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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 160 · 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 11 terms of the AP 3, 4, 5, …? (a) 88 (b) 13 (c) 176 (d) 89
  2. 2.Which term of the AP 4, 9, 14, 19, … is 154? (a) 33rd (b) 30th (c) 32nd (d) 31st
  3. 3.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 84 (b) 144 (c) 72 (d) 22
  4. 4.What is the 21st term of the AP 6, 8, 10, 12, …? (a) 40 (b) 42 (c) 48 (d) 46
  5. 5.What is the missing term in the AP 7, 16, 25, ?, 43? (a) 35 (b) 43 (c) 34 (d) 33
  6. 6.What is the 11th term of the AP 19, 27, 35, 43, …? (a) 88 (b) 107 (c) 80 (d) 99
  7. 7.What is the 31st term of the AP 7, 11, 15, 19, …? (a) 124 (b) 127 (c) 120 (d) 131
  8. 8.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 82 (b) 13 (c) 81 (d) 162
  9. 9.Which term of the AP 13, 15, 17, 19, … is 89? (a) 39th (b) 41st (c) 38th (d) 40th
  10. 10.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 120 (d) 29
  11. 11.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 47 (c) 300 (d) 600
  12. 12.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 2016 (c) 2080 (d) 4160
  13. 13.What is the missing term in the AP 9, 18, ?, 36, 45? (a) 28 (b) 36 (c) 27 (d) 26
  14. 14.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 110 (b) 220 (c) 20 (d) 120
  15. 15.What is the 17th term of the AP 9, 13, 17, 21, …? (a) 77 (b) 73 (c) 68 (d) 64
  16. 16.What is the sum of the first 6 terms of the AP 8, 14, 20, …? (a) 138 (b) 156 (c) 276 (d) 38
  17. 17.What is the 23rd term of the AP 14, 18, 22, 26, …? (a) 92 (b) 88 (c) 106 (d) 102
  18. 18.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 870 (c) 435 (d) 57
  19. 19.Which term of the AP 13, 16, 19, 22, … is 46? (a) 11th (b) 13th (c) 14th (d) 12th
  20. 20.What is the sum of the first 8 terms of the AP 9, 10, 11, …? (a) 200 (b) 100 (c) 16 (d) 104
  21. 21.Which term of the AP 17, 25, 33, 41, … is 201? (a) 24th (b) 26th (c) 25th (d) 23rd
  22. 22.Which term of the AP 11, 17, 23, 29, … is 233? (a) 37th (b) 39th (c) 40th (d) 38th
  23. 23.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 1260 (c) 630 (d) 595
  24. 24.What is the sum of all the whole numbers from 1 to 90? (a) 4050 (b) 4005 (c) 8190 (d) 4095
  25. 25.What is the 17th term of the AP 11, 16, 21, 26, …? (a) 85 (b) 96 (c) 91 (d) 80
  26. 26.What is the sum of the first 10 terms of the AP 10, 12, 14, …? (a) 380 (b) 200 (c) 28 (d) 190
  27. 27.What is the sum of all the whole numbers from 1 to 63? (a) 2017 (b) 2016 (c) 1953 (d) 4032
  28. 28.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 325 (c) 49 (d) 650
  29. 29.What is the 30th term of the AP 15, 24, 33, 42, …? (a) 276 (b) 270 (c) 261 (d) 285
  30. 30.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 312 (b) 588 (c) 294 (d) 41
  31. 31.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 408 (b) 216 (c) 28 (d) 204
  32. 32.Which term of the AP 11, 18, 25, 32, … is 179? (a) 27th (b) 26th (c) 24th (d) 25th
  33. 33.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 84 (b) 15 (c) 85 (d) 168
  34. 34.Which term of the AP 20, 29, 38, 47, … is 101? (a) 9th (b) 11th (c) 10th (d) 12th
  35. 35.What is the 21st term of the AP 14, 16, 18, 20, …? (a) 56 (b) 42 (c) 54 (d) 40
  36. 36.What is the 14th term of the AP 20, 29, 38, 47, …? (a) 137 (b) 117 (c) 146 (d) 126
  37. 37.What is the sum of the first 12 terms of the AP 1, 2, 3, …? (a) 84 (b) 156 (c) 12 (d) 78
  38. 38.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 138 (b) 123 (c) 246 (d) 33
  39. 39.What is the missing term in the AP 10, 17, 24, ?, 38? (a) 31 (b) 38 (c) 32 (d) 30
  40. 40.What is the 11th term of the AP 16, 24, 32, 40, …? (a) 104 (b) 80 (c) 88 (d) 96

Answer key

  1. 88
  2. 31st
  3. 72
  4. 46
  5. 34
  6. 99
  7. 127
  8. 81
  9. 39th
  10. 225
  11. 576
  12. 2080
  13. 27
  14. 110
  15. 73
  16. 138
  17. 102
  18. 841
  19. 12th
  20. 100
  21. 24th
  22. 38th
  23. 630
  24. 4095
  25. 91
  26. 190
  27. 2016
  28. 625
  29. 276
  30. 294
  31. 204
  32. 25th
  33. 84
  34. 10th
  35. 54
  36. 137
  37. 78
  38. 123
  39. 31
  40. 96

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