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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 889 · 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 sum of the first 6 terms of the AP 7, 8, 9, …? (a) 114 (b) 12 (c) 57 (d) 60
  2. 2.What is the 36th term of the AP 19, 28, 37, 46, …? (a) 315 (b) 324 (c) 343 (d) 334
  3. 3.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 72 (c) 15 (d) 36
  4. 4.What is the sum of all the whole numbers from 1 to 39? (a) 1560 (b) 780 (c) 781 (d) 741
  5. 5.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 162 (b) 165 (c) 30 (d) 324
  6. 6.What is the sum of all the whole numbers from 1 to 86? (a) 3741 (b) 7482 (c) 3655 (d) 3698
  7. 7.What is the sum of the first 9 terms of the AP 2, 8, 14, …? (a) 50 (b) 261 (c) 234 (d) 468
  8. 8.What is the missing term in the AP 8, ?, 20, 26, 32? (a) 13 (b) 20 (c) 15 (d) 14
  9. 9.What is the 25th term of the AP 20, 23, 26, 29, …? (a) 92 (b) 75 (c) 72 (d) 95
  10. 10.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 276 (c) 45 (d) 529
  11. 11.What is the 10th term of the AP 8, 17, 26, 35, …? (a) 89 (b) 81 (c) 90 (d) 98
  12. 12.Which term of the AP 12, 21, 30, 39, … is 192? (a) 20th (b) 22nd (c) 21st (d) 23rd
  13. 13.What is the sum of the first 12 terms of the AP 4, 10, 16, …? (a) 444 (b) 70 (c) 888 (d) 480
  14. 14.What is the 29th term of the AP 1, 10, 19, 28, …? (a) 261 (b) 252 (c) 253 (d) 262
  15. 15.What is the 26th term of the AP 10, 19, 28, 37, …? (a) 225 (b) 235 (c) 244 (d) 234
  16. 16.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 441 (c) 231 (d) 41
  17. 17.What is the 27th term of the AP 4, 13, 22, 31, …? (a) 234 (b) 243 (c) 238 (d) 247
  18. 18.What is the 39th term of the AP 13, 18, 23, 28, …? (a) 190 (b) 203 (c) 208 (d) 195
  19. 19.What is the sum of the first 8 terms of the AP 1, 4, 7, …? (a) 184 (b) 22 (c) 92 (d) 104
  20. 20.What is the missing term in the AP 11, 19, 27, ?, 43? (a) 36 (b) 35 (c) 43 (d) 34
  21. 21.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 14 (b) 40 (c) 80 (d) 43
  22. 22.What is the sum of the first 10 terms of the AP 8, 9, 10, …? (a) 250 (b) 130 (c) 125 (d) 17
  23. 23.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 49 (b) 56 (c) 13 (d) 98
  24. 24.What is the 38th term of the AP 5, 12, 19, 26, …? (a) 259 (b) 266 (c) 271 (d) 264
  25. 25.What is the 37th term of the AP 1, 7, 13, 19, …? (a) 223 (b) 222 (c) 217 (d) 216
  26. 26.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 47 (b) 270 (c) 245 (d) 490
  27. 27.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 26 (b) 85 (c) 140 (d) 70
  28. 28.Which term of the AP 18, 20, 22, 24, … is 50? (a) 17th (b) 25th (c) 16th (d) 18th
  29. 29.What is the sum of the first 11 terms of the AP 3, 8, 13, …? (a) 53 (b) 616 (c) 308 (d) 313
  30. 30.What is the 18th term of the AP 6, 10, 14, 18, …? (a) 78 (b) 68 (c) 74 (d) 72
  31. 31.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 62 (b) 444 (c) 414 (d) 828
  32. 32.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 225 (c) 120 (d) 240
  33. 33.What is the 14th term of the AP 5, 10, 15, 20, …? (a) 65 (b) 75 (c) 71 (d) 70
  34. 34.Which term of the AP 18, 26, 34, 42, … is 314? (a) 37th (b) 39th (c) 40th (d) 38th
  35. 35.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 100 (d) 110
  36. 36.What is the 14th term of the AP 11, 13, 15, 17, …? (a) 39 (b) 28 (c) 37 (d) 26
  37. 37.Which term of the AP 17, 25, 33, 41, … is 225? (a) 29th (b) 26th (c) 28th (d) 27th
  38. 38.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 126 (b) 127 (c) 252 (d) 18
  39. 39.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 37 (b) 154 (c) 133 (d) 266
  40. 40.What is the 16th term of the AP 7, 10, 13, 16, …? (a) 55 (b) 48 (c) 45 (d) 52

Answer key

  1. 57
  2. 334
  3. 64
  4. 780
  5. 162
  6. 3741
  7. 234
  8. 14
  9. 92
  10. 529
  11. 89
  12. 21st
  13. 444
  14. 253
  15. 235
  16. 441
  17. 238
  18. 203
  19. 92
  20. 35
  21. 40
  22. 125
  23. 49
  24. 264
  25. 217
  26. 245
  27. 70
  28. 17th
  29. 308
  30. 74
  31. 414
  32. 225
  33. 70
  34. 38th
  35. 100
  36. 37
  37. 27th
  38. 126
  39. 133
  40. 52

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