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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 8 · 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 missing term in the AP 20, 25, ?, 35, 40? (a) 29 (b) 31 (c) 35 (d) 30
  2. 2.What is the 34th term of the AP 15, 23, 31, 39, …? (a) 287 (b) 272 (c) 279 (d) 264
  3. 3.Which term of the AP 2, 5, 8, 11, … is 29? (a) 9th (b) 11th (c) 10th (d) 12th
  4. 4.What is the 29th term of the AP 1, 9, 17, 25, …? (a) 232 (b) 225 (c) 224 (d) 233
  5. 5.What is the 34th term of the AP 2, 5, 8, 11, …? (a) 104 (b) 102 (c) 99 (d) 101
  6. 6.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 78 (b) 19 (c) 69 (d) 138
  7. 7.What is the 26th term of the AP 16, 22, 28, 34, …? (a) 172 (b) 150 (c) 166 (d) 156
  8. 8.What is the sum of all the whole numbers from 1 to 61? (a) 1891 (b) 1830 (c) 1892 (d) 3782
  9. 9.What is the 20th term of the AP 7, 15, 23, 31, …? (a) 160 (b) 159 (c) 167 (d) 152
  10. 10.Which term of the AP 19, 23, 27, 31, … is 175? (a) 39th (b) 40th (c) 42nd (d) 41st
  11. 11.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 13 (b) 14 (c) 16 (d) 12
  12. 12.What is the missing term in the AP 2, 8, 14, ?, 26? (a) 26 (b) 21 (c) 19 (d) 20
  13. 13.What is the 32nd term of the AP 18, 21, 24, 27, …? (a) 111 (b) 93 (c) 96 (d) 114
  14. 14.What is the 11th term of the AP 1, 10, 19, 28, …? (a) 91 (b) 90 (c) 100 (d) 99
  15. 15.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 100 (b) 198 (c) 99 (d) 15
  16. 16.Which term of the AP 17, 25, 33, 41, … is 137? (a) 17th (b) 18th (c) 15th (d) 16th
  17. 17.Which term of the AP 1, 10, 19, 28, … is 145? (a) 17th (b) 19th (c) 18th (d) 16th
  18. 18.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 16 (b) 109 (c) 216 (d) 108
  19. 19.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 300 (b) 150 (c) 160 (d) 24
  20. 20.Which term of the AP 2, 5, 8, 11, … is 41? (a) 15th (b) 13th (c) 16th (d) 14th
  21. 21.What is the 14th term of the AP 17, 24, 31, 38, …? (a) 91 (b) 108 (c) 115 (d) 98
  22. 22.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5000 (c) 10100 (d) 5050
  23. 23.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 15 (c) 9 (d) 25
  24. 24.What is the sum of the first 11 terms of the AP 7, 11, 15, …? (a) 594 (b) 319 (c) 47 (d) 297
  25. 25.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 414 (b) 62 (c) 828 (d) 444
  26. 26.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 78 (c) 91 (d) 92
  27. 27.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 26 (b) 85 (c) 160 (d) 80
  28. 28.What is the 22nd term of the AP 20, 23, 26, 29, …? (a) 86 (b) 63 (c) 66 (d) 83
  29. 29.What is the sum of the first 10 terms of the AP 3, 7, 11, …? (a) 39 (b) 420 (c) 210 (d) 230
  30. 30.What is the 18th term of the AP 19, 25, 31, 37, …? (a) 108 (b) 121 (c) 127 (d) 102
  31. 31.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 378 (c) 406 (d) 812
  32. 32.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 253 (c) 277 (d) 276
  33. 33.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 75 (b) 140 (c) 70 (d) 24
  34. 34.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 378 (c) 379 (d) 756
  35. 35.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 120 (c) 29 (d) 240
  36. 36.What is the 19th term of the AP 2, 7, 12, 17, …? (a) 97 (b) 95 (c) 92 (d) 90
  37. 37.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 156 (b) 90 (c) 78 (d) 23
  38. 38.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 4160 (c) 2016 (d) 2080
  39. 39.What is the missing term in the AP 10, 19, 28, ?, 46? (a) 38 (b) 36 (c) 46 (d) 37
  40. 40.What is the sum of all the whole numbers from 1 to 84? (a) 3486 (b) 3528 (c) 7140 (d) 3570

Answer key

  1. 30
  2. 279
  3. 10th
  4. 225
  5. 101
  6. 69
  7. 166
  8. 1891
  9. 159
  10. 40th
  11. 13
  12. 20
  13. 111
  14. 91
  15. 99
  16. 16th
  17. 17th
  18. 108
  19. 150
  20. 14th
  21. 108
  22. 5050
  23. 25
  24. 297
  25. 414
  26. 91
  27. 80
  28. 83
  29. 210
  30. 121
  31. 406
  32. 276
  33. 70
  34. 378
  35. 225
  36. 92
  37. 78
  38. 2080
  39. 37
  40. 3570

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