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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 671 · 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 11 terms of the AP 10, 14, 18, …? (a) 50 (b) 352 (c) 330 (d) 660
  2. 2.What is the 28th term of the AP 19, 23, 27, 31, …? (a) 127 (b) 112 (c) 108 (d) 131
  3. 3.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 17 (b) 162 (c) 81 (d) 90
  4. 4.What is the 36th term of the AP 5, 7, 9, 11, …? (a) 70 (b) 77 (c) 75 (d) 72
  5. 5.Which term of the AP 4, 6, 8, 10, … is 54? (a) 28th (b) 25th (c) 27th (d) 26th
  6. 6.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 78 (b) 12 (c) 77 (d) 154
  7. 7.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 100 (b) 170 (c) 85 (d) 29
  8. 8.What is the sum of all the whole numbers from 1 to 24? (a) 276 (b) 288 (c) 600 (d) 300
  9. 9.What is the sum of all the whole numbers from 1 to 86? (a) 3741 (b) 3655 (c) 3698 (d) 7482
  10. 10.What is the missing term in the AP 3, 9, ?, 21, 27? (a) 15 (b) 16 (c) 21 (d) 14
  11. 11.What is the missing term in the AP 3, ?, 13, 18, 23? (a) 7 (b) 13 (c) 9 (d) 8
  12. 12.What is the sum of the first 12 terms of the AP 8, 10, 12, …? (a) 240 (b) 456 (c) 228 (d) 30
  13. 13.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 756 (c) 729 (d) 53
  14. 14.What is the 29th term of the AP 9, 15, 21, 27, …? (a) 174 (b) 177 (c) 183 (d) 168
  15. 15.What is the sum of the first 6 terms of the AP 8, 10, 12, …? (a) 84 (b) 78 (c) 156 (d) 18
  16. 16.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 22 (b) 240 (c) 120 (d) 128
  17. 17.What is the 28th term of the AP 20, 27, 34, 41, …? (a) 196 (b) 216 (c) 209 (d) 189
  18. 18.What is the sum of the first 12 terms of the AP 7, 10, 13, …? (a) 40 (b) 300 (c) 564 (d) 282
  19. 19.What is the missing term in the AP 11, 13, 15, ?, 19? (a) 16 (b) 19 (c) 17 (d) 18
  20. 20.What is the 13th term of the AP 9, 11, 13, 15, …? (a) 24 (b) 35 (c) 33 (d) 26
  21. 21.What is the 26th term of the AP 20, 27, 34, 41, …? (a) 202 (b) 195 (c) 182 (d) 175
  22. 22.What is the sum of all the whole numbers from 1 to 32? (a) 528 (b) 512 (c) 496 (d) 1056
  23. 23.What is the missing term in the AP 1, 10, 19, ?, 37? (a) 27 (b) 37 (c) 29 (d) 28
  24. 24.What is the missing term in the AP 7, ?, 17, 22, 27? (a) 11 (b) 17 (c) 12 (d) 13
  25. 25.What is the 20th term of the AP 14, 16, 18, 20, …? (a) 38 (b) 40 (c) 54 (d) 52
  26. 26.What is the sum of the first 11 terms of the AP 8, 14, 20, …? (a) 451 (b) 836 (c) 68 (d) 418
  27. 27.What is the 36th term of the AP 18, 20, 22, 24, …? (a) 90 (b) 88 (c) 70 (d) 72
  28. 28.What is the 29th term of the AP 2, 5, 8, 11, …? (a) 86 (b) 87 (c) 84 (d) 89
  29. 29.Which term of the AP 2, 5, 8, 11, … is 86? (a) 28th (b) 29th (c) 30th (d) 31st
  30. 30.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 435 (d) 57
  31. 31.What is the sum of the first 8 terms of the AP 4, 10, 16, …? (a) 46 (b) 224 (c) 400 (d) 200
  32. 32.What is the sum of all the whole numbers from 1 to 69? (a) 2346 (b) 2415 (c) 4830 (d) 2416
  33. 33.What is the missing term in the AP 17, ?, 31, 38, 45? (a) 23 (b) 31 (c) 24 (d) 25
  34. 34.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 196 (c) 27 (d) 105
  35. 35.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 15 (b) 66 (c) 120 (d) 60
  36. 36.Which term of the AP 17, 22, 27, 32, … is 182? (a) 36th (b) 35th (c) 34th (d) 33rd
  37. 37.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 64 (b) 126 (c) 12 (d) 63
  38. 38.What is the 16th term of the AP 10, 13, 16, 19, …? (a) 45 (b) 58 (c) 48 (d) 55
  39. 39.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 304 (b) 152 (c) 168 (d) 33
  40. 40.Which term of the AP 6, 9, 12, 15, … is 72? (a) 23rd (b) 24th (c) 22nd (d) 25th

Answer key

  1. 330
  2. 127
  3. 81
  4. 75
  5. 26th
  6. 77
  7. 85
  8. 300
  9. 3741
  10. 15
  11. 8
  12. 228
  13. 729
  14. 177
  15. 78
  16. 120
  17. 209
  18. 282
  19. 17
  20. 33
  21. 195
  22. 528
  23. 28
  24. 12
  25. 52
  26. 418
  27. 88
  28. 86
  29. 29th
  30. 841
  31. 200
  32. 2415
  33. 24
  34. 196
  35. 60
  36. 34th
  37. 63
  38. 55
  39. 152
  40. 23rd

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