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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 629 · 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 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 169 (c) 91 (d) 25
  2. 2.Which term of the AP 12, 19, 26, 33, … is 61? (a) 10th (b) 8th (c) 9th (d) 7th
  3. 3.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 96 (b) 192 (c) 31 (d) 114
  4. 4.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 27 (c) 196 (d) 210
  5. 5.Which term of the AP 7, 9, 11, 13, … is 39? (a) 17th (b) 19th (c) 18th (d) 16th
  6. 6.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 100 (b) 198 (c) 15 (d) 99
  7. 7.What is the missing term in the AP 19, 24, 29, ?, 39? (a) 35 (b) 33 (c) 39 (d) 34
  8. 8.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 29 (b) 100 (c) 95 (d) 190
  9. 9.What is the 25th term of the AP 16, 24, 32, 40, …? (a) 216 (b) 200 (c) 208 (d) 192
  10. 10.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 162 (b) 26 (c) 324 (d) 171
  11. 11.Which term of the AP 5, 8, 11, 14, … is 98? (a) 33rd (b) 32nd (c) 31st (d) 34th
  12. 12.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 36 (c) 21 (d) 42
  13. 13.What is the 27th term of the AP 20, 27, 34, 41, …? (a) 209 (b) 182 (c) 189 (d) 202
  14. 14.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 115 (b) 25 (c) 224 (d) 112
  15. 15.What is the 18th term of the AP 18, 24, 30, 36, …? (a) 120 (b) 108 (c) 126 (d) 102
  16. 16.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 784 (c) 812 (d) 55
  17. 17.What is the 31st term of the AP 3, 8, 13, 18, …? (a) 158 (b) 150 (c) 153 (d) 155
  18. 18.What is the sum of the first 7 terms of the AP 6, 10, 14, …? (a) 126 (b) 140 (c) 252 (d) 30
  19. 19.What is the 35th term of the AP 7, 15, 23, 31, …? (a) 287 (b) 279 (c) 280 (d) 272
  20. 20.What is the 12th term of the AP 16, 23, 30, 37, …? (a) 77 (b) 100 (c) 84 (d) 93
  21. 21.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 66 (c) 21 (d) 132
  22. 22.Which term of the AP 4, 10, 16, 22, … is 88? (a) 17th (b) 16th (c) 15th (d) 14th
  23. 23.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 29 (b) 240 (c) 136 (d) 120
  24. 24.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 85 (b) 84 (c) 15 (d) 168
  25. 25.Which term of the AP 12, 17, 22, 27, … is 182? (a) 35th (b) 37th (c) 34th (d) 36th
  26. 26.What is the sum of all the whole numbers from 1 to 53? (a) 1432 (b) 2862 (c) 1431 (d) 1378
  27. 27.What is the 34th term of the AP 7, 13, 19, 25, …? (a) 205 (b) 198 (c) 211 (d) 204
  28. 28.What is the 12th term of the AP 11, 20, 29, 38, …? (a) 119 (b) 110 (c) 108 (d) 99
  29. 29.What is the sum of all the whole numbers from 1 to 59? (a) 1711 (b) 1770 (c) 1771 (d) 3540
  30. 30.What is the missing term in the AP 17, ?, 27, 32, 37? (a) 23 (b) 22 (c) 27 (d) 21
  31. 31.What is the missing term in the AP 19, ?, 37, 46, 55? (a) 37 (b) 28 (c) 27 (d) 29
  32. 32.What is the 10th term of the AP 14, 23, 32, 41, …? (a) 95 (b) 81 (c) 90 (d) 104
  33. 33.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 288 (b) 147 (c) 28 (d) 144
  34. 34.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 23 (d) 144
  35. 35.Which term of the AP 12, 16, 20, 24, … is 120? (a) 29th (b) 28th (c) 27th (d) 30th
  36. 36.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 75 (b) 15 (c) 150 (d) 78
  37. 37.What is the missing term in the AP 7, 10, 13, ?, 19? (a) 15 (b) 17 (c) 19 (d) 16
  38. 38.What is the missing term in the AP 12, ?, 22, 27, 32? (a) 17 (b) 18 (c) 16 (d) 22
  39. 39.What is the 35th term of the AP 13, 22, 31, 40, …? (a) 328 (b) 315 (c) 306 (d) 319
  40. 40.What is the 10th term of the AP 4, 6, 8, 10, …? (a) 22 (b) 24 (c) 20 (d) 18

Answer key

  1. 169
  2. 8th
  3. 96
  4. 196
  5. 17th
  6. 99
  7. 34
  8. 95
  9. 208
  10. 162
  11. 32nd
  12. 36
  13. 202
  14. 112
  15. 120
  16. 784
  17. 153
  18. 126
  19. 279
  20. 93
  21. 121
  22. 15th
  23. 120
  24. 84
  25. 35th
  26. 1431
  27. 205
  28. 110
  29. 1770
  30. 22
  31. 28
  32. 95
  33. 144
  34. 144
  35. 28th
  36. 75
  37. 16
  38. 17
  39. 319
  40. 22

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