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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 715 · 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 23rd term of the AP 18, 27, 36, 45, …? (a) 207 (b) 198 (c) 225 (d) 216
  2. 2.What is the missing term in the AP 6, 14, 22, ?, 38? (a) 29 (b) 38 (c) 31 (d) 30
  3. 3.What is the missing term in the AP 20, 27, ?, 41, 48? (a) 41 (b) 35 (c) 33 (d) 34
  4. 4.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 217 (b) 46 (c) 392 (d) 196
  5. 5.What is the sum of all the whole numbers from 1 to 86? (a) 7482 (b) 3741 (c) 3655 (d) 3698
  6. 6.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 264 (b) 252 (c) 504 (d) 32
  7. 7.What is the 18th term of the AP 19, 28, 37, 46, …? (a) 153 (b) 172 (c) 162 (d) 181
  8. 8.What is the 37th term of the AP 5, 14, 23, 32, …? (a) 324 (b) 338 (c) 333 (d) 329
  9. 9.What is the 40th term of the AP 10, 16, 22, 28, …? (a) 244 (b) 250 (c) 240 (d) 234
  10. 10.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 118 (b) 234 (c) 17 (d) 117
  11. 11.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 112 (b) 26 (c) 98 (d) 196
  12. 12.What is the 18th term of the AP 11, 14, 17, 20, …? (a) 51 (b) 62 (c) 54 (d) 65
  13. 13.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 210 (c) 196 (d) 27
  14. 14.What is the 38th term of the AP 7, 9, 11, 13, …? (a) 83 (b) 76 (c) 74 (d) 81
  15. 15.What is the 22nd term of the AP 15, 20, 25, 30, …? (a) 125 (b) 120 (c) 105 (d) 110
  16. 16.What is the 16th term of the AP 7, 16, 25, 34, …? (a) 151 (b) 135 (c) 142 (d) 144
  17. 17.What is the 17th term of the AP 15, 20, 25, 30, …? (a) 95 (b) 80 (c) 85 (d) 100
  18. 18.Which term of the AP 7, 16, 25, 34, … is 340? (a) 39th (b) 38th (c) 40th (d) 37th
  19. 19.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 756 (b) 59 (c) 408 (d) 378
  20. 20.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 52 (b) 496 (c) 272 (d) 248
  21. 21.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 30 (c) 25 (d) 15
  22. 22.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 110 (b) 17 (c) 58 (d) 55
  23. 23.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 49 (b) 261 (c) 266 (d) 522
  24. 24.What is the sum of the first 9 terms of the AP 2, 5, 8, …? (a) 129 (b) 126 (c) 252 (d) 26
  25. 25.What is the 21st term of the AP 7, 10, 13, 16, …? (a) 63 (b) 60 (c) 70 (d) 67
  26. 26.Which term of the AP 18, 20, 22, 24, … is 38? (a) 19th (b) 11th (c) 12th (d) 10th
  27. 27.Which term of the AP 19, 22, 25, 28, … is 94? (a) 28th (b) 25th (c) 27th (d) 26th
  28. 28.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 552 (c) 277 (d) 276
  29. 29.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 625 (c) 650 (d) 325
  30. 30.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 560 (b) 310 (c) 55 (d) 280
  31. 31.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 105 (b) 210 (c) 24 (d) 108
  32. 32.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 14 (b) 40 (c) 43 (d) 80
  33. 33.What is the 21st term of the AP 12, 21, 30, 39, …? (a) 192 (b) 189 (c) 180 (d) 201
  34. 34.What is the 10th term of the AP 6, 13, 20, 27, …? (a) 76 (b) 70 (c) 63 (d) 69
  35. 35.What is the 18th term of the AP 9, 15, 21, 27, …? (a) 102 (b) 111 (c) 108 (d) 117
  36. 36.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 55 (c) 812 (d) 406
  37. 37.What is the 26th term of the AP 11, 16, 21, 26, …? (a) 125 (b) 136 (c) 130 (d) 141
  38. 38.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 380 (d) 361
  39. 39.Which term of the AP 13, 18, 23, 28, … is 73? (a) 12th (b) 14th (c) 15th (d) 13th
  40. 40.What is the missing term in the AP 12, 20, ?, 36, 44? (a) 27 (b) 28 (c) 29 (d) 36

Answer key

  1. 216
  2. 30
  3. 34
  4. 196
  5. 3741
  6. 252
  7. 172
  8. 329
  9. 244
  10. 117
  11. 98
  12. 62
  13. 196
  14. 81
  15. 120
  16. 142
  17. 95
  18. 38th
  19. 378
  20. 248
  21. 25
  22. 55
  23. 261
  24. 126
  25. 67
  26. 11th
  27. 26th
  28. 276
  29. 625
  30. 280
  31. 105
  32. 40
  33. 192
  34. 69
  35. 111
  36. 784
  37. 136
  38. 361
  39. 13th
  40. 28

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