, 20, …? (a) 190 (b) 191 (c) 185 (d) 195
  12. 12.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 80 (b) 88 (c) 160 (d) 17
  13. 13.What is the sum of the first 10 terms of the AP 2, 5, 8, …? (a) 155 (b) 310 (c) 170 (d) 29
  14. 14.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 96 (b) 20 (c) 90 (d) 180
  15. 15.What is the 39th term of the AP 8, 11, 14, 17, …? (a) 114 (b) 117 (c) 122 (d) 125
  16. 16.Which term of the AP 14, 23, 32, 41, … is 104? (a) 12th (b) 10th (c) 11th (d) 13th
  17. 17.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 39 (d) 400
  18. 18.What is the missing term in the AP 6, 9, 12, ?, 18? (a) 16 (b) 18 (c) 14 (d) 15
  19. 19.What is the sum of all the whole numbers from 1 to 66? (a) 2145 (b) 4422 (c) 2211 (d) 2178
  20. 20.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 70 (b) 35 (c) 36 (d) 8
  21. 21.What is the 40th term of the AP 17, 21, 25, 29, …? (a) 156 (b) 160 (c) 173 (d) 177
  22. 22.What is the 40th term of the AP 10, 19, 28, 37, …? (a) 361 (b) 370 (c) 351 (d) 360
  23. 23.What is the 19th term of the AP 1, 6, 11, 16, …? (a) 90 (b) 96 (c) 91 (d) 95
  24. 24.What is the missing term in the AP 8, ?, 18, 23, 28? (a) 14 (b) 18 (c) 12 (d) 13
  25. 25.What is the 32nd term of the AP 14, 19, 24, 29, …? (a) 169 (b) 160 (c) 174 (d) 155
  26. 26.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 100 (b) 32 (c) 200 (d) 115
  27. 27.What is the 10th term of the AP 19, 25, 31, 37, …? (a) 60 (b) 79 (c) 54 (d) 73
  28. 28.Which term of the AP 10, 16, 22, 28, … is 136? (a) 22nd (b) 24th (c) 23rd (d) 21st
  29. 29.What is the 21st term of the AP 3, 10, 17, 24, …? (a) 140 (b) 143 (c) 150 (d) 147
  30. 30.What is the 13th term of the AP 1, 4, 7, 10, …? (a) 37 (b) 39 (c) 40 (d) 36
  31. 31.Which term of the AP 18, 25, 32, 39, … is 88? (a) 11th (b) 12th (c) 10th (d) 13th
  32. 32.What is the missing term in the AP 8, 12, 16, ?, 24? (a) 20 (b) 24 (c) 19 (d) 21
  33. 33.What is the 25th term of the AP 16, 23, 30, 37, …? (a) 168 (b) 184 (c) 175 (d) 191
  34. 34.What is the missing term in the AP 2, 8, ?, 20, 26? (a) 13 (b) 14 (c) 15 (d) 20
  35. 35.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 144 (d) 156
  36. 36.What is the sum of all the whole numbers from 1 to 89? (a) 4006 (b) 8010 (c) 3916 (d) 4005
  37. 37.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 260 (b) 520 (c) 44 (d) 280
  38. 38.What is the sum of the first 12 terms of the AP 5, 10, 15, …? (a) 60 (b) 780 (c) 420 (d) 390
  39. 39.Which term of the AP 5, 7, 9, 11, … is 51? (a) 26th (b) 25th (c) 24th (d) 23rd
  40. 40.What is the 40th term of the AP 11, 15, 19, 23, …? (a) 167 (b) 171 (c) 156 (d) 160

Answer key

  1. 84
  2. 676
  3. 146
  4. 92
  5. 69
  6. 115
  7. 406
  8. 289
  9. 223
  10. 26th
  11. 190
  12. 80
  13. 155
  14. 90
  15. 122
  16. 11th
  17. 400
  18. 15
  19. 2211
  20. 35
  21. 173
  22. 361
  23. 91
  24. 13
  25. 169
  26. 100
  27. 73
  28. 22nd
  29. 143
  30. 37
  31. 11th
  32. 20
  33. 184
  34. 14
  35. 144
  36. 4005
  37. 260
  38. 390
  39. 24th
  40. 167

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