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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 848 · 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 25th term of the AP 12, 15, 18, 21, …? (a) 87 (b) 75 (c) 72 (d) 84
  2. 2.What is the 27th term of the AP 15, 22, 29, 36, …? (a) 182 (b) 197 (c) 189 (d) 204
  3. 3.What is the missing term in the AP 6, 11, ?, 21, 26? (a) 16 (b) 15 (c) 21 (d) 17
  4. 4.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 252 (b) 126 (c) 129 (d) 27
  5. 5.What is the sum of all the whole numbers from 1 to 66? (a) 4422 (b) 2145 (c) 2178 (d) 2211
  6. 6.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 12 (b) 45 (c) 80 (d) 40
  7. 7.What is the 29th term of the AP 10, 12, 14, 16, …? (a) 56 (b) 68 (c) 66 (d) 58
  8. 8.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 380 (c) 190 (d) 191
  9. 9.What is the 38th term of the AP 12, 20, 28, 36, …? (a) 308 (b) 304 (c) 296 (d) 316
  10. 10.What is the 31st term of the AP 9, 14, 19, 24, …? (a) 164 (b) 155 (c) 150 (d) 159
  11. 11.What is the sum of all the whole numbers from 1 to 55? (a) 1540 (b) 1541 (c) 1485 (d) 3080
  12. 12.What is the sum of all the whole numbers from 1 to 82? (a) 3362 (b) 6806 (c) 3321 (d) 3403
  13. 13.What is the sum of all the whole numbers from 1 to 53? (a) 2862 (b) 1378 (c) 1432 (d) 1431
  14. 14.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 22 (b) 128 (c) 240 (d) 120
  15. 15.What is the 18th term of the AP 13, 15, 17, 19, …? (a) 49 (b) 34 (c) 36 (d) 47
  16. 16.What is the 36th term of the AP 15, 17, 19, 21, …? (a) 85 (b) 70 (c) 72 (d) 87
  17. 17.What is the missing term in the AP 13, 15, 17, ?, 21? (a) 21 (b) 18 (c) 19 (d) 20
  18. 18.What is the missing term in the AP 3, 7, ?, 15, 19? (a) 12 (b) 10 (c) 15 (d) 11
  19. 19.What is the 35th term of the AP 12, 14, 16, 18, …? (a) 82 (b) 68 (c) 80 (d) 70
  20. 20.What is the 17th term of the AP 19, 24, 29, 34, …? (a) 85 (b) 104 (c) 99 (d) 80
  21. 21.What is the 35th term of the AP 4, 7, 10, 13, …? (a) 106 (b) 109 (c) 105 (d) 102
  22. 22.What is the 17th term of the AP 11, 15, 19, 23, …? (a) 64 (b) 79 (c) 68 (d) 75
  23. 23.What is the 14th term of the AP 19, 21, 23, 25, …? (a) 28 (b) 45 (c) 47 (d) 26
  24. 24.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 396 (b) 363 (c) 63 (d) 726
  25. 25.What is the 40th term of the AP 17, 25, 33, 41, …? (a) 337 (b) 329 (c) 320 (d) 312
  26. 26.What is the sum of all the whole numbers from 1 to 75? (a) 2850 (b) 2851 (c) 5700 (d) 2775
  27. 27.What is the 32nd term of the AP 12, 15, 18, 21, …? (a) 105 (b) 96 (c) 93 (d) 108
  28. 28.What is the 32nd term of the AP 15, 17, 19, 21, …? (a) 64 (b) 62 (c) 79 (d) 77
  29. 29.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 5050 (c) 10100 (d) 5000
  30. 30.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 144 (b) 16 (c) 72 (d) 80
  31. 31.What is the 17th term of the AP 5, 12, 19, 26, …? (a) 112 (b) 117 (c) 124 (d) 119
  32. 32.What is the 28th term of the AP 15, 17, 19, 21, …? (a) 54 (b) 71 (c) 56 (d) 69
  33. 33.What is the missing term in the AP 14, 23, ?, 41, 50? (a) 33 (b) 32 (c) 31 (d) 41
  34. 34.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 35 (b) 10 (c) 60 (d) 30
  35. 35.Which term of the AP 5, 11, 17, 23, … is 47? (a) 9th (b) 10th (c) 8th (d) 7th
  36. 36.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 59 (c) 900 (d) 465
  37. 37.What is the 34th term of the AP 10, 12, 14, 16, …? (a) 68 (b) 78 (c) 66 (d) 76
  38. 38.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 19 (c) 110 (d) 55
  39. 39.What is the 21st term of the AP 18, 20, 22, 24, …? (a) 42 (b) 58 (c) 60 (d) 40
  40. 40.What is the 11th term of the AP 18, 26, 34, 42, …? (a) 106 (b) 98 (c) 88 (d) 80

Answer key

  1. 84
  2. 197
  3. 16
  4. 126
  5. 2211
  6. 40
  7. 66
  8. 190
  9. 308
  10. 159
  11. 1540
  12. 3403
  13. 1431
  14. 120
  15. 47
  16. 85
  17. 19
  18. 11
  19. 80
  20. 99
  21. 106
  22. 75
  23. 45
  24. 363
  25. 329
  26. 2850
  27. 105
  28. 77
  29. 5050
  30. 72
  31. 117
  32. 69
  33. 32
  34. 30
  35. 8th
  36. 900
  37. 76
  38. 100
  39. 58
  40. 98

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