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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 782 · 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 28? (a) 378 (b) 406 (c) 812 (d) 392
  2. 2.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 36 (c) 21 (d) 11
  3. 3.What is the sum of all the whole numbers from 1 to 25? (a) 325 (b) 326 (c) 650 (d) 300
  4. 4.What is the 17th term of the AP 8, 14, 20, 26, …? (a) 110 (b) 104 (c) 102 (d) 96
  5. 5.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 57 (d) 435
  6. 6.What is the 29th term of the AP 4, 7, 10, 13, …? (a) 87 (b) 88 (c) 91 (d) 84
  7. 7.What is the 17th term of the AP 6, 14, 22, 30, …? (a) 134 (b) 142 (c) 128 (d) 136
  8. 8.What is the 21st term of the AP 4, 8, 12, 16, …? (a) 85 (b) 80 (c) 88 (d) 84
  9. 9.What is the 12th term of the AP 1, 10, 19, 28, …? (a) 99 (b) 100 (c) 108 (d) 109
  10. 10.What is the 33rd term of the AP 7, 16, 25, 34, …? (a) 295 (b) 288 (c) 297 (d) 304
  11. 11.Which term of the AP 13, 15, 17, 19, … is 55? (a) 24th (b) 22nd (c) 23rd (d) 21st
  12. 12.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 1953 (c) 2017 (d) 2016
  13. 13.What is the sum of all the whole numbers from 1 to 42? (a) 903 (b) 882 (c) 1806 (d) 861
  14. 14.What is the 27th term of the AP 14, 18, 22, 26, …? (a) 122 (b) 104 (c) 108 (d) 118
  15. 15.What is the sum of the first 12 terms of the AP 1, 2, 3, …? (a) 84 (b) 12 (c) 156 (d) 78
  16. 16.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 414 (b) 225 (c) 39 (d) 207
  17. 17.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 120 (b) 136 (c) 29 (d) 240
  18. 18.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 516 (b) 73 (c) 480 (d) 960
  19. 19.What is the sum of all the whole numbers from 1 to 79? (a) 3160 (b) 3161 (c) 6320 (d) 3081
  20. 20.What is the missing term in the AP 5, ?, 15, 20, 25? (a) 11 (b) 15 (c) 9 (d) 10
  21. 21.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 9312 (c) 4656 (d) 4560
  22. 22.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 121 (d) 66
  23. 23.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 136 (c) 31 (d) 256
  24. 24.What is the sum of the first 7 terms of the AP 4, 10, 16, …? (a) 308 (b) 40 (c) 154 (d) 175
  25. 25.What is the sum of the first 7 terms of the AP 10, 12, 14, …? (a) 119 (b) 224 (c) 22 (d) 112
  26. 26.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 20 (b) 150 (c) 84 (d) 75
  27. 27.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 19 (d) 55
  28. 28.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 130 (b) 65 (c) 70 (d) 11
  29. 29.What is the 12th term of the AP 11, 15, 19, 23, …? (a) 59 (b) 48 (c) 55 (d) 44
  30. 30.What is the sum of the first 8 terms of the AP 6, 7, 8, …? (a) 13 (b) 152 (c) 80 (d) 76
  31. 31.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 9 (b) 39 (c) 78 (d) 42
  32. 32.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 266 (b) 147 (c) 31 (d) 133
  33. 33.What is the missing term in the AP 19, ?, 33, 40, 47? (a) 26 (b) 27 (c) 25 (d) 33
  34. 34.What is the sum of all the whole numbers from 1 to 84? (a) 3486 (b) 3528 (c) 3570 (d) 7140
  35. 35.What is the missing term in the AP 10, 16, ?, 28, 34? (a) 21 (b) 28 (c) 22 (d) 23
  36. 36.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 11 (b) 132 (c) 67 (d) 66
  37. 37.What is the missing term in the AP 16, ?, 32, 40, 48? (a) 32 (b) 24 (c) 23 (d) 25
  38. 38.What is the 17th term of the AP 10, 13, 16, 19, …? (a) 61 (b) 58 (c) 48 (d) 51
  39. 39.What is the sum of the first 10 terms of the AP 5, 7, 9, …? (a) 280 (b) 150 (c) 23 (d) 140
  40. 40.What is the 21st term of the AP 4, 11, 18, 25, …? (a) 151 (b) 144 (c) 147 (d) 140

Answer key

  1. 406
  2. 36
  3. 325
  4. 104
  5. 841
  6. 88
  7. 134
  8. 84
  9. 100
  10. 295
  11. 22nd
  12. 2016
  13. 903
  14. 118
  15. 78
  16. 207
  17. 120
  18. 480
  19. 3160
  20. 10
  21. 4656
  22. 121
  23. 256
  24. 154
  25. 112
  26. 75
  27. 100
  28. 65
  29. 55
  30. 76
  31. 39
  32. 133
  33. 26
  34. 3570
  35. 22
  36. 66
  37. 24
  38. 58
  39. 140
  40. 144

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