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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 907 · 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 7 terms of the AP 4, 7, 10, …? (a) 182 (b) 91 (c) 22 (d) 94
  2. 2.What is the sum of the first 8 terms of the AP 8, 14, 20, …? (a) 464 (b) 50 (c) 256 (d) 232
  3. 3.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 406 (d) 784
  4. 4.What is the 13th term of the AP 5, 7, 9, 11, …? (a) 26 (b) 24 (c) 29 (d) 31
  5. 5.What is the 13th term of the AP 4, 8, 12, 16, …? (a) 48 (b) 52 (c) 56 (d) 53
  6. 6.What is the 40th term of the AP 14, 22, 30, 38, …? (a) 334 (b) 320 (c) 326 (d) 312
  7. 7.What is the sum of all the whole numbers from 1 to 51? (a) 1327 (b) 1275 (c) 1326 (d) 2652
  8. 8.What is the 13th term of the AP 16, 25, 34, 43, …? (a) 133 (b) 117 (c) 108 (d) 124
  9. 9.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 204 (b) 102 (c) 108 (d) 14
  10. 10.What is the 15th term of the AP 2, 9, 16, 23, …? (a) 100 (b) 98 (c) 105 (d) 107
  11. 11.What is the 24th term of the AP 1, 8, 15, 22, …? (a) 168 (b) 169 (c) 161 (d) 162
  12. 12.What is the missing term in the AP 12, ?, 24, 30, 36? (a) 18 (b) 17 (c) 19 (d) 24
  13. 13.What is the 10th term of the AP 16, 25, 34, 43, …? (a) 90 (b) 97 (c) 106 (d) 81
  14. 14.What is the 16th term of the AP 6, 9, 12, 15, …? (a) 45 (b) 48 (c) 51 (d) 54
  15. 15.What is the 38th term of the AP 6, 10, 14, 18, …? (a) 158 (b) 148 (c) 152 (d) 154
  16. 16.What is the 37th term of the AP 1, 7, 13, 19, …? (a) 222 (b) 217 (c) 223 (d) 216
  17. 17.What is the 36th term of the AP 2, 4, 6, 8, …? (a) 74 (b) 72 (c) 73 (d) 70
  18. 18.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 420 (c) 39 (d) 210
  19. 19.What is the 19th term of the AP 17, 26, 35, 44, …? (a) 179 (b) 162 (c) 188 (d) 171
  20. 20.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 49 (c) 13 (d) 56
  21. 21.What is the sum of the first 9 terms of the AP 1, 5, 9, …? (a) 306 (b) 171 (c) 153 (d) 33
  22. 22.What is the 17th term of the AP 8, 11, 14, 17, …? (a) 51 (b) 59 (c) 48 (d) 56
  23. 23.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 14 (b) 180 (c) 91 (d) 90
  24. 24.What is the 17th term of the AP 15, 17, 19, 21, …? (a) 49 (b) 34 (c) 32 (d) 47
  25. 25.What is the 17th term of the AP 11, 13, 15, 17, …? (a) 32 (b) 43 (c) 45 (d) 34
  26. 26.What is the 14th term of the AP 10, 14, 18, 22, …? (a) 62 (b) 52 (c) 56 (d) 66
  27. 27.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
  28. 28.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 132 (c) 66 (d) 21
  29. 29.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 110 (b) 17 (c) 55 (d) 58
  30. 30.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 144 (c) 78 (d) 156
  31. 31.What is the 35th term of the AP 5, 14, 23, 32, …? (a) 320 (b) 306 (c) 311 (d) 315
  32. 32.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 470 (b) 235 (c) 46 (d) 260
  33. 33.What is the sum of all the whole numbers from 1 to 45? (a) 1035 (b) 2070 (c) 990 (d) 1036
  34. 34.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 196 (c) 27 (d) 210
  35. 35.Which term of the AP 1, 3, 5, 7, … is 19? (a) 10th (b) 9th (c) 12th (d) 11th
  36. 36.What is the 40th term of the AP 17, 23, 29, 35, …? (a) 251 (b) 257 (c) 234 (d) 240
  37. 37.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 45 (d) 90
  38. 38.What is the missing term in the AP 2, 6, 10, ?, 18? (a) 18 (b) 14 (c) 15 (d) 13
  39. 39.Which term of the AP 4, 9, 14, 19, … is 159? (a) 31st (b) 33rd (c) 34th (d) 32nd
  40. 40.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 340 (b) 180 (c) 26 (d) 170

Answer key

  1. 91
  2. 232
  3. 784
  4. 29
  5. 52
  6. 326
  7. 1326
  8. 124
  9. 102
  10. 100
  11. 162
  12. 18
  13. 97
  14. 51
  15. 154
  16. 217
  17. 72
  18. 400
  19. 179
  20. 49
  21. 153
  22. 56
  23. 90
  24. 47
  25. 43
  26. 62
  27. 25
  28. 121
  29. 55
  30. 144
  31. 311
  32. 235
  33. 1035
  34. 196
  35. 10th
  36. 251
  37. 81
  38. 14
  39. 32nd
  40. 170

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