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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 891 · 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 6, 12, 18, …? (a) 36 (b) 144 (c) 126 (d) 252
  2. 2.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 784 (c) 406 (d) 812
  3. 3.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 5 (b) 4 (c) 3 (d) 7
  4. 4.What is the 16th term of the AP 18, 24, 30, 36, …? (a) 96 (b) 90 (c) 108 (d) 114
  5. 5.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 81 (c) 90 (d) 45
  6. 6.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 13 (b) 88 (c) 176 (d) 89
  7. 7.What is the 38th term of the AP 2, 5, 8, 11, …? (a) 111 (b) 113 (c) 116 (d) 114
  8. 8.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 105 (d) 196
  9. 9.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 408 (b) 378 (c) 756 (d) 59
  10. 10.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 65 (b) 16 (c) 120 (d) 60
  11. 11.Which term of the AP 16, 19, 22, 25, … is 85? (a) 25th (b) 26th (c) 23rd (d) 24th
  12. 12.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 138 (b) 240 (c) 35 (d) 120
  13. 13.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 54 (b) 11 (c) 51 (d) 102
  14. 14.What is the missing term in the AP 13, 15, ?, 19, 21? (a) 16 (b) 19 (c) 18 (d) 17
  15. 15.What is the sum of all the whole numbers from 1 to 50? (a) 1275 (b) 1225 (c) 2550 (d) 1250
  16. 16.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 272 (c) 136 (d) 256
  17. 17.What is the 32nd term of the AP 3, 5, 7, 9, …? (a) 64 (b) 62 (c) 65 (d) 67
  18. 18.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 110 (b) 60 (c) 55 (d) 15
  19. 19.What is the missing term in the AP 8, 14, ?, 26, 32? (a) 20 (b) 21 (c) 26 (d) 19
  20. 20.What is the missing term in the AP 12, ?, 22, 27, 32? (a) 17 (b) 18 (c) 22 (d) 16
  21. 21.What is the 24th term of the AP 19, 22, 25, 28, …? (a) 69 (b) 91 (c) 72 (d) 88
  22. 22.What is the missing term in the AP 11, ?, 23, 29, 35? (a) 18 (b) 16 (c) 17 (d) 23
  23. 23.What is the 15th term of the AP 9, 13, 17, 21, …? (a) 60 (b) 56 (c) 65 (d) 69
  24. 24.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 10 (b) 6 (c) 7 (d) 5
  25. 25.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 196 (b) 42 (c) 392 (d) 216
  26. 26.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 21 (c) 42 (d) 36
  27. 27.What is the missing term in the AP 16, 18, ?, 22, 24? (a) 21 (b) 19 (c) 20 (d) 22
  28. 28.What is the missing term in the AP 12, ?, 20, 24, 28? (a) 15 (b) 17 (c) 16 (d) 20
  29. 29.Which term of the AP 12, 20, 28, 36, … is 252? (a) 32nd (b) 31st (c) 30th (d) 33rd
  30. 30.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 17 (b) 45 (c) 90 (d) 55
  31. 31.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 14 (b) 55 (c) 50 (d) 100
  32. 32.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 84 (b) 144 (c) 22 (d) 72
  33. 33.What is the 17th term of the AP 18, 22, 26, 30, …? (a) 68 (b) 64 (c) 82 (d) 86
  34. 34.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 200 (b) 28 (c) 190 (d) 380
  35. 35.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 110 (b) 31 (c) 190 (d) 95
  36. 36.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 37 (b) 176 (c) 312 (d) 156
  37. 37.Which term of the AP 8, 12, 16, 20, … is 56? (a) 14th (b) 13th (c) 15th (d) 12th
  38. 38.What is the 35th term of the AP 12, 19, 26, 33, …? (a) 238 (b) 257 (c) 245 (d) 250
  39. 39.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 51 (c) 351 (d) 702
  40. 40.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 528 (c) 496 (d) 512

Answer key

  1. 126
  2. 784
  3. 4
  4. 108
  5. 81
  6. 88
  7. 113
  8. 196
  9. 378
  10. 60
  11. 24th
  12. 120
  13. 51
  14. 17
  15. 1275
  16. 256
  17. 65
  18. 55
  19. 20
  20. 17
  21. 88
  22. 17
  23. 65
  24. 6
  25. 196
  26. 36
  27. 20
  28. 16
  29. 31st
  30. 45
  31. 50
  32. 72
  33. 82
  34. 190
  35. 95
  36. 156
  37. 13th
  38. 250
  39. 676
  40. 528

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