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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 870 · 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 38th term of the AP 1, 7, 13, 19, …? (a) 222 (b) 223 (c) 228 (d) 229
  2. 2.Which term of the AP 8, 11, 14, 17, … is 71? (a) 21st (b) 23rd (c) 22nd (d) 24th
  3. 3.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 3570 (c) 7140 (d) 3486
  4. 4.What is the sum of all the whole numbers from 1 to 74? (a) 2738 (b) 5550 (c) 2775 (d) 2701
  5. 5.What is the 40th term of the AP 10, 16, 22, 28, …? (a) 234 (b) 240 (c) 250 (d) 244
  6. 6.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 870 (c) 841 (d) 435
  7. 7.What is the 18th term of the AP 3, 8, 13, 18, …? (a) 93 (b) 88 (c) 90 (d) 85
  8. 8.What is the missing term in the AP 15, 18, ?, 24, 27? (a) 24 (b) 22 (c) 20 (d) 21
  9. 9.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 64 (c) 15 (d) 36
  10. 10.What is the 24th term of the AP 18, 23, 28, 33, …? (a) 120 (b) 115 (c) 138 (d) 133
  11. 11.What is the 14th term of the AP 6, 13, 20, 27, …? (a) 104 (b) 97 (c) 98 (d) 91
  12. 12.What is the 13th term of the AP 8, 13, 18, 23, …? (a) 68 (b) 73 (c) 65 (d) 60
  13. 13.What is the sum of the first 10 terms of the AP 5, 6, 7, …? (a) 100 (b) 95 (c) 14 (d) 190
  14. 14.Which term of the AP 20, 27, 34, 41, … is 195? (a) 25th (b) 27th (c) 26th (d) 28th
  15. 15.What is the 32nd term of the AP 17, 20, 23, 26, …? (a) 96 (b) 113 (c) 110 (d) 93
  16. 16.Which term of the AP 7, 13, 19, 25, … is 151? (a) 27th (b) 25th (c) 26th (d) 24th
  17. 17.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 56 (c) 13 (d) 28
  18. 18.What is the missing term in the AP 9, ?, 23, 30, 37? (a) 17 (b) 23 (c) 15 (d) 16
  19. 19.What is the sum of the first 11 terms of the AP 5, 7, 9, …? (a) 330 (b) 176 (c) 25 (d) 165
  20. 20.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 90 (d) 81
  21. 21.What is the sum of all the whole numbers from 1 to 90? (a) 4095 (b) 4050 (c) 4005 (d) 8190
  22. 22.What is the missing term in the AP 6, 8, 10, ?, 14? (a) 14 (b) 12 (c) 11 (d) 13
  23. 23.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 120 (b) 65 (c) 16 (d) 60
  24. 24.Which term of the AP 17, 24, 31, 38, … is 129? (a) 18th (b) 19th (c) 17th (d) 16th
  25. 25.Which term of the AP 7, 11, 15, 19, … is 91? (a) 22nd (b) 23rd (c) 21st (d) 24th
  26. 26.What is the 24th term of the AP 19, 23, 27, 31, …? (a) 115 (b) 96 (c) 111 (d) 92
  27. 27.What is the 32nd term of the AP 20, 22, 24, 26, …? (a) 82 (b) 62 (c) 84 (d) 64
  28. 28.What is the missing term in the AP 6, 15, ?, 33, 42? (a) 33 (b) 24 (c) 25 (d) 23
  29. 29.Which term of the AP 12, 14, 16, 18, … is 42? (a) 21st (b) 15th (c) 17th (d) 16th
  30. 30.Which term of the AP 19, 26, 33, 40, … is 68? (a) 10th (b) 7th (c) 9th (d) 8th
  31. 31.What is the sum of all the whole numbers from 1 to 76? (a) 2888 (b) 2850 (c) 2926 (d) 5852
  32. 32.Which term of the AP 7, 11, 15, 19, … is 159? (a) 40th (b) 38th (c) 41st (d) 39th
  33. 33.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 100 (c) 19 (d) 110
  34. 34.Which term of the AP 5, 14, 23, 32, … is 230? (a) 25th (b) 27th (c) 28th (d) 26th
  35. 35.What is the 33rd term of the AP 1, 6, 11, 16, …? (a) 161 (b) 166 (c) 160 (d) 165
  36. 36.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 361 (c) 190 (d) 37
  37. 37.What is the 12th term of the AP 20, 22, 24, 26, …? (a) 44 (b) 24 (c) 22 (d) 42
  38. 38.What is the sum of all the whole numbers from 1 to 61? (a) 1830 (b) 3782 (c) 1892 (d) 1891
  39. 39.What is the sum of the first 11 terms of the AP 1, 7, 13, …? (a) 682 (b) 61 (c) 341 (d) 374
  40. 40.What is the 12th term of the AP 7, 10, 13, 16, …? (a) 36 (b) 40 (c) 33 (d) 43

Answer key

  1. 223
  2. 22nd
  3. 3570
  4. 2775
  5. 244
  6. 841
  7. 88
  8. 21
  9. 64
  10. 133
  11. 97
  12. 68
  13. 95
  14. 26th
  15. 110
  16. 25th
  17. 49
  18. 16
  19. 165
  20. 81
  21. 4095
  22. 12
  23. 60
  24. 17th
  25. 22nd
  26. 111
  27. 82
  28. 24
  29. 16th
  30. 8th
  31. 2926
  32. 39th
  33. 100
  34. 26th
  35. 161
  36. 361
  37. 42
  38. 1891
  39. 341
  40. 40

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