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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 942 · 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 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 812 (d) 784
  2. 2.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 15 (b) 11 (c) 12 (d) 13
  3. 3.What is the missing term in the AP 16, 24, 32, ?, 48? (a) 48 (b) 40 (c) 39 (d) 41
  4. 4.What is the 20th term of the AP 15, 21, 27, 33, …? (a) 129 (b) 120 (c) 135 (d) 114
  5. 5.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 168 (b) 84 (c) 14 (d) 88
  6. 6.What is the 16th term of the AP 5, 11, 17, 23, …? (a) 101 (b) 96 (c) 90 (d) 95
  7. 7.Which term of the AP 20, 28, 36, 44, … is 332? (a) 41st (b) 40th (c) 39th (d) 42nd
  8. 8.What is the 21st term of the AP 3, 6, 9, 12, …? (a) 64 (b) 63 (c) 66 (d) 60
  9. 9.What is the 20th term of the AP 9, 16, 23, 30, …? (a) 142 (b) 149 (c) 140 (d) 133
  10. 10.What is the missing term in the AP 16, 25, 34, ?, 52? (a) 43 (b) 44 (c) 52 (d) 42
  11. 11.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 506 (c) 253 (d) 43
  12. 12.What is the missing term in the AP 18, ?, 22, 24, 26? (a) 21 (b) 19 (c) 22 (d) 20
  13. 13.What is the 26th term of the AP 13, 22, 31, 40, …? (a) 238 (b) 225 (c) 247 (d) 234
  14. 14.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 9 (c) 15 (d) 30
  15. 15.Which term of the AP 4, 8, 12, 16, … is 112? (a) 27th (b) 30th (c) 28th (d) 29th
  16. 16.What is the 13th term of the AP 5, 14, 23, 32, …? (a) 108 (b) 113 (c) 117 (d) 122
  17. 17.What is the missing term in the AP 12, 19, 26, ?, 40? (a) 33 (b) 40 (c) 32 (d) 34
  18. 18.What is the 10th term of the AP 17, 25, 33, 41, …? (a) 89 (b) 80 (c) 97 (d) 72
  19. 19.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1176 (c) 1152 (d) 1128
  20. 20.What is the 21st term of the AP 14, 17, 20, 23, …? (a) 74 (b) 60 (c) 77 (d) 63
  21. 21.What is the 39th term of the AP 8, 16, 24, 32, …? (a) 304 (b) 312 (c) 313 (d) 320
  22. 22.What is the 30th term of the AP 5, 14, 23, 32, …? (a) 261 (b) 275 (c) 266 (d) 270
  23. 23.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 19 (b) 192 (c) 104 (d) 96
  24. 24.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 14 (b) 102 (c) 204 (d) 108
  25. 25.What is the 32nd term of the AP 17, 24, 31, 38, …? (a) 224 (b) 234 (c) 241 (d) 217
  26. 26.What is the 23rd term of the AP 4, 11, 18, 25, …? (a) 158 (b) 161 (c) 154 (d) 165
  27. 27.What is the missing term in the AP 9, ?, 23, 30, 37? (a) 23 (b) 17 (c) 15 (d) 16
  28. 28.What is the sum of the first 6 terms of the AP 3, 4, 5, …? (a) 36 (b) 8 (c) 66 (d) 33
  29. 29.What is the 40th term of the AP 3, 9, 15, 21, …? (a) 240 (b) 243 (c) 234 (d) 237
  30. 30.What is the sum of the first 12 terms of the AP 5, 6, 7, …? (a) 126 (b) 16 (c) 132 (d) 252
  31. 31.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 32 (b) 204 (c) 120 (d) 102
  32. 32.Which term of the AP 4, 8, 12, 16, … is 92? (a) 23rd (b) 22nd (c) 25th (d) 24th
  33. 33.What is the 39th term of the AP 9, 13, 17, 21, …? (a) 156 (b) 165 (c) 152 (d) 161
  34. 34.What is the 22nd term of the AP 17, 25, 33, 41, …? (a) 193 (b) 176 (c) 185 (d) 168
  35. 35.What is the missing term in the AP 9, 12, 15, ?, 21? (a) 21 (b) 18 (c) 19 (d) 17
  36. 36.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 114 (b) 17 (c) 57 (d) 66
  37. 37.What is the sum of the first 9 terms of the AP 7, 9, 11, …? (a) 270 (b) 23 (c) 144 (d) 135
  38. 38.What is the 36th term of the AP 3, 11, 19, 27, …? (a) 291 (b) 283 (c) 280 (d) 288
  39. 39.What is the missing term in the AP 4, 11, ?, 25, 32? (a) 17 (b) 19 (c) 25 (d) 18
  40. 40.What is the missing term in the AP 9, ?, 19, 24, 29? (a) 13 (b) 15 (c) 19 (d) 14

Answer key

  1. 784
  2. 12
  3. 40
  4. 129
  5. 84
  6. 95
  7. 40th
  8. 63
  9. 142
  10. 43
  11. 484
  12. 20
  13. 238
  14. 25
  15. 28th
  16. 113
  17. 33
  18. 89
  19. 1176
  20. 74
  21. 312
  22. 266
  23. 96
  24. 102
  25. 234
  26. 158
  27. 16
  28. 33
  29. 237
  30. 126
  31. 102
  32. 23rd
  33. 161
  34. 185
  35. 18
  36. 57
  37. 135
  38. 283
  39. 18
  40. 14

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