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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 756 · 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, 8, 11, …? (a) 276 (b) 516 (c) 38 (d) 258
  2. 2.What is the 16th term of the AP 17, 23, 29, 35, …? (a) 90 (b) 113 (c) 96 (d) 107
  3. 3.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 96 (b) 114 (c) 192 (d) 31
  4. 4.What is the 11th term of the AP 4, 6, 8, 10, …? (a) 24 (b) 20 (c) 26 (d) 22
  5. 5.What is the sum of the first 11 terms of the AP 4, 8, 12, …? (a) 528 (b) 286 (c) 264 (d) 44
  6. 6.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 119 (b) 22 (c) 112 (d) 224
  7. 7.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 31 (c) 256 (d) 136
  8. 8.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 429 (b) 69 (c) 462 (d) 858
  9. 9.What is the sum of all the whole numbers from 1 to 13? (a) 92 (b) 182 (c) 78 (d) 91
  10. 10.What is the 12th term of the AP 16, 25, 34, 43, …? (a) 99 (b) 108 (c) 115 (d) 124
  11. 11.What is the 11th term of the AP 8, 12, 16, 20, …? (a) 40 (b) 44 (c) 48 (d) 52
  12. 12.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 3081 (c) 6162 (d) 3003
  13. 13.Which term of the AP 16, 18, 20, 22, … is 92? (a) 38th (b) 46th (c) 40th (d) 39th
  14. 14.What is the 11th term of the AP 5, 9, 13, 17, …? (a) 49 (b) 45 (c) 40 (d) 44
  15. 15.What is the sum of all the whole numbers from 1 to 93? (a) 4278 (b) 8742 (c) 4371 (d) 4372
  16. 16.What is the 11th term of the AP 3, 5, 7, 9, …? (a) 20 (b) 25 (c) 22 (d) 23
  17. 17.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 67 (b) 11 (c) 132 (d) 66
  18. 18.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 11 (b) 17 (c) 12 (d) 13
  19. 19.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 19 (b) 200 (c) 100 (d) 110
  20. 20.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5050 (c) 5000 (d) 10100
  21. 21.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
  22. 22.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 380 (c) 190 (d) 361
  23. 23.What is the sum of the first 6 terms of the AP 8, 11, 14, …? (a) 186 (b) 102 (c) 23 (d) 93
  24. 24.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 231 (c) 210 (d) 462
  25. 25.What is the sum of the first 9 terms of the AP 4, 10, 16, …? (a) 504 (b) 279 (c) 52 (d) 252
  26. 26.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 456 (b) 240 (c) 30 (d) 228
  27. 27.What is the sum of the first 8 terms of the AP 10, 15, 20, …? (a) 45 (b) 220 (c) 440 (d) 240
  28. 28.What is the sum of the first 7 terms of the AP 4, 10, 16, …? (a) 154 (b) 308 (c) 40 (d) 175
  29. 29.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 105 (b) 30 (c) 200 (d) 100
  30. 30.What is the sum of the first 9 terms of the AP 1, 6, 11, …? (a) 194 (b) 41 (c) 189 (d) 378
  31. 31.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 15 (b) 110 (c) 60 (d) 55
  32. 32.What is the missing term in the AP 13, 16, ?, 22, 25? (a) 22 (b) 20 (c) 18 (d) 19
  33. 33.What is the 19th term of the AP 17, 20, 23, 26, …? (a) 57 (b) 71 (c) 54 (d) 74
  34. 34.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 2450 (c) 1226 (d) 1225
  35. 35.What is the 22nd term of the AP 18, 21, 24, 27, …? (a) 63 (b) 84 (c) 66 (d) 81
  36. 36.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 784 (c) 55 (d) 812
  37. 37.What is the missing term in the AP 9, 11, 13, ?, 17? (a) 17 (b) 14 (c) 16 (d) 15
  38. 38.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 21 (b) 210 (c) 105 (d) 112
  39. 39.Which term of the AP 5, 9, 13, 17, … is 93? (a) 24th (b) 23rd (c) 22nd (d) 25th
  40. 40.What is the sum of all the whole numbers from 1 to 81? (a) 3322 (b) 3240 (c) 6642 (d) 3321

Answer key

  1. 258
  2. 107
  3. 96
  4. 24
  5. 264
  6. 112
  7. 256
  8. 429
  9. 91
  10. 115
  11. 48
  12. 3081
  13. 39th
  14. 45
  15. 4371
  16. 23
  17. 66
  18. 12
  19. 100
  20. 5050
  21. 25
  22. 361
  23. 93
  24. 231
  25. 252
  26. 228
  27. 220
  28. 154
  29. 100
  30. 189
  31. 55
  32. 19
  33. 71
  34. 1225
  35. 81
  36. 784
  37. 15
  38. 105
  39. 23rd
  40. 3321

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