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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 494 · 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 all the whole numbers from 1 to 80? (a) 3240 (b) 3200 (c) 3160 (d) 6480
  2. 2.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 37 (b) 200 (c) 368 (d) 184
  3. 3.Which term of the AP 13, 15, 17, 19, … is 51? (a) 19th (b) 21st (c) 20th (d) 22nd
  4. 4.What is the 22nd term of the AP 5, 7, 9, 11, …? (a) 49 (b) 47 (c) 42 (d) 44
  5. 5.What is the missing term in the AP 11, ?, 21, 26, 31? (a) 16 (b) 21 (c) 15 (d) 17
  6. 6.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 154 (b) 37 (c) 133 (d) 266
  7. 7.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 210 (c) 420 (d) 400
  8. 8.What is the missing term in the AP 3, 7, 11, ?, 19? (a) 19 (b) 16 (c) 14 (d) 15
  9. 9.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 370 (b) 200 (c) 185 (d) 32
  10. 10.What is the 17th term of the AP 5, 9, 13, 17, …? (a) 68 (b) 73 (c) 69 (d) 64
  11. 11.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 9 (c) 30 (d) 15
  12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 53 (c) 729 (d) 756
  13. 13.What is the sum of the first 8 terms of the AP 9, 14, 19, …? (a) 44 (b) 212 (c) 232 (d) 424
  14. 14.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 121 (d) 132
  15. 15.What is the 25th term of the AP 19, 28, 37, 46, …? (a) 235 (b) 244 (c) 216 (d) 225
  16. 16.Which term of the AP 7, 13, 19, 25, … is 85? (a) 13th (b) 14th (c) 15th (d) 16th
  17. 17.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 740 (b) 64 (c) 370 (d) 400
  18. 18.What is the sum of the first 6 terms of the AP 7, 10, 13, …? (a) 174 (b) 96 (c) 22 (d) 87
  19. 19.What is the 31st term of the AP 1, 4, 7, 10, …? (a) 91 (b) 94 (c) 90 (d) 93
  20. 20.What is the missing term in the AP 18, 22, 26, ?, 34? (a) 31 (b) 29 (c) 30 (d) 34
  21. 21.What is the sum of all the whole numbers from 1 to 42? (a) 903 (b) 882 (c) 1806 (d) 861
  22. 22.What is the 38th term of the AP 9, 13, 17, 21, …? (a) 152 (b) 161 (c) 157 (d) 148
  23. 23.What is the sum of all the whole numbers from 1 to 83? (a) 3487 (b) 3486 (c) 6972 (d) 3403
  24. 24.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 1260 (c) 630 (d) 595
  25. 25.What is the missing term in the AP 13, 20, ?, 34, 41? (a) 34 (b) 27 (c) 26 (d) 28
  26. 26.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 36 (c) 11 (d) 42
  27. 27.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 24 (b) 144 (c) 272 (d) 136
  28. 28.What is the 18th term of the AP 12, 16, 20, 24, …? (a) 84 (b) 72 (c) 80 (d) 68
  29. 29.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 117 (b) 234 (c) 118 (d) 17
  30. 30.Which term of the AP 16, 20, 24, 28, … is 80? (a) 20th (b) 16th (c) 18th (d) 17th
  31. 31.Which term of the AP 5, 10, 15, 20, … is 180? (a) 36th (b) 38th (c) 37th (d) 35th
  32. 32.What is the missing term in the AP 14, 23, 32, ?, 50? (a) 42 (b) 40 (c) 41 (d) 50
  33. 33.What is the 31st term of the AP 6, 15, 24, 33, …? (a) 285 (b) 276 (c) 270 (d) 279
  34. 34.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 322 (b) 166 (c) 161 (d) 38
  35. 35.What is the 21st term of the AP 9, 11, 13, 15, …? (a) 42 (b) 51 (c) 49 (d) 40
  36. 36.What is the 24th term of the AP 3, 10, 17, 24, …? (a) 171 (b) 161 (c) 164 (d) 168
  37. 37.What is the sum of all the whole numbers from 1 to 88? (a) 7832 (b) 3872 (c) 3828 (d) 3916
  38. 38.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 55 (d) 100
  39. 39.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 5 (b) 7 (c) 4 (d) 6
  40. 40.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 47 (c) 300 (d) 576

Answer key

  1. 3240
  2. 184
  3. 20th
  4. 47
  5. 16
  6. 133
  7. 400
  8. 15
  9. 185
  10. 69
  11. 25
  12. 729
  13. 212
  14. 121
  15. 235
  16. 14th
  17. 370
  18. 87
  19. 91
  20. 30
  21. 903
  22. 157
  23. 3486
  24. 630
  25. 27
  26. 36
  27. 136
  28. 80
  29. 117
  30. 17th
  31. 36th
  32. 41
  33. 276
  34. 161
  35. 49
  36. 164
  37. 3916
  38. 100
  39. 5
  40. 576

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