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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 252 · 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 37th term of the AP 19, 22, 25, 28, …? (a) 130 (b) 127 (c) 108 (d) 111
  2. 2.What is the sum of the first 5 terms of the AP 9, 12, 15, …? (a) 75 (b) 21 (c) 150 (d) 78
  3. 3.What is the 18th term of the AP 7, 13, 19, 25, …? (a) 102 (b) 108 (c) 115 (d) 109
  4. 4.What is the 27th term of the AP 17, 20, 23, 26, …? (a) 98 (b) 81 (c) 95 (d) 78
  5. 5.What is the 40th term of the AP 5, 14, 23, 32, …? (a) 351 (b) 360 (c) 365 (d) 356
  6. 6.What is the missing term in the AP 4, ?, 20, 28, 36? (a) 20 (b) 13 (c) 11 (d) 12
  7. 7.Which term of the AP 19, 21, 23, 25, … is 73? (a) 29th (b) 28th (c) 30th (d) 27th
  8. 8.What is the 11th term of the AP 9, 14, 19, 24, …? (a) 59 (b) 50 (c) 64 (d) 55
  9. 9.What is the 37th term of the AP 3, 6, 9, 12, …? (a) 114 (b) 111 (c) 108 (d) 112
  10. 10.What is the sum of all the whole numbers from 1 to 59? (a) 1711 (b) 1770 (c) 3540 (d) 1771
  11. 11.What is the 19th term of the AP 12, 20, 28, 36, …? (a) 156 (b) 144 (c) 164 (d) 152
  12. 12.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 132 (d) 66
  13. 13.What is the 17th term of the AP 1, 3, 5, 7, …? (a) 32 (b) 33 (c) 35 (d) 34
  14. 14.What is the missing term in the AP 4, ?, 10, 13, 16? (a) 8 (b) 10 (c) 6 (d) 7
  15. 15.What is the 12th term of the AP 16, 24, 32, 40, …? (a) 112 (b) 104 (c) 96 (d) 88
  16. 16.What is the sum of all the whole numbers from 1 to 34? (a) 595 (b) 1190 (c) 561 (d) 578
  17. 17.What is the 17th term of the AP 3, 6, 9, 12, …? (a) 52 (b) 54 (c) 51 (d) 48
  18. 18.What is the 35th term of the AP 12, 18, 24, 30, …? (a) 222 (b) 204 (c) 216 (d) 210
  19. 19.What is the 12th term of the AP 15, 24, 33, 42, …? (a) 123 (b) 99 (c) 108 (d) 114
  20. 20.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 342 (c) 171 (d) 162
  21. 21.What is the 38th term of the AP 3, 8, 13, 18, …? (a) 188 (b) 193 (c) 190 (d) 185
  22. 22.Which term of the AP 12, 21, 30, 39, … is 147? (a) 18th (b) 15th (c) 17th (d) 16th
  23. 23.What is the sum of all the whole numbers from 1 to 20? (a) 200 (b) 190 (c) 210 (d) 420
  24. 24.What is the 10th term of the AP 1, 8, 15, 22, …? (a) 70 (b) 71 (c) 63 (d) 64
  25. 25.What is the 11th term of the AP 13, 20, 27, 34, …? (a) 77 (b) 83 (c) 70 (d) 90
  26. 26.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 117 (b) 118 (c) 234 (d) 17
  27. 27.What is the 16th term of the AP 10, 15, 20, 25, …? (a) 75 (b) 85 (c) 90 (d) 80
  28. 28.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 14 (b) 16 (c) 13 (d) 12
  29. 29.What is the missing term in the AP 3, 12, ?, 30, 39? (a) 20 (b) 30 (c) 21 (d) 22
  30. 30.What is the 12th term of the AP 11, 20, 29, 38, …? (a) 110 (b) 99 (c) 108 (d) 119
  31. 31.What is the 21st term of the AP 1, 10, 19, 28, …? (a) 180 (b) 189 (c) 190 (d) 181
  32. 32.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 352 (b) 31 (c) 176 (d) 179
  33. 33.What is the sum of all the whole numbers from 1 to 11? (a) 55 (b) 66 (c) 67 (d) 132
  34. 34.What is the 25th term of the AP 15, 24, 33, 42, …? (a) 225 (b) 231 (c) 216 (d) 240
  35. 35.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 166 (b) 38 (c) 322 (d) 161
  36. 36.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 600 (c) 47 (d) 300
  37. 37.What is the 26th term of the AP 7, 13, 19, 25, …? (a) 156 (b) 150 (c) 163 (d) 157
  38. 38.What is the sum of the first 6 terms of the AP 8, 14, 20, …? (a) 38 (b) 156 (c) 276 (d) 138
  39. 39.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 43 (c) 484 (d) 506
  40. 40.Which term of the AP 10, 15, 20, 25, … is 55? (a) 12th (b) 9th (c) 11th (d) 10th

Answer key

  1. 127
  2. 75
  3. 109
  4. 95
  5. 356
  6. 12
  7. 28th
  8. 59
  9. 111
  10. 1770
  11. 156
  12. 121
  13. 33
  14. 7
  15. 104
  16. 595
  17. 51
  18. 216
  19. 114
  20. 171
  21. 188
  22. 16th
  23. 210
  24. 64
  25. 83
  26. 117
  27. 85
  28. 13
  29. 21
  30. 110
  31. 181
  32. 176
  33. 66
  34. 231
  35. 161
  36. 576
  37. 157
  38. 138
  39. 484
  40. 10th

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