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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 935 · 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 12 terms of the AP 5, 6, 7, …? (a) 132 (b) 252 (c) 16 (d) 126
  2. 2.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 256 (b) 38 (c) 506 (d) 253
  3. 3.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 115 (b) 200 (c) 32 (d) 100
  4. 4.What is the sum of all the whole numbers from 1 to 19? (a) 190 (b) 380 (c) 171 (d) 191
  5. 5.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 105 (d) 210
  6. 6.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 43 (c) 506 (d) 253
  7. 7.What is the 26th term of the AP 9, 16, 23, 30, …? (a) 182 (b) 184 (c) 175 (d) 191
  8. 8.What is the 14th term of the AP 19, 28, 37, 46, …? (a) 126 (b) 117 (c) 136 (d) 145
  9. 9.What is the 27th term of the AP 14, 16, 18, 20, …? (a) 52 (b) 66 (c) 68 (d) 54
  10. 10.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 600 (d) 576
  11. 11.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 576 (b) 46 (c) 312 (d) 288
  12. 12.Which term of the AP 4, 11, 18, 25, … is 270? (a) 40th (b) 39th (c) 41st (d) 38th
  13. 13.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 81 (d) 45
  14. 14.What is the missing term in the AP 5, 11, ?, 23, 29? (a) 16 (b) 18 (c) 17 (d) 23
  15. 15.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 11 (b) 65 (c) 70 (d) 130
  16. 16.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 378 (b) 189 (c) 41 (d) 194
  17. 17.What is the sum of all the whole numbers from 1 to 67? (a) 4556 (b) 2279 (c) 2278 (d) 2211
  18. 18.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 108 (b) 216 (c) 24 (d) 120
  19. 19.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 420 (b) 230 (c) 39 (d) 210
  20. 20.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 23 (b) 256 (c) 136 (d) 128
  21. 21.What is the missing term in the AP 19, 23, 27, ?, 35? (a) 31 (b) 32 (c) 30 (d) 35
  22. 22.What is the 11th term of the AP 19, 26, 33, 40, …? (a) 77 (b) 96 (c) 89 (d) 70
  23. 23.What is the 39th term of the AP 4, 10, 16, 22, …? (a) 232 (b) 238 (c) 228 (d) 234
  24. 24.Which term of the AP 7, 11, 15, 19, … is 135? (a) 32nd (b) 34th (c) 35th (d) 33rd
  25. 25.What is the 18th term of the AP 17, 21, 25, 29, …? (a) 72 (b) 89 (c) 85 (d) 68
  26. 26.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 156 (c) 78 (d) 66
  27. 27.What is the 17th term of the AP 18, 27, 36, 45, …? (a) 162 (b) 144 (c) 153 (d) 171
  28. 28.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 200 (b) 43 (c) 176 (d) 352
  29. 29.Which term of the AP 17, 25, 33, 41, … is 257? (a) 31st (b) 32nd (c) 30th (d) 33rd
  30. 30.What is the sum of all the whole numbers from 1 to 86? (a) 7482 (b) 3655 (c) 3698 (d) 3741
  31. 31.What is the sum of the first 7 terms of the AP 5, 8, 11, …? (a) 23 (b) 101 (c) 196 (d) 98
  32. 32.What is the 24th term of the AP 12, 14, 16, 18, …? (a) 46 (b) 60 (c) 58 (d) 48
  33. 33.What is the 26th term of the AP 4, 13, 22, 31, …? (a) 229 (b) 238 (c) 234 (d) 225
  34. 34.What is the 40th term of the AP 7, 13, 19, 25, …? (a) 240 (b) 234 (c) 241 (d) 247
  35. 35.What is the missing term in the AP 20, 28, ?, 44, 52? (a) 44 (b) 37 (c) 36 (d) 35
  36. 36.What is the sum of all the whole numbers from 1 to 47? (a) 1081 (b) 1128 (c) 1129 (d) 2256
  37. 37.What is the sum of all the whole numbers from 1 to 81? (a) 3322 (b) 6642 (c) 3240 (d) 3321
  38. 38.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 166 (b) 161 (c) 38 (d) 322
  39. 39.What is the missing term in the AP 15, 24, ?, 42, 51? (a) 34 (b) 32 (c) 42 (d) 33
  40. 40.Which term of the AP 13, 21, 29, 37, … is 245? (a) 32nd (b) 30th (c) 29th (d) 31st

Answer key

  1. 126
  2. 253
  3. 100
  4. 190
  5. 196
  6. 484
  7. 184
  8. 136
  9. 66
  10. 576
  11. 288
  12. 39th
  13. 81
  14. 17
  15. 65
  16. 189
  17. 2278
  18. 108
  19. 210
  20. 128
  21. 31
  22. 89
  23. 232
  24. 33rd
  25. 85
  26. 78
  27. 162
  28. 176
  29. 31st
  30. 3741
  31. 98
  32. 58
  33. 229
  34. 241
  35. 36
  36. 1128
  37. 3321
  38. 161
  39. 33
  40. 30th

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