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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 993 · 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) 144 (b) 126 (c) 36 (d) 252
  2. 2.What is the 35th term of the AP 4, 11, 18, 25, …? (a) 245 (b) 249 (c) 242 (d) 238
  3. 3.Which term of the AP 12, 16, 20, 24, … is 156? (a) 39th (b) 38th (c) 37th (d) 36th
  4. 4.What is the missing term in the AP 17, 22, 27, ?, 37? (a) 37 (b) 32 (c) 33 (d) 31
  5. 5.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 44 (b) 48 (c) 9 (d) 88
  6. 6.What is the sum of the first 5 terms of the AP 8, 11, 14, …? (a) 70 (b) 20 (c) 140 (d) 73
  7. 7.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 37 (b) 132 (c) 150 (d) 264
  8. 8.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 2211 (c) 2279 (d) 4556
  9. 9.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 784 (c) 406 (d) 812
  10. 10.Which term of the AP 2, 10, 18, 26, … is 250? (a) 34th (b) 31st (c) 32nd (d) 33rd
  11. 11.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 576 (c) 47 (d) 300
  12. 12.What is the sum of all the whole numbers from 1 to 71? (a) 2485 (b) 2557 (c) 5112 (d) 2556
  13. 13.What is the 25th term of the AP 3, 9, 15, 21, …? (a) 150 (b) 153 (c) 144 (d) 147
  14. 14.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 441 (c) 41 (d) 231
  15. 15.What is the 33rd term of the AP 2, 6, 10, 14, …? (a) 134 (b) 132 (c) 130 (d) 128
  16. 16.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 30 (b) 60 (c) 8 (d) 31
  17. 17.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 17 (b) 108 (c) 112 (d) 216
  18. 18.Which term of the AP 20, 25, 30, 35, … is 170? (a) 30th (b) 32nd (c) 31st (d) 34th
  19. 19.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 64 (c) 15 (d) 72
  20. 20.What is the 39th term of the AP 14, 16, 18, 20, …? (a) 76 (b) 78 (c) 90 (d) 92
  21. 21.What is the 27th term of the AP 15, 20, 25, 30, …? (a) 150 (b) 145 (c) 135 (d) 130
  22. 22.Which term of the AP 18, 22, 26, 30, … is 130? (a) 30th (b) 28th (c) 31st (d) 29th
  23. 23.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 65 (b) 130 (c) 68 (d) 19
  24. 24.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 253 (c) 506 (d) 43
  25. 25.What is the 16th term of the AP 5, 14, 23, 32, …? (a) 149 (b) 144 (c) 140 (d) 135
  26. 26.What is the 33rd term of the AP 20, 24, 28, 32, …? (a) 152 (b) 128 (c) 148 (d) 132
  27. 27.What is the missing term in the AP 9, 14, 19, ?, 29? (a) 29 (b) 25 (c) 24 (d) 23
  28. 28.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 406 (c) 378 (d) 392
  29. 29.What is the 28th term of the AP 2, 9, 16, 23, …? (a) 189 (b) 191 (c) 196 (d) 198
  30. 30.What is the 37th term of the AP 8, 12, 16, 20, …? (a) 156 (b) 144 (c) 148 (d) 152
  31. 31.What is the 30th term of the AP 6, 8, 10, 12, …? (a) 64 (b) 60 (c) 66 (d) 58
  32. 32.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 25 (b) 33 (c) 27 (d) 26
  33. 33.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 27 (c) 210 (d) 196
  34. 34.What is the missing term in the AP 8, 10, ?, 14, 16? (a) 13 (b) 11 (c) 14 (d) 12
  35. 35.What is the 35th term of the AP 10, 14, 18, 22, …? (a) 136 (b) 150 (c) 146 (d) 140
  36. 36.What is the missing term in the AP 20, 24, ?, 32, 36? (a) 29 (b) 32 (c) 27 (d) 28
  37. 37.Which term of the AP 5, 7, 9, 11, … is 69? (a) 34th (b) 32nd (c) 35th (d) 33rd
  38. 38.What is the 34th term of the AP 8, 14, 20, 26, …? (a) 204 (b) 198 (c) 212 (d) 206
  39. 39.What is the 29th term of the AP 7, 11, 15, 19, …? (a) 123 (b) 112 (c) 116 (d) 119
  40. 40.What is the sum of all the whole numbers from 1 to 44? (a) 1980 (b) 990 (c) 968 (d) 946

Answer key

  1. 126
  2. 242
  3. 37th
  4. 32
  5. 44
  6. 70
  7. 132
  8. 2278
  9. 784
  10. 32nd
  11. 576
  12. 2556
  13. 147
  14. 441
  15. 130
  16. 30
  17. 108
  18. 31st
  19. 64
  20. 90
  21. 145
  22. 29th
  23. 65
  24. 484
  25. 140
  26. 148
  27. 24
  28. 406
  29. 191
  30. 152
  31. 64
  32. 26
  33. 196
  34. 12
  35. 146
  36. 28
  37. 33rd
  38. 206
  39. 119
  40. 990

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