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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 726 · 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 33rd term of the AP 6, 8, 10, 12, …? (a) 72 (b) 66 (c) 70 (d) 64
  2. 2.Which term of the AP 14, 20, 26, 32, … is 146? (a) 22nd (b) 23rd (c) 24th (d) 25th
  3. 3.Which term of the AP 8, 14, 20, 26, … is 134? (a) 21st (b) 23rd (c) 24th (d) 22nd
  4. 4.What is the missing term in the AP 18, ?, 34, 42, 50? (a) 25 (b) 26 (c) 34 (d) 27
  5. 5.What is the 14th term of the AP 15, 23, 31, 39, …? (a) 112 (b) 127 (c) 119 (d) 104
  6. 6.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 26 (b) 22 (c) 23 (d) 24
  7. 7.What is the missing term in the AP 5, 8, 11, ?, 17? (a) 15 (b) 17 (c) 13 (d) 14
  8. 8.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 190 (c) 380 (d) 191
  9. 9.Which term of the AP 5, 13, 21, 29, … is 77? (a) 12th (b) 10th (c) 9th (d) 11th
  10. 10.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 26 (b) 85 (c) 140 (d) 70
  11. 11.What is the sum of the first 7 terms of the AP 6, 10, 14, …? (a) 252 (b) 30 (c) 126 (d) 140
  12. 12.What is the 39th term of the AP 4, 9, 14, 19, …? (a) 195 (b) 190 (c) 199 (d) 194
  13. 13.What is the 19th term of the AP 10, 12, 14, 16, …? (a) 48 (b) 46 (c) 38 (d) 36
  14. 14.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 81 (d) 17
  15. 15.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1152 (c) 1128 (d) 1176
  16. 16.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 468 (b) 936 (c) 504 (d) 72
  17. 17.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 121 (d) 21
  18. 18.What is the sum of all the whole numbers from 1 to 55? (a) 1541 (b) 1485 (c) 1540 (d) 3080
  19. 19.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 12 (b) 64 (c) 63 (d) 126
  20. 20.What is the missing term in the AP 5, 13, 21, ?, 37? (a) 37 (b) 30 (c) 28 (d) 29
  21. 21.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 702 (d) 676
  22. 22.What is the sum of the first 6 terms of the AP 10, 14, 18, …? (a) 30 (b) 132 (c) 120 (d) 240
  23. 23.What is the 24th term of the AP 6, 9, 12, 15, …? (a) 78 (b) 72 (c) 69 (d) 75
  24. 24.What is the 32nd term of the AP 19, 27, 35, 43, …? (a) 267 (b) 248 (c) 256 (d) 275
  25. 25.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 462 (c) 231 (d) 41
  26. 26.What is the 15th term of the AP 14, 22, 30, 38, …? (a) 120 (b) 134 (c) 126 (d) 112
  27. 27.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 31 (b) 222 (c) 111 (d) 126
  28. 28.What is the sum of the first 10 terms of the AP 10, 13, 16, …? (a) 37 (b) 235 (c) 250 (d) 470
  29. 29.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 240 (b) 30 (c) 228 (d) 456
  30. 30.What is the 16th term of the AP 8, 12, 16, 20, …? (a) 64 (b) 60 (c) 72 (d) 68
  31. 31.What is the 36th term of the AP 15, 21, 27, 33, …? (a) 231 (b) 225 (c) 210 (d) 216
  32. 32.What is the missing term in the AP 17, 25, 33, ?, 49? (a) 49 (b) 41 (c) 42 (d) 40
  33. 33.What is the 11th term of the AP 3, 10, 17, 24, …? (a) 77 (b) 80 (c) 73 (d) 70
  34. 34.What is the sum of all the whole numbers from 1 to 85? (a) 3656 (b) 7310 (c) 3655 (d) 3570
  35. 35.What is the 13th term of the AP 20, 22, 24, 26, …? (a) 44 (b) 46 (c) 24 (d) 26
  36. 36.What is the sum of all the whole numbers from 1 to 75? (a) 2851 (b) 5700 (c) 2775 (d) 2850
  37. 37.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 114 (b) 204 (c) 27 (d) 102
  38. 38.Which term of the AP 5, 8, 11, 14, … is 38? (a) 13th (b) 12th (c) 11th (d) 14th
  39. 39.What is the missing term in the AP 13, 19, ?, 31, 37? (a) 24 (b) 25 (c) 26 (d) 31
  40. 40.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 756 (c) 378 (d) 729

Answer key

  1. 70
  2. 23rd
  3. 22nd
  4. 26
  5. 119
  6. 23
  7. 14
  8. 190
  9. 10th
  10. 70
  11. 126
  12. 194
  13. 46
  14. 81
  15. 1176
  16. 468
  17. 121
  18. 1540
  19. 63
  20. 29
  21. 676
  22. 120
  23. 75
  24. 267
  25. 441
  26. 126
  27. 111
  28. 235
  29. 228
  30. 68
  31. 225
  32. 41
  33. 73
  34. 3655
  35. 44
  36. 2850
  37. 102
  38. 12th
  39. 25
  40. 729

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