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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 391 · 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 22nd term of the AP 4, 6, 8, 10, …? (a) 46 (b) 42 (c) 44 (d) 48
  2. 2.Which term of the AP 2, 4, 6, 8, … is 18? (a) 8th (b) 11th (c) 9th (d) 10th
  3. 3.Which term of the AP 20, 25, 30, 35, … is 125? (a) 21st (b) 25th (c) 23rd (d) 22nd
  4. 4.What is the sum of the first 9 terms of the AP 8, 12, 16, …? (a) 216 (b) 40 (c) 432 (d) 234
  5. 5.What is the 11th term of the AP 2, 5, 8, 11, …? (a) 35 (b) 30 (c) 32 (d) 33
  6. 6.What is the 36th term of the AP 19, 24, 29, 34, …? (a) 175 (b) 194 (c) 180 (d) 199
  7. 7.What is the missing term in the AP 6, 10, ?, 18, 22? (a) 13 (b) 18 (c) 15 (d) 14
  8. 8.What is the sum of the first 11 terms of the AP 8, 14, 20, …? (a) 418 (b) 68 (c) 451 (d) 836
  9. 9.What is the sum of all the whole numbers from 1 to 88? (a) 7832 (b) 3872 (c) 3916 (d) 3828
  10. 10.What is the 34th term of the AP 6, 13, 20, 27, …? (a) 231 (b) 244 (c) 238 (d) 237
  11. 11.What is the missing term in the AP 19, 25, ?, 37, 43? (a) 37 (b) 30 (c) 32 (d) 31
  12. 12.What is the 17th term of the AP 14, 17, 20, 23, …? (a) 51 (b) 62 (c) 48 (d) 65
  13. 13.What is the missing term in the AP 20, ?, 28, 32, 36? (a) 25 (b) 28 (c) 24 (d) 23
  14. 14.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 40 (b) 20 (c) 21 (d) 6
  15. 15.What is the 31st term of the AP 14, 17, 20, 23, …? (a) 93 (b) 90 (c) 107 (d) 104
  16. 16.What is the missing term in the AP 19, ?, 27, 31, 35? (a) 23 (b) 27 (c) 22 (d) 24
  17. 17.What is the 38th term of the AP 9, 15, 21, 27, …? (a) 222 (b) 237 (c) 228 (d) 231
  18. 18.What is the missing term in the AP 6, 12, 18, ?, 30? (a) 30 (b) 23 (c) 24 (d) 25
  19. 19.Which term of the AP 3, 6, 9, 12, … is 54? (a) 17th (b) 20th (c) 19th (d) 18th
  20. 20.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 70 (b) 13 (c) 38 (d) 35
  21. 21.What is the missing term in the AP 2, 9, ?, 23, 30? (a) 15 (b) 16 (c) 17 (d) 23
  22. 22.What is the 11th term of the AP 5, 10, 15, 20, …? (a) 56 (b) 60 (c) 50 (d) 55
  23. 23.What is the 18th term of the AP 17, 26, 35, 44, …? (a) 179 (b) 162 (c) 170 (d) 153
  24. 24.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 21 (b) 65 (c) 130 (d) 75
  25. 25.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 120 (b) 240 (c) 130 (d) 21
  26. 26.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 70 (b) 17 (c) 130 (d) 65
  27. 27.Which term of the AP 16, 22, 28, 34, … is 184? (a) 30th (b) 28th (c) 29th (d) 31st
  28. 28.What is the 20th term of the AP 5, 10, 15, 20, …? (a) 95 (b) 100 (c) 101 (d) 105
  29. 29.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 104 (b) 184 (c) 22 (d) 92
  30. 30.What is the missing term in the AP 14, 19, ?, 29, 34? (a) 25 (b) 29 (c) 24 (d) 23
  31. 31.What is the sum of all the whole numbers from 1 to 100? (a) 10100 (b) 4950 (c) 5050 (d) 5000
  32. 32.What is the sum of the first 7 terms of the AP 7, 12, 17, …? (a) 37 (b) 159 (c) 154 (d) 308
  33. 33.Which term of the AP 13, 19, 25, 31, … is 229? (a) 38th (b) 36th (c) 37th (d) 39th
  34. 34.Which term of the AP 15, 20, 25, 30, … is 210? (a) 41st (b) 42nd (c) 39th (d) 40th
  35. 35.What is the missing term in the AP 2, ?, 14, 20, 26? (a) 7 (b) 8 (c) 9 (d) 14
  36. 36.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2312 (c) 2278 (d) 2346
  37. 37.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 201 (b) 198 (c) 34 (d) 396
  38. 38.What is the 33rd term of the AP 14, 21, 28, 35, …? (a) 245 (b) 224 (c) 231 (d) 238
  39. 39.What is the missing term in the AP 1, ?, 9, 13, 17? (a) 5 (b) 4 (c) 6 (d) 9
  40. 40.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 462 (c) 231 (d) 41

Answer key

  1. 46
  2. 9th
  3. 22nd
  4. 216
  5. 32
  6. 194
  7. 14
  8. 418
  9. 3916
  10. 237
  11. 31
  12. 62
  13. 24
  14. 20
  15. 104
  16. 23
  17. 231
  18. 24
  19. 18th
  20. 35
  21. 16
  22. 55
  23. 170
  24. 65
  25. 120
  26. 65
  27. 29th
  28. 100
  29. 92
  30. 24
  31. 5050
  32. 154
  33. 37th
  34. 40th
  35. 8
  36. 2346
  37. 198
  38. 238
  39. 5
  40. 441

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