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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 183 · 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 missing term in the AP 18, 26, ?, 42, 50? (a) 42 (b) 35 (c) 34 (d) 33
  2. 2.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 7 (b) 8 (c) 6 (d) 9
  3. 3.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 240 (b) 220 (c) 40 (d) 440
  4. 4.What is the missing term in the AP 1, 10, ?, 28, 37? (a) 18 (b) 20 (c) 28 (d) 19
  5. 5.What is the 32nd term of the AP 16, 24, 32, 40, …? (a) 272 (b) 264 (c) 256 (d) 248
  6. 6.What is the 32nd term of the AP 20, 27, 34, 41, …? (a) 217 (b) 237 (c) 224 (d) 244
  7. 7.What is the 25th term of the AP 5, 14, 23, 32, …? (a) 230 (b) 225 (c) 221 (d) 216
  8. 8.What is the 24th term of the AP 16, 19, 22, 25, …? (a) 72 (b) 88 (c) 85 (d) 69
  9. 9.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 858 (b) 462 (c) 429 (d) 69
  10. 10.Which term of the AP 8, 16, 24, 32, … is 304? (a) 39th (b) 38th (c) 40th (d) 37th
  11. 11.Which term of the AP 17, 20, 23, 26, … is 116? (a) 36th (b) 34th (c) 33rd (d) 35th
  12. 12.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 253 (c) 231 (d) 506
  13. 13.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 42 (d) 21
  14. 14.Which term of the AP 1, 3, 5, 7, … is 25? (a) 13th (b) 15th (c) 14th (d) 12th
  15. 15.What is the 33rd term of the AP 10, 18, 26, 34, …? (a) 256 (b) 266 (c) 274 (d) 264
  16. 16.What is the sum of the first 7 terms of the AP 8, 13, 18, …? (a) 38 (b) 161 (c) 322 (d) 166
  17. 17.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 78 (c) 156 (d) 66
  18. 18.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 306 (c) 153 (d) 33
  19. 19.What is the 21st term of the AP 5, 10, 15, 20, …? (a) 110 (b) 105 (c) 100 (d) 106
  20. 20.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 250 (b) 43 (c) 270 (d) 500
  21. 21.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 105 (c) 196 (d) 210
  22. 22.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 242 (b) 21 (c) 121 (d) 132
  23. 23.What is the 21st term of the AP 10, 17, 24, 31, …? (a) 140 (b) 157 (c) 147 (d) 150
  24. 24.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 430 (b) 35 (c) 230 (d) 215
  25. 25.What is the sum of the first 12 terms of the AP 4, 7, 10, …? (a) 37 (b) 246 (c) 264 (d) 492
  26. 26.Which term of the AP 8, 16, 24, 32, … is 272? (a) 33rd (b) 35th (c) 34th (d) 36th
  27. 27.What is the sum of the first 9 terms of the AP 6, 11, 16, …? (a) 234 (b) 46 (c) 239 (d) 468
  28. 28.What is the sum of the first 12 terms of the AP 9, 14, 19, …? (a) 876 (b) 468 (c) 438 (d) 64
  29. 29.What is the sum of all the whole numbers from 1 to 53? (a) 1432 (b) 1431 (c) 1378 (d) 2862
  30. 30.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 160 (b) 85 (c) 26 (d) 80
  31. 31.What is the 12th term of the AP 5, 8, 11, 14, …? (a) 41 (b) 38 (c) 36 (d) 33
  32. 32.What is the 25th term of the AP 12, 16, 20, 24, …? (a) 100 (b) 112 (c) 108 (d) 96
  33. 33.What is the 17th term of the AP 15, 21, 27, 33, …? (a) 117 (b) 102 (c) 96 (d) 111
  34. 34.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 484 (c) 43 (d) 506
  35. 35.Which term of the AP 3, 11, 19, 27, … is 299? (a) 40th (b) 38th (c) 39th (d) 37th
  36. 36.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 81 (c) 17 (d) 90
  37. 37.What is the 14th term of the AP 9, 16, 23, 30, …? (a) 91 (b) 98 (c) 107 (d) 100
  38. 38.What is the 11th term of the AP 3, 9, 15, 21, …? (a) 69 (b) 63 (c) 66 (d) 60
  39. 39.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 187 (b) 374 (c) 32 (d) 190
  40. 40.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 66 (c) 121 (d) 132

Answer key

  1. 34
  2. 7
  3. 220
  4. 19
  5. 264
  6. 237
  7. 221
  8. 85
  9. 429
  10. 38th
  11. 34th
  12. 253
  13. 36
  14. 13th
  15. 266
  16. 161
  17. 78
  18. 289
  19. 105
  20. 250
  21. 196
  22. 121
  23. 150
  24. 215
  25. 246
  26. 34th
  27. 234
  28. 438
  29. 1431
  30. 80
  31. 38
  32. 108
  33. 111
  34. 484
  35. 38th
  36. 81
  37. 100
  38. 63
  39. 187
  40. 121

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