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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 591 · 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.Which term of the AP 2, 6, 10, 14, … is 98? (a) 27th (b) 24th (c) 26th (d) 25th
  2. 2.Which term of the AP 19, 27, 35, 43, … is 259? (a) 30th (b) 31st (c) 32nd (d) 33rd
  3. 3.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 540 (b) 50 (c) 275 (d) 270
  4. 4.What is the 12th term of the AP 8, 12, 16, 20, …? (a) 44 (b) 56 (c) 52 (d) 48
  5. 5.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 88 (b) 44 (c) 9 (d) 48
  6. 6.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 143 (b) 286 (c) 23 (d) 154
  7. 7.Which term of the AP 1, 9, 17, 25, … is 305? (a) 39th (b) 41st (c) 40th (d) 38th
  8. 8.What is the 12th term of the AP 3, 10, 17, 24, …? (a) 77 (b) 80 (c) 87 (d) 84
  9. 9.What is the sum of all the whole numbers from 1 to 51? (a) 1275 (b) 1326 (c) 1327 (d) 2652
  10. 10.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 31 (c) 256 (d) 136
  11. 11.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 379 (c) 378 (d) 756
  12. 12.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 210 (b) 27 (c) 119 (d) 105
  13. 13.What is the 24th term of the AP 8, 10, 12, 14, …? (a) 56 (b) 46 (c) 54 (d) 48
  14. 14.What is the sum of all the whole numbers from 1 to 68? (a) 2312 (b) 2278 (c) 4692 (d) 2346
  15. 15.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 420 (c) 210 (d) 39
  16. 16.What is the 29th term of the AP 15, 22, 29, 36, …? (a) 203 (b) 196 (c) 211 (d) 218
  17. 17.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 100 (d) 110
  18. 18.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 441 (c) 462 (d) 231
  19. 19.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 625 (c) 325 (d) 49
  20. 20.What is the 22nd term of the AP 2, 5, 8, 11, …? (a) 63 (b) 65 (c) 66 (d) 68
  21. 21.What is the 20th term of the AP 16, 24, 32, 40, …? (a) 152 (b) 160 (c) 176 (d) 168
  22. 22.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 576 (c) 47 (d) 300
  23. 23.What is the 20th term of the AP 9, 16, 23, 30, …? (a) 149 (b) 140 (c) 133 (d) 142
  24. 24.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 81 (b) 90 (c) 17 (d) 162
  25. 25.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 240 (c) 120 (d) 225
  26. 26.What is the sum of all the whole numbers from 1 to 54? (a) 1458 (b) 1431 (c) 2970 (d) 1485
  27. 27.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 22 (b) 14 (c) 15 (d) 16
  28. 28.Which term of the AP 1, 7, 13, 19, … is 235? (a) 42nd (b) 41st (c) 39th (d) 40th
  29. 29.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 75 (b) 1008 (c) 540 (d) 504
  30. 30.What is the missing term in the AP 1, ?, 13, 19, 25? (a) 13 (b) 7 (c) 8 (d) 6
  31. 31.What is the sum of the first 7 terms of the AP 9, 14, 19, …? (a) 173 (b) 336 (c) 39 (d) 168
  32. 32.What is the sum of all the whole numbers from 1 to 77? (a) 2926 (b) 6006 (c) 3003 (d) 3004
  33. 33.What is the sum of all the whole numbers from 1 to 61? (a) 1892 (b) 1891 (c) 3782 (d) 1830
  34. 34.What is the missing term in the AP 7, 16, 25, ?, 43? (a) 43 (b) 33 (c) 34 (d) 35
  35. 35.What is the sum of the first 9 terms of the AP 6, 11, 16, …? (a) 468 (b) 239 (c) 234 (d) 46
  36. 36.What is the 27th term of the AP 5, 10, 15, 20, …? (a) 140 (b) 136 (c) 130 (d) 135
  37. 37.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 372 (b) 342 (c) 56 (d) 684
  38. 38.What is the 11th term of the AP 8, 15, 22, 29, …? (a) 78 (b) 70 (c) 85 (d) 77
  39. 39.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 26 (b) 25 (c) 7 (d) 50
  40. 40.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 89 (b) 13 (c) 88 (d) 176

Answer key

  1. 25th
  2. 31st
  3. 270
  4. 52
  5. 44
  6. 143
  7. 39th
  8. 80
  9. 1326
  10. 256
  11. 378
  12. 105
  13. 54
  14. 2346
  15. 400
  16. 211
  17. 100
  18. 441
  19. 625
  20. 65
  21. 168
  22. 576
  23. 142
  24. 81
  25. 225
  26. 1485
  27. 15
  28. 40th
  29. 504
  30. 7
  31. 168
  32. 3003
  33. 1891
  34. 34
  35. 234
  36. 135
  37. 342
  38. 78
  39. 25
  40. 88

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