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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 489 · 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 5, 9, 13, 17, … is 41? (a) 9th (b) 12th (c) 10th (d) 11th
  2. 2.What is the sum of the first 8 terms of the AP 5, 11, 17, …? (a) 416 (b) 208 (c) 47 (d) 232
  3. 3.What is the sum of all the whole numbers from 1 to 47? (a) 1129 (b) 2256 (c) 1081 (d) 1128
  4. 4.What is the missing term in the AP 20, 27, ?, 41, 48? (a) 33 (b) 35 (c) 34 (d) 41
  5. 5.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 99 (b) 180 (c) 90 (d) 18
  6. 6.What is the 13th term of the AP 9, 12, 15, 18, …? (a) 39 (b) 48 (c) 45 (d) 36
  7. 7.What is the 34th term of the AP 11, 19, 27, 35, …? (a) 283 (b) 272 (c) 275 (d) 264
  8. 8.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 2211 (c) 2279 (d) 4556
  9. 9.What is the 19th term of the AP 6, 8, 10, 12, …? (a) 38 (b) 36 (c) 44 (d) 42
  10. 10.What is the sum of the first 7 terms of the AP 4, 9, 14, …? (a) 133 (b) 138 (c) 34 (d) 266
  11. 11.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 57 (b) 300 (c) 330 (d) 600
  12. 12.What is the 35th term of the AP 1, 10, 19, 28, …? (a) 316 (b) 306 (c) 315 (d) 307
  13. 13.Which term of the AP 16, 19, 22, 25, … is 100? (a) 30th (b) 28th (c) 31st (d) 29th
  14. 14.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 1035 (c) 2070 (d) 1036
  15. 15.What is the missing term in the AP 12, 16, 20, ?, 28? (a) 25 (b) 24 (c) 23 (d) 28
  16. 16.What is the sum of all the whole numbers from 1 to 63? (a) 2016 (b) 2017 (c) 4032 (d) 1953
  17. 17.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 650 (c) 300 (d) 325
  18. 18.What is the 20th term of the AP 15, 21, 27, 33, …? (a) 135 (b) 114 (c) 120 (d) 129
  19. 19.What is the 21st term of the AP 4, 9, 14, 19, …? (a) 109 (b) 105 (c) 100 (d) 104
  20. 20.Which term of the AP 17, 22, 27, 32, … is 192? (a) 35th (b) 37th (c) 38th (d) 36th
  21. 21.What is the sum of the first 11 terms of the AP 7, 13, 19, …? (a) 407 (b) 67 (c) 440 (d) 814
  22. 22.Which term of the AP 2, 5, 8, 11, … is 86? (a) 28th (b) 29th (c) 30th (d) 31st
  23. 23.What is the 28th term of the AP 1, 4, 7, 10, …? (a) 85 (b) 81 (c) 82 (d) 84
  24. 24.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1225 (c) 1226 (d) 1176
  25. 25.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 25 (d) 15
  26. 26.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 260 (b) 470 (c) 46 (d) 235
  27. 27.Which term of the AP 13, 21, 29, 37, … is 269? (a) 34th (b) 33rd (c) 32nd (d) 35th
  28. 28.What is the missing term in the AP 19, 21, 23, ?, 27? (a) 24 (b) 27 (c) 26 (d) 25
  29. 29.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 414 (b) 444 (c) 62 (d) 828
  30. 30.What is the 15th term of the AP 6, 12, 18, 24, …? (a) 90 (b) 91 (c) 84 (d) 96
  31. 31.What is the 14th term of the AP 15, 20, 25, 30, …? (a) 80 (b) 85 (c) 65 (d) 70
  32. 32.Which term of the AP 2, 4, 6, 8, … is 70? (a) 34th (b) 35th (c) 37th (d) 36th
  33. 33.What is the sum of the first 5 terms of the AP 8, 9, 10, …? (a) 50 (b) 100 (c) 51 (d) 12
  34. 34.What is the 21st term of the AP 20, 27, 34, 41, …? (a) 147 (b) 140 (c) 160 (d) 167
  35. 35.Which term of the AP 20, 23, 26, 29, … is 98? (a) 27th (b) 29th (c) 26th (d) 28th
  36. 36.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 870 (c) 435 (d) 841
  37. 37.Which term of the AP 15, 18, 21, 24, … is 96? (a) 27th (b) 28th (c) 32nd (d) 29th
  38. 38.What is the 15th term of the AP 1, 10, 19, 28, …? (a) 135 (b) 136 (c) 126 (d) 127
  39. 39.What is the sum of all the whole numbers from 1 to 10? (a) 110 (b) 45 (c) 55 (d) 50
  40. 40.What is the 39th term of the AP 13, 18, 23, 28, …? (a) 190 (b) 208 (c) 203 (d) 195

Answer key

  1. 10th
  2. 208
  3. 1128
  4. 34
  5. 90
  6. 45
  7. 275
  8. 2278
  9. 42
  10. 133
  11. 300
  12. 307
  13. 29th
  14. 1035
  15. 24
  16. 2016
  17. 325
  18. 129
  19. 104
  20. 36th
  21. 407
  22. 29th
  23. 82
  24. 1225
  25. 25
  26. 235
  27. 33rd
  28. 25
  29. 414
  30. 90
  31. 80
  32. 35th
  33. 50
  34. 160
  35. 27th
  36. 841
  37. 28th
  38. 127
  39. 55
  40. 203

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