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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 285 · 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 6, 9, 12, …? (a) 105 (b) 108 (c) 24 (d) 210
  2. 2.What is the 12th term of the AP 14, 19, 24, 29, …? (a) 69 (b) 74 (c) 55 (d) 60
  3. 3.What is the 21st term of the AP 1, 5, 9, 13, …? (a) 81 (b) 84 (c) 85 (d) 80
  4. 4.Which term of the AP 15, 21, 27, 33, … is 135? (a) 22nd (b) 23rd (c) 21st (d) 20th
  5. 5.What is the missing term in the AP 13, ?, 21, 25, 29? (a) 21 (b) 17 (c) 18 (d) 16
  6. 6.What is the 12th term of the AP 13, 19, 25, 31, …? (a) 66 (b) 72 (c) 85 (d) 79
  7. 7.Which term of the AP 16, 21, 26, 31, … is 56? (a) 10th (b) 8th (c) 9th (d) 11th
  8. 8.What is the 23rd term of the AP 20, 27, 34, 41, …? (a) 161 (b) 181 (c) 154 (d) 174
  9. 9.What is the sum of the first 12 terms of the AP 2, 7, 12, …? (a) 384 (b) 354 (c) 708 (d) 57
  10. 10.Which term of the AP 10, 18, 26, 34, … is 90? (a) 13th (b) 12th (c) 10th (d) 11th
  11. 11.What is the 39th term of the AP 2, 7, 12, 17, …? (a) 190 (b) 195 (c) 192 (d) 197
  12. 12.What is the sum of all the whole numbers from 1 to 30? (a) 465 (b) 435 (c) 450 (d) 930
  13. 13.What is the 40th term of the AP 2, 6, 10, 14, …? (a) 156 (b) 162 (c) 160 (d) 158
  14. 14.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 25 (b) 7 (c) 26 (d) 50
  15. 15.Which term of the AP 1, 8, 15, 22, … is 50? (a) 7th (b) 9th (c) 8th (d) 10th
  16. 16.Which term of the AP 5, 12, 19, 26, … is 271? (a) 40th (b) 38th (c) 41st (d) 39th
  17. 17.What is the 17th term of the AP 20, 23, 26, 29, …? (a) 71 (b) 51 (c) 68 (d) 48
  18. 18.What is the sum of all the whole numbers from 1 to 81? (a) 3322 (b) 6642 (c) 3240 (d) 3321
  19. 19.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 126 (b) 111 (c) 31 (d) 222
  20. 20.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 1035 (c) 2070 (d) 990
  21. 21.What is the missing term in the AP 5, 13, 21, ?, 37? (a) 30 (b) 28 (c) 37 (d) 29
  22. 22.Which term of the AP 12, 18, 24, 30, … is 192? (a) 31st (b) 32nd (c) 33rd (d) 30th
  23. 23.What is the missing term in the AP 10, ?, 20, 25, 30? (a) 20 (b) 16 (c) 14 (d) 15
  24. 24.What is the missing term in the AP 19, 28, 37, ?, 55? (a) 55 (b) 47 (c) 45 (d) 46
  25. 25.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 45 (c) 90 (d) 17
  26. 26.What is the 36th term of the AP 12, 14, 16, 18, …? (a) 70 (b) 72 (c) 84 (d) 82
  27. 27.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 276 (c) 552 (d) 529
  28. 28.What is the missing term in the AP 14, 21, ?, 35, 42? (a) 27 (b) 28 (c) 35 (d) 29
  29. 29.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 342 (b) 189 (c) 171 (d) 35
  30. 30.What is the sum of all the whole numbers from 1 to 29? (a) 435 (b) 870 (c) 436 (d) 406
  31. 31.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 1980 (c) 990 (d) 968
  32. 32.What is the 12th term of the AP 3, 11, 19, 27, …? (a) 91 (b) 96 (c) 88 (d) 99
  33. 33.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 30 (d) 25
  34. 34.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 78 (c) 92 (d) 91
  35. 35.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 38 (b) 322 (c) 166 (d) 161
  36. 36.What is the 33rd term of the AP 6, 9, 12, 15, …? (a) 96 (b) 99 (c) 105 (d) 102
  37. 37.Which term of the AP 17, 23, 29, 35, … is 107? (a) 18th (b) 16th (c) 17th (d) 15th
  38. 38.What is the sum of all the whole numbers from 1 to 61? (a) 1830 (b) 3782 (c) 1891 (d) 1892
  39. 39.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 184 (b) 37 (c) 200 (d) 368
  40. 40.Which term of the AP 14, 20, 26, 32, … is 194? (a) 32nd (b) 30th (c) 31st (d) 33rd

Answer key

  1. 105
  2. 69
  3. 81
  4. 21st
  5. 17
  6. 79
  7. 9th
  8. 174
  9. 354
  10. 11th
  11. 192
  12. 465
  13. 158
  14. 25
  15. 8th
  16. 39th
  17. 68
  18. 3321
  19. 111
  20. 1035
  21. 29
  22. 31st
  23. 15
  24. 46
  25. 81
  26. 82
  27. 529
  28. 28
  29. 171
  30. 435
  31. 990
  32. 91
  33. 25
  34. 91
  35. 161
  36. 102
  37. 16th
  38. 1891
  39. 184
  40. 31st

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