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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 574 · 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 7 terms of the AP 9, 11, 13, …? (a) 112 (b) 21 (c) 105 (d) 210
  2. 2.What is the 12th term of the AP 3, 10, 17, 24, …? (a) 84 (b) 80 (c) 87 (d) 77
  3. 3.What is the missing term in the AP 14, 17, ?, 23, 26? (a) 21 (b) 23 (c) 19 (d) 20
  4. 4.What is the 15th term of the AP 3, 7, 11, 15, …? (a) 59 (b) 60 (c) 56 (d) 63
  5. 5.What is the sum of all the whole numbers from 1 to 37? (a) 704 (b) 1406 (c) 703 (d) 666
  6. 6.Which term of the AP 6, 8, 10, 12, … is 22? (a) 10th (b) 8th (c) 11th (d) 9th
  7. 7.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 29 (b) 198 (c) 114 (d) 99
  8. 8.What is the sum of all the whole numbers from 1 to 60? (a) 1800 (b) 1770 (c) 3660 (d) 1830
  9. 9.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 91 (c) 78 (d) 92
  10. 10.Which term of the AP 1, 5, 9, 13, … is 45? (a) 13th (b) 12th (c) 14th (d) 11th
  11. 11.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 370 (b) 200 (c) 32 (d) 185
  12. 12.What is the sum of the first 10 terms of the AP 9, 14, 19, …? (a) 54 (b) 315 (c) 630 (d) 340
  13. 13.What is the 18th term of the AP 6, 13, 20, 27, …? (a) 132 (b) 125 (c) 126 (d) 119
  14. 14.What is the sum of the first 5 terms of the AP 8, 12, 16, …? (a) 160 (b) 90 (c) 80 (d) 24
  15. 15.Which term of the AP 10, 19, 28, 37, … is 217? (a) 26th (b) 25th (c) 23rd (d) 24th
  16. 16.What is the sum of all the whole numbers from 1 to 79? (a) 3161 (b) 3160 (c) 3081 (d) 6320
  17. 17.What is the sum of the first 7 terms of the AP 4, 5, 6, …? (a) 98 (b) 10 (c) 49 (d) 50
  18. 18.What is the sum of the first 12 terms of the AP 9, 14, 19, …? (a) 64 (b) 438 (c) 876 (d) 468
  19. 19.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 351 (c) 702 (d) 338
  20. 20.What is the missing term in the AP 18, ?, 30, 36, 42? (a) 23 (b) 25 (c) 30 (d) 24
  21. 21.What is the sum of all the whole numbers from 1 to 85? (a) 7310 (b) 3655 (c) 3656 (d) 3570
  22. 22.What is the missing term in the AP 15, ?, 29, 36, 43? (a) 29 (b) 22 (c) 23 (d) 21
  23. 23.What is the missing term in the AP 11, ?, 29, 38, 47? (a) 21 (b) 19 (c) 20 (d) 29
  24. 24.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 529 (d) 552
  25. 25.What is the sum of the first 8 terms of the AP 5, 8, 11, …? (a) 136 (b) 124 (c) 248 (d) 26
  26. 26.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 108 (b) 28 (c) 216 (d) 120
  27. 27.Which term of the AP 18, 24, 30, 36, … is 162? (a) 26th (b) 27th (c) 24th (d) 25th
  28. 28.What is the sum of all the whole numbers from 1 to 66? (a) 2211 (b) 4422 (c) 2145 (d) 2178
  29. 29.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 784 (c) 55 (d) 406
  30. 30.What is the sum of all the whole numbers from 1 to 51? (a) 2652 (b) 1275 (c) 1327 (d) 1326
  31. 31.What is the 39th term of the AP 17, 22, 27, 32, …? (a) 190 (b) 212 (c) 207 (d) 195
  32. 32.What is the sum of the first 11 terms of the AP 5, 9, 13, …? (a) 550 (b) 275 (c) 45 (d) 297
  33. 33.What is the missing term in the AP 18, ?, 36, 45, 54? (a) 36 (b) 28 (c) 26 (d) 27
  34. 34.Which term of the AP 6, 12, 18, 24, … is 144? (a) 24th (b) 25th (c) 26th (d) 23rd
  35. 35.What is the missing term in the AP 4, 6, 8, ?, 12? (a) 9 (b) 12 (c) 11 (d) 10
  36. 36.What is the 34th term of the AP 9, 14, 19, 24, …? (a) 174 (b) 179 (c) 170 (d) 165
  37. 37.What is the 13th term of the AP 8, 10, 12, 14, …? (a) 32 (b) 34 (c) 24 (d) 26
  38. 38.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 341 (b) 56 (c) 346 (d) 682
  39. 39.What is the 32nd term of the AP 13, 16, 19, 22, …? (a) 106 (b) 93 (c) 96 (d) 109
  40. 40.What is the sum of all the whole numbers from 1 to 87? (a) 3828 (b) 3829 (c) 3741 (d) 7656

Answer key

  1. 105
  2. 80
  3. 20
  4. 59
  5. 703
  6. 9th
  7. 99
  8. 1830
  9. 91
  10. 12th
  11. 185
  12. 315
  13. 125
  14. 80
  15. 24th
  16. 3160
  17. 49
  18. 438
  19. 351
  20. 24
  21. 3655
  22. 22
  23. 20
  24. 529
  25. 124
  26. 108
  27. 25th
  28. 2211
  29. 784
  30. 1326
  31. 207
  32. 275
  33. 27
  34. 24th
  35. 10
  36. 174
  37. 32
  38. 341
  39. 106
  40. 3828

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