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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 226 · 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 31st term of the AP 14, 20, 26, 32, …? (a) 200 (b) 180 (c) 186 (d) 194
  2. 2.What is the 33rd term of the AP 9, 11, 13, 15, …? (a) 66 (b) 73 (c) 64 (d) 75
  3. 3.What is the 23rd term of the AP 6, 15, 24, 33, …? (a) 198 (b) 213 (c) 204 (d) 207
  4. 4.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 140 (b) 70 (c) 13 (d) 71
  5. 5.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 14 (b) 63 (c) 112 (d) 56
  6. 6.What is the sum of the first 10 terms of the AP 10, 14, 18, …? (a) 560 (b) 280 (c) 46 (d) 300
  7. 7.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 3200 (c) 6480 (d) 3240
  8. 8.What is the sum of the first 5 terms of the AP 5, 11, 17, …? (a) 170 (b) 29 (c) 85 (d) 100
  9. 9.What is the missing term in the AP 6, 15, ?, 33, 42? (a) 25 (b) 33 (c) 23 (d) 24
  10. 10.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 25 (b) 112 (c) 224 (d) 115
  11. 11.What is the sum of all the whole numbers from 1 to 24? (a) 276 (b) 288 (c) 600 (d) 300
  12. 12.What is the missing term in the AP 9, 15, ?, 27, 33? (a) 20 (b) 21 (c) 22 (d) 27
  13. 13.What is the missing term in the AP 9, 12, 15, ?, 21? (a) 19 (b) 18 (c) 21 (d) 17
  14. 14.What is the sum of all the whole numbers from 1 to 72? (a) 5256 (b) 2592 (c) 2628 (d) 2556
  15. 15.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 27 (b) 129 (c) 126 (d) 252
  16. 16.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 276 (b) 144 (c) 17 (d) 138
  17. 17.What is the 10th term of the AP 5, 14, 23, 32, …? (a) 81 (b) 86 (c) 95 (d) 90
  18. 18.What is the 20th term of the AP 13, 18, 23, 28, …? (a) 113 (b) 100 (c) 108 (d) 95
  19. 19.What is the sum of the first 7 terms of the AP 4, 10, 16, …? (a) 40 (b) 308 (c) 175 (d) 154
  20. 20.What is the 35th term of the AP 17, 20, 23, 26, …? (a) 105 (b) 102 (c) 119 (d) 122
  21. 21.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 520 (b) 280 (c) 260 (d) 44
  22. 22.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 162 (b) 96 (c) 26 (d) 81
  23. 23.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 10 (b) 108 (c) 55 (d) 54
  24. 24.What is the missing term in the AP 7, 11, ?, 19, 23? (a) 19 (b) 14 (c) 15 (d) 16
  25. 25.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 400 (d) 39
  26. 26.What is the sum of the first 8 terms of the AP 9, 10, 11, …? (a) 200 (b) 100 (c) 16 (d) 104
  27. 27.What is the 22nd term of the AP 2, 9, 16, 23, …? (a) 149 (b) 156 (c) 154 (d) 147
  28. 28.What is the missing term in the AP 5, 12, ?, 26, 33? (a) 20 (b) 26 (c) 18 (d) 19
  29. 29.What is the sum of the first 10 terms of the AP 4, 6, 8, …? (a) 22 (b) 260 (c) 130 (d) 140
  30. 30.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 240 (c) 29 (d) 120
  31. 31.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 110 (b) 60 (c) 10 (d) 55
  32. 32.What is the sum of the first 10 terms of the AP 6, 12, 18, …? (a) 330 (b) 660 (c) 60 (d) 360
  33. 33.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 324 (b) 180 (c) 34 (d) 162
  34. 34.What is the 40th term of the AP 11, 17, 23, 29, …? (a) 245 (b) 251 (c) 240 (d) 234
  35. 35.What is the missing term in the AP 5, ?, 11, 14, 17? (a) 7 (b) 11 (c) 9 (d) 8
  36. 36.What is the 38th term of the AP 4, 11, 18, 25, …? (a) 263 (b) 259 (c) 266 (d) 270
  37. 37.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 144 (c) 156 (d) 78
  38. 38.What is the 17th term of the AP 4, 13, 22, 31, …? (a) 148 (b) 144 (c) 153 (d) 157
  39. 39.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 506 (c) 484 (d) 253
  40. 40.Which term of the AP 8, 15, 22, 29, … is 225? (a) 33rd (b) 31st (c) 32nd (d) 34th

Answer key

  1. 194
  2. 73
  3. 204
  4. 70
  5. 56
  6. 280
  7. 3240
  8. 85
  9. 24
  10. 112
  11. 300
  12. 21
  13. 18
  14. 2628
  15. 126
  16. 138
  17. 86
  18. 108
  19. 154
  20. 119
  21. 260
  22. 81
  23. 54
  24. 15
  25. 400
  26. 100
  27. 149
  28. 19
  29. 130
  30. 225
  31. 55
  32. 330
  33. 162
  34. 245
  35. 8
  36. 263
  37. 144
  38. 148
  39. 484
  40. 32nd

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