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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 788 · 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.Which term of the AP 20, 23, 26, 29, … is 86? (a) 23rd (b) 25th (c) 24th (d) 22nd
  2. 2.What is the 35th term of the AP 2, 9, 16, 23, …? (a) 245 (b) 238 (c) 247 (d) 240
  3. 3.What is the 27th term of the AP 13, 15, 17, 19, …? (a) 54 (b) 67 (c) 65 (d) 52
  4. 4.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 610 (b) 305 (c) 53 (d) 330
  5. 5.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 92 (c) 91 (d) 78
  6. 6.What is the sum of the first 7 terms of the AP 5, 10, 15, …? (a) 35 (b) 145 (c) 280 (d) 140
  7. 7.What is the 38th term of the AP 2, 10, 18, 26, …? (a) 296 (b) 298 (c) 304 (d) 306
  8. 8.What is the sum of the first 7 terms of the AP 10, 15, 20, …? (a) 175 (b) 180 (c) 40 (d) 350
  9. 9.What is the 34th term of the AP 6, 13, 20, 27, …? (a) 237 (b) 231 (c) 244 (d) 238
  10. 10.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 380 (c) 37 (d) 361
  11. 11.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 189 (b) 342 (c) 35 (d) 171
  12. 12.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 7832 (c) 3916 (d) 3828
  13. 13.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 184 (b) 44 (c) 208 (d) 368
  14. 14.What is the sum of all the whole numbers from 1 to 59? (a) 1770 (b) 1771 (c) 3540 (d) 1711
  15. 15.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 20 (b) 21 (c) 40 (d) 6
  16. 16.What is the missing term in the AP 12, 21, ?, 39, 48? (a) 39 (b) 29 (c) 30 (d) 31
  17. 17.What is the sum of the first 12 terms of the AP 5, 7, 9, …? (a) 204 (b) 192 (c) 384 (d) 27
  18. 18.What is the missing term in the AP 20, 25, ?, 35, 40? (a) 29 (b) 30 (c) 35 (d) 31
  19. 19.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 55 (d) 100
  20. 20.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 600 (c) 300 (d) 576
  21. 21.What is the 27th term of the AP 2, 9, 16, 23, …? (a) 189 (b) 182 (c) 191 (d) 184
  22. 22.Which term of the AP 13, 18, 23, 28, … is 158? (a) 32nd (b) 31st (c) 30th (d) 29th
  23. 23.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1653 (c) 1711 (d) 1682
  24. 24.What is the 22nd term of the AP 8, 10, 12, 14, …? (a) 42 (b) 50 (c) 44 (d) 52
  25. 25.What is the 22nd term of the AP 16, 18, 20, 22, …? (a) 60 (b) 44 (c) 58 (d) 42
  26. 26.What is the 37th term of the AP 14, 23, 32, 41, …? (a) 333 (b) 324 (c) 347 (d) 338
  27. 27.What is the sum of all the whole numbers from 1 to 27? (a) 379 (b) 378 (c) 756 (d) 351
  28. 28.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 234 (b) 252 (c) 468 (d) 36
  29. 29.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 110 (b) 10 (c) 60 (d) 55
  30. 30.What is the sum of all the whole numbers from 1 to 42? (a) 1806 (b) 903 (c) 861 (d) 882
  31. 31.What is the missing term in the AP 1, 7, 13, ?, 25? (a) 18 (b) 20 (c) 19 (d) 25
  32. 32.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 210 (c) 105 (d) 196
  33. 33.What is the sum of all the whole numbers from 1 to 86? (a) 3741 (b) 3655 (c) 3698 (d) 7482
  34. 34.What is the sum of all the whole numbers from 1 to 81? (a) 3240 (b) 6642 (c) 3321 (d) 3322
  35. 35.Which term of the AP 10, 17, 24, 31, … is 255? (a) 37th (b) 38th (c) 36th (d) 35th
  36. 36.What is the 10th term of the AP 19, 21, 23, 25, …? (a) 18 (b) 20 (c) 37 (d) 39
  37. 37.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 14 (b) 108 (c) 54 (d) 60
  38. 38.What is the sum of the first 9 terms of the AP 9, 11, 13, …? (a) 25 (b) 306 (c) 162 (d) 153
  39. 39.What is the 14th term of the AP 5, 8, 11, 14, …? (a) 42 (b) 47 (c) 39 (d) 44
  40. 40.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 136 (c) 306 (d) 154

Answer key

  1. 23rd
  2. 240
  3. 65
  4. 305
  5. 91
  6. 140
  7. 298
  8. 175
  9. 237
  10. 361
  11. 171
  12. 3916
  13. 184
  14. 1770
  15. 20
  16. 30
  17. 192
  18. 30
  19. 100
  20. 576
  21. 184
  22. 30th
  23. 1711
  24. 50
  25. 58
  26. 338
  27. 378
  28. 234
  29. 55
  30. 903
  31. 19
  32. 196
  33. 3741
  34. 3321
  35. 36th
  36. 37
  37. 54
  38. 153
  39. 44
  40. 153

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