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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 898 · 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.Which term of the AP 4, 12, 20, 28, … is 292? (a) 38th (b) 36th (c) 39th (d) 37th
  2. 2.What is the 16th term of the AP 20, 29, 38, 47, …? (a) 164 (b) 135 (c) 155 (d) 144
  3. 3.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 242 (b) 121 (c) 16 (d) 122
  4. 4.What is the 14th term of the AP 11, 16, 21, 26, …? (a) 65 (b) 70 (c) 76 (d) 81
  5. 5.What is the sum of all the whole numbers from 1 to 77? (a) 6006 (b) 3004 (c) 3003 (d) 2926
  6. 6.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 21 (b) 42 (c) 6 (d) 24
  7. 7.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 108 (b) 24 (c) 120 (d) 216
  8. 8.What is the missing term in the AP 12, ?, 16, 18, 20? (a) 15 (b) 16 (c) 14 (d) 13
  9. 9.What is the 18th term of the AP 3, 10, 17, 24, …? (a) 129 (b) 122 (c) 126 (d) 119
  10. 10.What is the 26th term of the AP 10, 18, 26, 34, …? (a) 218 (b) 200 (c) 208 (d) 210
  11. 11.What is the missing term in the AP 4, ?, 8, 10, 12? (a) 6 (b) 8 (c) 7 (d) 5
  12. 12.What is the 28th term of the AP 7, 12, 17, 22, …? (a) 140 (b) 135 (c) 142 (d) 147
  13. 13.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 160 (b) 29 (c) 148 (d) 296
  14. 14.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 55 (d) 100
  15. 15.What is the 16th term of the AP 1, 10, 19, 28, …? (a) 135 (b) 144 (c) 136 (d) 145
  16. 16.What is the 30th term of the AP 12, 19, 26, 33, …? (a) 203 (b) 215 (c) 222 (d) 210
  17. 17.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 90 (b) 11 (c) 46 (d) 45
  18. 18.What is the 10th term of the AP 1, 8, 15, 22, …? (a) 71 (b) 64 (c) 70 (d) 63
  19. 19.What is the 25th term of the AP 1, 4, 7, 10, …? (a) 72 (b) 75 (c) 73 (d) 76
  20. 20.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 324 (d) 342
  21. 21.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 92 (c) 91 (d) 78
  22. 22.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 126 (b) 63 (c) 64 (d) 11
  23. 23.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 80 (b) 88 (c) 160 (d) 17
  24. 24.What is the missing term in the AP 6, ?, 12, 15, 18? (a) 9 (b) 8 (c) 12 (d) 10
  25. 25.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 13 (b) 96 (c) 90 (d) 180
  26. 26.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 63 (b) 396 (c) 726 (d) 363
  27. 27.What is the 38th term of the AP 7, 11, 15, 19, …? (a) 148 (b) 159 (c) 155 (d) 152
  28. 28.What is the 39th term of the AP 11, 16, 21, 26, …? (a) 195 (b) 206 (c) 190 (d) 201
  29. 29.What is the 16th term of the AP 3, 11, 19, 27, …? (a) 120 (b) 131 (c) 123 (d) 128
  30. 30.What is the 27th term of the AP 6, 14, 22, 30, …? (a) 216 (b) 222 (c) 208 (d) 214
  31. 31.What is the sum of all the whole numbers from 1 to 96? (a) 9312 (b) 4608 (c) 4656 (d) 4560
  32. 32.Which term of the AP 16, 20, 24, 28, … is 92? (a) 19th (b) 20th (c) 21st (d) 23rd
  33. 33.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 66 (c) 156 (d) 78
  34. 34.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 30 (c) 9 (d) 15
  35. 35.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 182 (c) 91 (d) 169
  36. 36.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 43 (c) 506 (d) 253
  37. 37.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 28 (c) 13 (d) 49
  38. 38.What is the missing term in the AP 11, 20, 29, ?, 47? (a) 37 (b) 47 (c) 38 (d) 39
  39. 39.What is the 29th term of the AP 7, 16, 25, 34, …? (a) 261 (b) 268 (c) 252 (d) 259
  40. 40.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 325 (c) 338 (d) 702

Answer key

  1. 37th
  2. 155
  3. 121
  4. 76
  5. 3003
  6. 21
  7. 108
  8. 14
  9. 122
  10. 210
  11. 6
  12. 142
  13. 148
  14. 100
  15. 136
  16. 215
  17. 45
  18. 64
  19. 73
  20. 324
  21. 91
  22. 63
  23. 80
  24. 9
  25. 90
  26. 363
  27. 155
  28. 201
  29. 123
  30. 214
  31. 4656
  32. 20th
  33. 78
  34. 25
  35. 169
  36. 484
  37. 49
  38. 38
  39. 259
  40. 351

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