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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 264 · 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 67? (a) 2279 (b) 2278 (c) 2211 (d) 4556
  2. 2.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 266 (b) 154 (c) 133 (d) 37
  3. 3.Which term of the AP 19, 22, 25, 28, … is 79? (a) 23rd (b) 20th (c) 21st (d) 22nd
  4. 4.What is the sum of all the whole numbers from 1 to 79? (a) 3081 (b) 3160 (c) 6320 (d) 3161
  5. 5.What is the sum of the first 9 terms of the AP 10, 13, 16, …? (a) 198 (b) 396 (c) 201 (d) 34
  6. 6.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 30 (b) 50 (c) 25 (d) 9
  7. 7.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 11 (c) 36 (d) 42
  8. 8.What is the 13th term of the AP 10, 14, 18, 22, …? (a) 52 (b) 62 (c) 58 (d) 48
  9. 9.What is the 21st term of the AP 13, 15, 17, 19, …? (a) 40 (b) 42 (c) 53 (d) 55
  10. 10.Which term of the AP 10, 15, 20, 25, … is 115? (a) 22nd (b) 21st (c) 24th (d) 23rd
  11. 11.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 11 (b) 64 (c) 60 (d) 120
  12. 12.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 153 (c) 154 (d) 136
  13. 13.What is the sum of all the whole numbers from 1 to 26? (a) 338 (b) 351 (c) 325 (d) 702
  14. 14.What is the sum of all the whole numbers from 1 to 42? (a) 861 (b) 1806 (c) 882 (d) 903
  15. 15.What is the 30th term of the AP 1, 7, 13, 19, …? (a) 180 (b) 175 (c) 181 (d) 174
  16. 16.What is the sum of all the whole numbers from 1 to 34? (a) 578 (b) 595 (c) 561 (d) 1190
  17. 17.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 456 (b) 68 (c) 840 (d) 420
  18. 18.Which term of the AP 2, 4, 6, 8, … is 32? (a) 18th (b) 16th (c) 15th (d) 17th
  19. 19.What is the sum of all the whole numbers from 1 to 13? (a) 92 (b) 91 (c) 78 (d) 182
  20. 20.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 104 (b) 92 (c) 184 (d) 22
  21. 21.What is the 33rd term of the AP 15, 17, 19, 21, …? (a) 66 (b) 64 (c) 79 (d) 81
  22. 22.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 60 (b) 55 (c) 10 (d) 110
  23. 23.What is the sum of the first 9 terms of the AP 8, 12, 16, …? (a) 40 (b) 432 (c) 234 (d) 216
  24. 24.Which term of the AP 19, 28, 37, 46, … is 217? (a) 24th (b) 25th (c) 23rd (d) 22nd
  25. 25.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 55 (c) 812 (d) 406
  26. 26.What is the 24th term of the AP 1, 3, 5, 7, …? (a) 47 (b) 49 (c) 46 (d) 48
  27. 27.What is the 38th term of the AP 6, 13, 20, 27, …? (a) 266 (b) 259 (c) 265 (d) 272
  28. 28.What is the 22nd term of the AP 10, 18, 26, 34, …? (a) 168 (b) 186 (c) 176 (d) 178
  29. 29.What is the missing term in the AP 2, ?, 14, 20, 26? (a) 7 (b) 8 (c) 14 (d) 9
  30. 30.What is the missing term in the AP 19, ?, 31, 37, 43? (a) 24 (b) 25 (c) 31 (d) 26
  31. 31.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 6162 (c) 3003 (d) 3081
  32. 32.What is the 20th term of the AP 5, 8, 11, 14, …? (a) 60 (b) 65 (c) 57 (d) 62
  33. 33.What is the 10th term of the AP 5, 7, 9, 11, …? (a) 18 (b) 20 (c) 23 (d) 25
  34. 34.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 68 (b) 130 (c) 19 (d) 65
  35. 35.Which term of the AP 3, 10, 17, 24, … is 94? (a) 13th (b) 15th (c) 14th (d) 16th
  36. 36.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 16 (b) 53 (c) 100 (d) 50
  37. 37.What is the 35th term of the AP 13, 21, 29, 37, …? (a) 280 (b) 285 (c) 272 (d) 293
  38. 38.What is the sum of all the whole numbers from 1 to 33? (a) 1122 (b) 561 (c) 528 (d) 562
  39. 39.What is the 15th term of the AP 15, 24, 33, 42, …? (a) 135 (b) 141 (c) 150 (d) 126
  40. 40.What is the 11th term of the AP 3, 12, 21, 30, …? (a) 90 (b) 93 (c) 99 (d) 102

Answer key

  1. 2278
  2. 133
  3. 21st
  4. 3160
  5. 198
  6. 25
  7. 36
  8. 58
  9. 53
  10. 22nd
  11. 60
  12. 153
  13. 351
  14. 903
  15. 175
  16. 595
  17. 420
  18. 16th
  19. 91
  20. 92
  21. 79
  22. 55
  23. 216
  24. 23rd
  25. 784
  26. 47
  27. 265
  28. 178
  29. 8
  30. 25
  31. 3081
  32. 62
  33. 23
  34. 65
  35. 14th
  36. 50
  37. 285
  38. 561
  39. 141
  40. 93

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