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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 856 · 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 18th term of the AP 2, 8, 14, 20, …? (a) 110 (b) 104 (c) 102 (d) 108
  2. 2.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 784 (d) 55
  3. 3.What is the 11th term of the AP 3, 5, 7, 9, …? (a) 25 (b) 23 (c) 22 (d) 20
  4. 4.What is the sum of the first 10 terms of the AP 6, 7, 8, …? (a) 210 (b) 15 (c) 105 (d) 110
  5. 5.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 441 (c) 462 (d) 231
  6. 6.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 224 (b) 117 (c) 31 (d) 112
  7. 7.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 26 (b) 162 (c) 171 (d) 324
  8. 8.What is the sum of all the whole numbers from 1 to 40? (a) 780 (b) 1640 (c) 820 (d) 800
  9. 9.What is the missing term in the AP 10, 13, 16, ?, 22? (a) 20 (b) 18 (c) 22 (d) 19
  10. 10.What is the missing term in the AP 5, 9, ?, 17, 21? (a) 14 (b) 17 (c) 12 (d) 13
  11. 11.What is the sum of the first 6 terms of the AP 10, 13, 16, …? (a) 114 (b) 105 (c) 210 (d) 25
  12. 12.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 380 (c) 361 (d) 37
  13. 13.What is the 17th term of the AP 3, 5, 7, 9, …? (a) 34 (b) 32 (c) 37 (d) 35
  14. 14.Which term of the AP 17, 25, 33, 41, … is 273? (a) 35th (b) 32nd (c) 33rd (d) 34th
  15. 15.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 144 (c) 23 (d) 156
  16. 16.What is the 27th term of the AP 14, 16, 18, 20, …? (a) 54 (b) 68 (c) 52 (d) 66
  17. 17.What is the missing term in the AP 14, 17, 20, ?, 26? (a) 26 (b) 23 (c) 22 (d) 24
  18. 18.What is the 19th term of the AP 1, 6, 11, 16, …? (a) 95 (b) 96 (c) 90 (d) 91
  19. 19.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 27 (b) 150 (c) 75 (d) 90
  20. 20.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 114 (b) 31 (c) 192 (d) 96
  21. 21.What is the sum of all the whole numbers from 1 to 99? (a) 4951 (b) 4851 (c) 9900 (d) 4950
  22. 22.What is the 13th term of the AP 19, 22, 25, 28, …? (a) 39 (b) 55 (c) 58 (d) 36
  23. 23.What is the 18th term of the AP 15, 17, 19, 21, …? (a) 34 (b) 51 (c) 49 (d) 36
  24. 24.What is the missing term in the AP 7, ?, 11, 13, 15? (a) 9 (b) 8 (c) 11 (d) 10
  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 missing term in the AP 3, 12, ?, 30, 39? (a) 30 (b) 20 (c) 21 (d) 22
  27. 27.What is the sum of all the whole numbers from 1 to 38? (a) 741 (b) 703 (c) 1482 (d) 722
  28. 28.What is the 17th term of the AP 1, 4, 7, 10, …? (a) 51 (b) 52 (c) 49 (d) 48
  29. 29.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 80 (b) 20 (c) 77 (d) 154
  30. 30.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 435 (c) 436 (d) 406
  31. 31.What is the 13th term of the AP 17, 24, 31, 38, …? (a) 91 (b) 108 (c) 101 (d) 84
  32. 32.What is the sum of all the whole numbers from 1 to 52? (a) 1352 (b) 2756 (c) 1378 (d) 1326
  33. 33.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 121 (c) 105 (d) 120
  34. 34.What is the 20th term of the AP 9, 14, 19, 24, …? (a) 104 (b) 100 (c) 109 (d) 95
  35. 35.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 130 (b) 19 (c) 65 (d) 68
  36. 36.Which term of the AP 19, 23, 27, 31, … is 151? (a) 34th (b) 36th (c) 35th (d) 33rd
  37. 37.What is the sum of all the whole numbers from 1 to 24? (a) 276 (b) 600 (c) 300 (d) 288
  38. 38.Which term of the AP 2, 7, 12, 17, … is 162? (a) 35th (b) 34th (c) 33rd (d) 32nd
  39. 39.What is the 16th term of the AP 17, 22, 27, 32, …? (a) 92 (b) 75 (c) 97 (d) 80
  40. 40.What is the 34th term of the AP 12, 18, 24, 30, …? (a) 204 (b) 198 (c) 216 (d) 210

Answer key

  1. 104
  2. 784
  3. 23
  4. 105
  5. 441
  6. 112
  7. 162
  8. 820
  9. 19
  10. 13
  11. 105
  12. 361
  13. 35
  14. 33rd
  15. 144
  16. 66
  17. 23
  18. 91
  19. 75
  20. 96
  21. 4950
  22. 55
  23. 49
  24. 9
  25. 400
  26. 21
  27. 741
  28. 49
  29. 77
  30. 435
  31. 101
  32. 1378
  33. 120
  34. 104
  35. 65
  36. 34th
  37. 300
  38. 33rd
  39. 92
  40. 210

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