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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 446 · 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 38th term of the AP 11, 17, 23, 29, …? (a) 228 (b) 222 (c) 233 (d) 239
  2. 2.Which term of the AP 12, 17, 22, 27, … is 182? (a) 37th (b) 35th (c) 36th (d) 34th
  3. 3.What is the sum of all the whole numbers from 1 to 74? (a) 2775 (b) 2738 (c) 5550 (d) 2701
  4. 4.What is the 22nd term of the AP 4, 7, 10, 13, …? (a) 70 (b) 63 (c) 66 (d) 67
  5. 5.What is the missing term in the AP 17, 24, ?, 38, 45? (a) 38 (b) 32 (c) 31 (d) 30
  6. 6.What is the sum of all the whole numbers from 1 to 42? (a) 903 (b) 861 (c) 882 (d) 1806
  7. 7.What is the 32nd term of the AP 3, 6, 9, 12, …? (a) 97 (b) 93 (c) 96 (d) 99
  8. 8.What is the 15th term of the AP 11, 18, 25, 32, …? (a) 98 (b) 105 (c) 116 (d) 109
  9. 9.What is the 38th term of the AP 14, 16, 18, 20, …? (a) 76 (b) 90 (c) 88 (d) 74
  10. 10.What is the 37th term of the AP 19, 25, 31, 37, …? (a) 216 (b) 222 (c) 241 (d) 235
  11. 11.What is the 30th term of the AP 6, 11, 16, 21, …? (a) 145 (b) 150 (c) 151 (d) 156
  12. 12.Which term of the AP 1, 9, 17, 25, … is 257? (a) 32nd (b) 35th (c) 33rd (d) 34th
  13. 13.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 156 (d) 144
  14. 14.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 414 (b) 225 (c) 39 (d) 207
  15. 15.What is the 13th term of the AP 4, 6, 8, 10, …? (a) 24 (b) 28 (c) 26 (d) 30
  16. 16.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 35 (b) 430 (c) 215 (d) 230
  17. 17.What is the 15th term of the AP 20, 29, 38, 47, …? (a) 155 (b) 126 (c) 146 (d) 135
  18. 18.What is the 37th term of the AP 4, 9, 14, 19, …? (a) 185 (b) 189 (c) 184 (d) 180
  19. 19.What is the 38th term of the AP 16, 19, 22, 25, …? (a) 127 (b) 111 (c) 114 (d) 130
  20. 20.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 184 (b) 15 (c) 96 (d) 92
  21. 21.What is the missing term in the AP 11, ?, 25, 32, 39? (a) 19 (b) 17 (c) 25 (d) 18
  22. 22.What is the missing term in the AP 13, 21, ?, 37, 45? (a) 28 (b) 30 (c) 37 (d) 29
  23. 23.What is the 29th term of the AP 2, 8, 14, 20, …? (a) 176 (b) 174 (c) 170 (d) 168
  24. 24.What is the 22nd term of the AP 13, 19, 25, 31, …? (a) 126 (b) 145 (c) 132 (d) 139
  25. 25.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 21 (c) 36 (d) 11
  26. 26.What is the sum of the first 5 terms of the AP 10, 14, 18, …? (a) 100 (b) 90 (c) 26 (d) 180
  27. 27.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 40 (b) 220 (c) 440 (d) 240
  28. 28.What is the sum of all the whole numbers from 1 to 97? (a) 4754 (b) 9506 (c) 4753 (d) 4656
  29. 29.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 29 (b) 296 (c) 160 (d) 148
  30. 30.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 72 (c) 64 (d) 15
  31. 31.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 360 (b) 190 (c) 180 (d) 27
  32. 32.What is the missing term in the AP 10, ?, 14, 16, 18? (a) 14 (b) 12 (c) 11 (d) 13
  33. 33.What is the 22nd term of the AP 2, 4, 6, 8, …? (a) 42 (b) 46 (c) 45 (d) 44
  34. 34.What is the sum of all the whole numbers from 1 to 86? (a) 7482 (b) 3741 (c) 3698 (d) 3655
  35. 35.What is the missing term in the AP 19, ?, 27, 31, 35? (a) 22 (b) 24 (c) 27 (d) 23
  36. 36.What is the sum of all the whole numbers from 1 to 41? (a) 820 (b) 861 (c) 862 (d) 1722
  37. 37.What is the 40th term of the AP 10, 15, 20, 25, …? (a) 200 (b) 210 (c) 205 (d) 195
  38. 38.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 306 (c) 289 (d) 33
  39. 39.What is the 25th term of the AP 4, 8, 12, 16, …? (a) 101 (b) 96 (c) 100 (d) 104
  40. 40.What is the 28th term of the AP 13, 18, 23, 28, …? (a) 148 (b) 153 (c) 140 (d) 135

Answer key

  1. 233
  2. 35th
  3. 2775
  4. 67
  5. 31
  6. 903
  7. 96
  8. 109
  9. 88
  10. 235
  11. 151
  12. 33rd
  13. 144
  14. 207
  15. 28
  16. 215
  17. 146
  18. 184
  19. 127
  20. 92
  21. 18
  22. 29
  23. 170
  24. 139
  25. 36
  26. 90
  27. 220
  28. 4753
  29. 148
  30. 64
  31. 180
  32. 12
  33. 44
  34. 3741
  35. 23
  36. 861
  37. 205
  38. 289
  39. 100
  40. 148

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