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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 643 · 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 40th term of the AP 2, 7, 12, 17, …? (a) 195 (b) 200 (c) 197 (d) 202
  2. 2.What is the missing term in the AP 1, 9, ?, 25, 33? (a) 16 (b) 17 (c) 25 (d) 18
  3. 3.What is the 29th term of the AP 6, 14, 22, 30, …? (a) 230 (b) 238 (c) 232 (d) 224
  4. 4.What is the sum of the first 10 terms of the AP 5, 6, 7, …? (a) 100 (b) 190 (c) 95 (d) 14
  5. 5.What is the sum of the first 10 terms of the AP 6, 12, 18, …? (a) 360 (b) 660 (c) 330 (d) 60
  6. 6.Which term of the AP 9, 17, 25, 33, … is 297? (a) 38th (b) 37th (c) 39th (d) 36th
  7. 7.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 261 (b) 49 (c) 266 (d) 522
  8. 8.What is the sum of all the whole numbers from 1 to 81? (a) 6642 (b) 3240 (c) 3322 (d) 3321
  9. 9.What is the 20th term of the AP 8, 16, 24, 32, …? (a) 168 (b) 161 (c) 152 (d) 160
  10. 10.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 8 (b) 5 (c) 6 (d) 7
  11. 11.What is the 27th term of the AP 2, 4, 6, 8, …? (a) 56 (b) 55 (c) 54 (d) 52
  12. 12.What is the sum of all the whole numbers from 1 to 50? (a) 1275 (b) 2550 (c) 1225 (d) 1250
  13. 13.What is the sum of the first 12 terms of the AP 6, 10, 14, …? (a) 336 (b) 50 (c) 672 (d) 360
  14. 14.What is the 16th term of the AP 12, 21, 30, 39, …? (a) 144 (b) 135 (c) 147 (d) 156
  15. 15.What is the 29th term of the AP 10, 13, 16, 19, …? (a) 84 (b) 94 (c) 97 (d) 87
  16. 16.What is the 14th term of the AP 15, 19, 23, 27, …? (a) 71 (b) 67 (c) 56 (d) 52
  17. 17.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3916 (c) 7832 (d) 3828
  18. 18.Which term of the AP 15, 21, 27, 33, … is 129? (a) 22nd (b) 20th (c) 21st (d) 19th
  19. 19.What is the 30th term of the AP 12, 17, 22, 27, …? (a) 162 (b) 150 (c) 157 (d) 145
  20. 20.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 435 (c) 841 (d) 870
  21. 21.Which term of the AP 13, 18, 23, 28, … is 208? (a) 42nd (b) 41st (c) 40th (d) 39th
  22. 22.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 21 (b) 105 (c) 112 (d) 210
  23. 23.What is the 14th term of the AP 2, 9, 16, 23, …? (a) 98 (b) 91 (c) 93 (d) 100
  24. 24.What is the 31st term of the AP 10, 13, 16, 19, …? (a) 100 (b) 103 (c) 90 (d) 93
  25. 25.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 67 (c) 55 (d) 132
  26. 26.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 625 (d) 650
  27. 27.What is the missing term in the AP 17, 19, ?, 23, 25? (a) 20 (b) 23 (c) 21 (d) 22
  28. 28.What is the sum of all the whole numbers from 1 to 93? (a) 4278 (b) 8742 (c) 4372 (d) 4371
  29. 29.What is the sum of all the whole numbers from 1 to 43? (a) 1892 (b) 903 (c) 947 (d) 946
  30. 30.What is the sum of the first 11 terms of the AP 2, 3, 4, …? (a) 78 (b) 77 (c) 154 (d) 12
  31. 31.What is the sum of all the whole numbers from 1 to 90? (a) 8190 (b) 4005 (c) 4095 (d) 4050
  32. 32.What is the 12th term of the AP 6, 11, 16, 21, …? (a) 66 (b) 61 (c) 60 (d) 55
  33. 33.What is the 12th term of the AP 6, 9, 12, 15, …? (a) 39 (b) 42 (c) 36 (d) 33
  34. 34.What is the 19th term of the AP 20, 23, 26, 29, …? (a) 54 (b) 74 (c) 77 (d) 57
  35. 35.What is the 13th term of the AP 19, 26, 33, 40, …? (a) 84 (b) 110 (c) 91 (d) 103
  36. 36.What is the missing term in the AP 2, 5, 8, ?, 14? (a) 10 (b) 12 (c) 14 (d) 11
  37. 37.What is the missing term in the AP 11, 15, ?, 23, 27? (a) 19 (b) 18 (c) 23 (d) 20
  38. 38.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 162 (b) 26 (c) 96 (d) 81
  39. 39.Which term of the AP 11, 13, 15, 17, … is 75? (a) 35th (b) 32nd (c) 33rd (d) 34th
  40. 40.What is the 31st term of the AP 12, 18, 24, 30, …? (a) 198 (b) 180 (c) 192 (d) 186

Answer key

  1. 197
  2. 17
  3. 230
  4. 95
  5. 330
  6. 37th
  7. 261
  8. 3321
  9. 160
  10. 6
  11. 54
  12. 1275
  13. 336
  14. 147
  15. 94
  16. 67
  17. 3916
  18. 20th
  19. 157
  20. 841
  21. 40th
  22. 105
  23. 93
  24. 100
  25. 66
  26. 625
  27. 21
  28. 4371
  29. 946
  30. 77
  31. 4095
  32. 61
  33. 39
  34. 74
  35. 103
  36. 11
  37. 19
  38. 81
  39. 33rd
  40. 192

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