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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 280 · 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 20th term of the AP 9, 13, 17, 21, …? (a) 85 (b) 76 (c) 80 (d) 89
  2. 2.What is the 39th term of the AP 1, 5, 9, 13, …? (a) 157 (b) 152 (c) 156 (d) 153
  3. 3.Which term of the AP 11, 16, 21, 26, … is 156? (a) 29th (b) 30th (c) 32nd (d) 31st
  4. 4.Which term of the AP 3, 6, 9, 12, … is 45? (a) 15th (b) 16th (c) 14th (d) 17th
  5. 5.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 13 (b) 14 (c) 16 (d) 12
  6. 6.What is the missing term in the AP 1, 7, 13, ?, 25? (a) 25 (b) 18 (c) 19 (d) 20
  7. 7.What is the sum of all the whole numbers from 1 to 94? (a) 4465 (b) 4418 (c) 8930 (d) 4371
  8. 8.What is the sum of all the whole numbers from 1 to 91? (a) 4186 (b) 8372 (c) 4187 (d) 4095
  9. 9.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 1485 (c) 2970 (d) 1458
  10. 10.Which term of the AP 6, 9, 12, 15, … is 57? (a) 18th (b) 19th (c) 17th (d) 20th
  11. 11.What is the 21st term of the AP 9, 14, 19, 24, …? (a) 105 (b) 100 (c) 114 (d) 109
  12. 12.What is the sum of all the whole numbers from 1 to 72? (a) 2628 (b) 2592 (c) 2556 (d) 5256
  13. 13.What is the 32nd term of the AP 19, 22, 25, 28, …? (a) 112 (b) 115 (c) 96 (d) 93
  14. 14.What is the 21st term of the AP 3, 6, 9, 12, …? (a) 66 (b) 64 (c) 63 (d) 60
  15. 15.What is the missing term in the AP 3, ?, 9, 12, 15? (a) 9 (b) 5 (c) 6 (d) 7
  16. 16.What is the 14th term of the AP 2, 10, 18, 26, …? (a) 112 (b) 106 (c) 104 (d) 114
  17. 17.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 144 (b) 22 (c) 84 (d) 72
  18. 18.Which term of the AP 15, 24, 33, 42, … is 312? (a) 33rd (b) 35th (c) 34th (d) 36th
  19. 19.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 20 (b) 40 (c) 6 (d) 21
  20. 20.What is the sum of all the whole numbers from 1 to 62? (a) 3906 (b) 1922 (c) 1953 (d) 1891
  21. 21.What is the sum of the first 6 terms of the AP 8, 11, 14, …? (a) 23 (b) 93 (c) 186 (d) 102
  22. 22.What is the missing term in the AP 2, 8, ?, 20, 26? (a) 13 (b) 20 (c) 14 (d) 15
  23. 23.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 72 (b) 17 (c) 78 (d) 144
  24. 24.What is the missing term in the AP 1, 9, 17, ?, 33? (a) 24 (b) 25 (c) 33 (d) 26
  25. 25.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 15 (b) 72 (c) 128 (d) 64
  26. 26.What is the sum of the first 10 terms of the AP 2, 6, 10, …? (a) 200 (b) 38 (c) 400 (d) 220
  27. 27.What is the sum of all the whole numbers from 1 to 40? (a) 800 (b) 820 (c) 1640 (d) 780
  28. 28.What is the 11th term of the AP 12, 16, 20, 24, …? (a) 44 (b) 52 (c) 40 (d) 56
  29. 29.What is the 13th term of the AP 5, 13, 21, 29, …? (a) 101 (b) 109 (c) 96 (d) 104
  30. 30.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 168 (b) 24 (c) 96 (d) 84
  31. 31.What is the sum of all the whole numbers from 1 to 24? (a) 300 (b) 288 (c) 276 (d) 600
  32. 32.Which term of the AP 12, 19, 26, 33, … is 61? (a) 10th (b) 8th (c) 9th (d) 7th
  33. 33.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 936 (b) 504 (c) 468 (d) 72
  34. 34.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 53 (c) 378 (d) 756
  35. 35.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 276 (b) 138 (c) 17 (d) 144
  36. 36.What is the 28th term of the AP 18, 25, 32, 39, …? (a) 196 (b) 189 (c) 214 (d) 207
  37. 37.What is the missing term in the AP 3, ?, 13, 18, 23? (a) 7 (b) 13 (c) 9 (d) 8
  38. 38.What is the 30th term of the AP 17, 22, 27, 32, …? (a) 150 (b) 162 (c) 167 (d) 145
  39. 39.What is the 29th term of the AP 18, 27, 36, 45, …? (a) 261 (b) 252 (c) 270 (d) 279
  40. 40.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 90 (b) 45 (c) 17 (d) 55

Answer key

  1. 85
  2. 153
  3. 30th
  4. 15th
  5. 13
  6. 19
  7. 4465
  8. 4186
  9. 1485
  10. 18th
  11. 109
  12. 2628
  13. 112
  14. 63
  15. 6
  16. 106
  17. 72
  18. 34th
  19. 20
  20. 1953
  21. 93
  22. 14
  23. 72
  24. 25
  25. 64
  26. 200
  27. 820
  28. 52
  29. 101
  30. 84
  31. 300
  32. 8th
  33. 468
  34. 729
  35. 138
  36. 207
  37. 8
  38. 162
  39. 270
  40. 45

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