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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 911 · 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 all the whole numbers from 1 to 78? (a) 3003 (b) 3081 (c) 3042 (d) 6162
  2. 2.What is the 38th term of the AP 5, 7, 9, 11, …? (a) 74 (b) 76 (c) 81 (d) 79
  3. 3.What is the sum of all the whole numbers from 1 to 83? (a) 3403 (b) 6972 (c) 3486 (d) 3487
  4. 4.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 784 (c) 812 (d) 406
  5. 5.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 216 (b) 221 (c) 432 (d) 44
  6. 6.What is the 36th term of the AP 5, 14, 23, 32, …? (a) 315 (b) 324 (c) 329 (d) 320
  7. 7.What is the 29th term of the AP 6, 10, 14, 18, …? (a) 116 (b) 112 (c) 122 (d) 118
  8. 8.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 25 (c) 91 (d) 169
  9. 9.What is the missing term in the AP 4, 12, ?, 28, 36? (a) 21 (b) 28 (c) 20 (d) 19
  10. 10.What is the missing term in the AP 3, 10, ?, 24, 31? (a) 16 (b) 18 (c) 17 (d) 24
  11. 11.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 286 (b) 154 (c) 143 (d) 23
  12. 12.What is the sum of the first 9 terms of the AP 4, 6, 8, …? (a) 216 (b) 117 (c) 108 (d) 20
  13. 13.What is the 37th term of the AP 20, 22, 24, 26, …? (a) 74 (b) 72 (c) 92 (d) 94
  14. 14.What is the missing term in the AP 15, ?, 23, 27, 31? (a) 19 (b) 23 (c) 20 (d) 18
  15. 15.What is the sum of the first 10 terms of the AP 10, 13, 16, …? (a) 235 (b) 470 (c) 250 (d) 37
  16. 16.Which term of the AP 5, 11, 17, 23, … is 155? (a) 27th (b) 26th (c) 28th (d) 25th
  17. 17.What is the 19th term of the AP 16, 18, 20, 22, …? (a) 52 (b) 54 (c) 38 (d) 36
  18. 18.Which term of the AP 3, 10, 17, 24, … is 80? (a) 13th (b) 11th (c) 12th (d) 14th
  19. 19.What is the 23rd term of the AP 16, 18, 20, 22, …? (a) 44 (b) 60 (c) 46 (d) 62
  20. 20.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 456 (b) 228 (c) 240 (d) 30
  21. 21.What is the sum of the first 10 terms of the AP 8, 14, 20, …? (a) 62 (b) 350 (c) 380 (d) 700
  22. 22.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 60 (b) 55 (c) 110 (d) 10
  23. 23.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 96 (b) 108 (c) 192 (d) 26
  24. 24.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 234 (b) 118 (c) 117 (d) 17
  25. 25.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 96 (b) 192 (c) 104 (d) 19
  26. 26.What is the missing term in the AP 5, ?, 11, 14, 17? (a) 8 (b) 11 (c) 7 (d) 9
  27. 27.What is the 11th term of the AP 8, 11, 14, 17, …? (a) 30 (b) 33 (c) 38 (d) 41
  28. 28.What is the missing term in the AP 6, 8, ?, 12, 14? (a) 9 (b) 10 (c) 12 (d) 11
  29. 29.What is the missing term in the AP 1, 7, 13, ?, 25? (a) 19 (b) 25 (c) 20 (d) 18
  30. 30.Which term of the AP 13, 15, 17, 19, … is 55? (a) 21st (b) 22nd (c) 24th (d) 23rd
  31. 31.What is the 10th term of the AP 2, 4, 6, 8, …? (a) 21 (b) 22 (c) 18 (d) 20
  32. 32.What is the 34th term of the AP 9, 15, 21, 27, …? (a) 198 (b) 213 (c) 204 (d) 207
  33. 33.What is the 24th term of the AP 17, 23, 29, 35, …? (a) 138 (b) 144 (c) 155 (d) 161
  34. 34.Which term of the AP 10, 12, 14, 16, … is 42? (a) 16th (b) 18th (c) 21st (d) 17th
  35. 35.What is the 30th term of the AP 16, 19, 22, 25, …? (a) 103 (b) 90 (c) 106 (d) 87
  36. 36.What is the sum of the first 12 terms of the AP 6, 10, 14, …? (a) 50 (b) 336 (c) 360 (d) 672
  37. 37.What is the 11th term of the AP 11, 20, 29, 38, …? (a) 99 (b) 101 (c) 90 (d) 110
  38. 38.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 128 (b) 23 (c) 136 (d) 256
  39. 39.Which term of the AP 10, 18, 26, 34, … is 82? (a) 11th (b) 10th (c) 12th (d) 9th
  40. 40.What is the 23rd term of the AP 8, 15, 22, 29, …? (a) 161 (b) 169 (c) 154 (d) 162

Answer key

  1. 3081
  2. 79
  3. 3486
  4. 784
  5. 216
  6. 320
  7. 118
  8. 169
  9. 20
  10. 17
  11. 143
  12. 108
  13. 92
  14. 19
  15. 235
  16. 26th
  17. 52
  18. 12th
  19. 60
  20. 228
  21. 350
  22. 55
  23. 96
  24. 117
  25. 96
  26. 8
  27. 38
  28. 10
  29. 19
  30. 22nd
  31. 20
  32. 207
  33. 155
  34. 17th
  35. 103
  36. 336
  37. 101
  38. 128
  39. 10th
  40. 162

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