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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 38 · 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 18th term of the AP 19, 26, 33, 40, …? (a) 126 (b) 138 (c) 119 (d) 145
  2. 2.Which term of the AP 19, 24, 29, 34, … is 79? (a) 13th (b) 12th (c) 15th (d) 14th
  3. 3.Which term of the AP 20, 27, 34, 41, … is 202? (a) 27th (b) 26th (c) 29th (d) 28th
  4. 4.What is the 38th term of the AP 16, 22, 28, 34, …? (a) 238 (b) 222 (c) 244 (d) 228
  5. 5.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 21 (b) 24 (c) 42 (d) 6
  6. 6.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 19 (b) 104 (c) 96 (d) 192
  7. 7.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 729 (c) 756 (d) 53
  8. 8.What is the 39th term of the AP 9, 11, 13, 15, …? (a) 78 (b) 87 (c) 85 (d) 76
  9. 9.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 100 (c) 55 (d) 110
  10. 10.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 144 (c) 156 (d) 78
  11. 11.What is the missing term in the AP 7, ?, 15, 19, 23? (a) 12 (b) 11 (c) 10 (d) 15
  12. 12.What is the sum of all the whole numbers from 1 to 90? (a) 4095 (b) 8190 (c) 4005 (d) 4050
  13. 13.What is the 31st term of the AP 20, 25, 30, 35, …? (a) 155 (b) 170 (c) 175 (d) 150
  14. 14.What is the 17th term of the AP 8, 13, 18, 23, …? (a) 80 (b) 85 (c) 93 (d) 88
  15. 15.What is the missing term in the AP 15, 21, 27, ?, 39? (a) 32 (b) 34 (c) 33 (d) 39
  16. 16.What is the missing term in the AP 19, ?, 37, 46, 55? (a) 28 (b) 27 (c) 29 (d) 37
  17. 17.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 360 (b) 190 (c) 27 (d) 180
  18. 18.What is the missing term in the AP 14, ?, 22, 26, 30? (a) 18 (b) 22 (c) 19 (d) 17
  19. 19.What is the missing term in the AP 6, ?, 16, 21, 26? (a) 11 (b) 10 (c) 16 (d) 12
  20. 20.What is the missing term in the AP 13, 18, ?, 28, 33? (a) 28 (b) 24 (c) 22 (d) 23
  21. 21.What is the 29th term of the AP 12, 17, 22, 27, …? (a) 145 (b) 140 (c) 157 (d) 152
  22. 22.What is the 28th term of the AP 20, 29, 38, 47, …? (a) 272 (b) 263 (c) 243 (d) 252
  23. 23.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 17 (b) 18 (c) 22 (d) 19
  24. 24.What is the 18th term of the AP 14, 17, 20, 23, …? (a) 65 (b) 68 (c) 51 (d) 54
  25. 25.What is the 24th term of the AP 10, 13, 16, 19, …? (a) 82 (b) 72 (c) 69 (d) 79
  26. 26.What is the 29th term of the AP 4, 13, 22, 31, …? (a) 252 (b) 261 (c) 256 (d) 265
  27. 27.Which term of the AP 6, 15, 24, 33, … is 213? (a) 26th (b) 25th (c) 24th (d) 23rd
  28. 28.What is the 31st term of the AP 13, 22, 31, 40, …? (a) 292 (b) 279 (c) 283 (d) 270
  29. 29.What is the sum of all the whole numbers from 1 to 92? (a) 4232 (b) 4186 (c) 4278 (d) 8556
  30. 30.Which term of the AP 16, 23, 30, 37, … is 240? (a) 34th (b) 35th (c) 33rd (d) 32nd
  31. 31.What is the missing term in the AP 12, 14, ?, 18, 20? (a) 15 (b) 18 (c) 17 (d) 16
  32. 32.What is the sum of all the whole numbers from 1 to 71? (a) 2557 (b) 2485 (c) 5112 (d) 2556
  33. 33.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 7 (b) 9 (c) 10 (d) 8
  34. 34.What is the sum of all the whole numbers from 1 to 74? (a) 5550 (b) 2701 (c) 2775 (d) 2738
  35. 35.Which term of the AP 11, 16, 21, 26, … is 46? (a) 7th (b) 9th (c) 10th (d) 8th
  36. 36.What is the missing term in the AP 1, 10, 19, ?, 37? (a) 29 (b) 37 (c) 28 (d) 27
  37. 37.Which term of the AP 16, 23, 30, 37, … is 275? (a) 40th (b) 39th (c) 38th (d) 37th
  38. 38.What is the sum of the first 12 terms of the AP 1, 5, 9, …? (a) 276 (b) 45 (c) 552 (d) 300
  39. 39.What is the 16th term of the AP 11, 13, 15, 17, …? (a) 43 (b) 30 (c) 32 (d) 41
  40. 40.What is the missing term in the AP 19, ?, 25, 28, 31? (a) 22 (b) 21 (c) 23 (d) 25

Answer key

  1. 138
  2. 13th
  3. 27th
  4. 238
  5. 21
  6. 96
  7. 729
  8. 85
  9. 100
  10. 144
  11. 11
  12. 4095
  13. 170
  14. 88
  15. 33
  16. 28
  17. 180
  18. 18
  19. 11
  20. 23
  21. 152
  22. 263
  23. 18
  24. 65
  25. 79
  26. 256
  27. 24th
  28. 283
  29. 4278
  30. 33rd
  31. 16
  32. 2556
  33. 8
  34. 2775
  35. 8th
  36. 28
  37. 38th
  38. 276
  39. 41
  40. 22

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