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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 796 · 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 19, 26, ?, 40, 47? (a) 33 (b) 40 (c) 32 (d) 34
  2. 2.What is the 23rd term of the AP 20, 28, 36, 44, …? (a) 204 (b) 196 (c) 184 (d) 176
  3. 3.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 256 (b) 506 (c) 253 (d) 38
  4. 4.Which term of the AP 3, 10, 17, 24, … is 262? (a) 38th (b) 40th (c) 37th (d) 39th
  5. 5.What is the missing term in the AP 6, 15, 24, ?, 42? (a) 42 (b) 34 (c) 32 (d) 33
  6. 6.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 64 (d) 72
  7. 7.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 19 (b) 68 (c) 130 (d) 65
  8. 8.What is the 32nd term of the AP 13, 15, 17, 19, …? (a) 62 (b) 64 (c) 77 (d) 75
  9. 9.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 231 (c) 210 (d) 462
  10. 10.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 465 (c) 930 (d) 59
  11. 11.What is the missing term in the AP 11, 15, 19, ?, 27? (a) 23 (b) 22 (c) 27 (d) 24
  12. 12.What is the 14th term of the AP 20, 28, 36, 44, …? (a) 132 (b) 104 (c) 124 (d) 112
  13. 13.Which term of the AP 1, 5, 9, 13, … is 101? (a) 25th (b) 27th (c) 26th (d) 28th
  14. 14.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 154 (c) 306 (d) 136
  15. 15.What is the missing term in the AP 4, ?, 12, 16, 20? (a) 12 (b) 7 (c) 8 (d) 9
  16. 16.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 30 (b) 10 (c) 35 (d) 60
  17. 17.What is the sum of all the whole numbers from 1 to 98? (a) 4851 (b) 4802 (c) 4753 (d) 9702
  18. 18.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 529 (c) 45 (d) 552
  19. 19.Which term of the AP 9, 14, 19, 24, … is 154? (a) 30th (b) 32nd (c) 31st (d) 29th
  20. 20.What is the missing term in the AP 20, 24, 28, ?, 36? (a) 33 (b) 31 (c) 32 (d) 36
  21. 21.What is the sum of all the whole numbers from 1 to 64? (a) 2016 (b) 2048 (c) 2080 (d) 4160
  22. 22.What is the sum of all the whole numbers from 1 to 81? (a) 3240 (b) 3321 (c) 3322 (d) 6642
  23. 23.What is the sum of the first 7 terms of the AP 2, 8, 14, …? (a) 140 (b) 280 (c) 161 (d) 38
  24. 24.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 406 (c) 392 (d) 378
  25. 25.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 10 (b) 56 (c) 52 (d) 104
  26. 26.What is the sum of the first 10 terms of the AP 3, 8, 13, …? (a) 510 (b) 48 (c) 280 (d) 255
  27. 27.What is the sum of all the whole numbers from 1 to 87? (a) 3741 (b) 3828 (c) 7656 (d) 3829
  28. 28.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 32 (b) 115 (c) 200 (d) 100
  29. 29.What is the sum of the first 12 terms of the AP 8, 13, 18, …? (a) 63 (b) 456 (c) 852 (d) 426
  30. 30.What is the missing term in the AP 10, 17, ?, 31, 38? (a) 31 (b) 24 (c) 25 (d) 23
  31. 31.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 77 (b) 16 (c) 70 (d) 140
  32. 32.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 12 (b) 48 (c) 84 (d) 42
  33. 33.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 21 (d) 36
  34. 34.What is the missing term in the AP 2, 7, 12, ?, 22? (a) 16 (b) 17 (c) 22 (d) 18
  35. 35.What is the 27th term of the AP 8, 14, 20, 26, …? (a) 164 (b) 170 (c) 162 (d) 156
  36. 36.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 29 (b) 28 (c) 56 (d) 7
  37. 37.What is the missing term in the AP 13, 20, ?, 34, 41? (a) 28 (b) 27 (c) 26 (d) 34
  38. 38.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 4754 (c) 4753 (d) 9506
  39. 39.What is the sum of all the whole numbers from 1 to 69? (a) 2416 (b) 2346 (c) 4830 (d) 2415
  40. 40.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 91 (c) 182 (d) 25

Answer key

  1. 33
  2. 196
  3. 253
  4. 38th
  5. 33
  6. 64
  7. 65
  8. 75
  9. 231
  10. 900
  11. 23
  12. 124
  13. 26th
  14. 153
  15. 8
  16. 30
  17. 4851
  18. 529
  19. 30th
  20. 32
  21. 2080
  22. 3321
  23. 140
  24. 406
  25. 52
  26. 255
  27. 3828
  28. 100
  29. 426
  30. 24
  31. 70
  32. 42
  33. 36
  34. 17
  35. 164
  36. 28
  37. 27
  38. 4753
  39. 2415
  40. 169

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