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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 658 · 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 27th term of the AP 10, 12, 14, 16, …? (a) 54 (b) 62 (c) 64 (d) 52
  2. 2.Which term of the AP 4, 8, 12, 16, … is 80? (a) 19th (b) 21st (c) 20th (d) 22nd
  3. 3.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 64 (c) 72 (d) 36
  4. 4.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 378 (c) 53 (d) 729
  5. 5.What is the 24th term of the AP 9, 17, 25, 33, …? (a) 184 (b) 201 (c) 192 (d) 193
  6. 6.What is the 25th term of the AP 15, 17, 19, 21, …? (a) 48 (b) 63 (c) 65 (d) 50
  7. 7.What is the sum of the first 6 terms of the AP 10, 15, 20, …? (a) 35 (b) 270 (c) 135 (d) 150
  8. 8.What is the missing term in the AP 7, 10, ?, 16, 19? (a) 12 (b) 16 (c) 13 (d) 14
  9. 9.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 143 (b) 18 (c) 144 (d) 286
  10. 10.What is the sum of all the whole numbers from 1 to 56? (a) 1568 (b) 1596 (c) 3192 (d) 1540
  11. 11.What is the 14th term of the AP 2, 4, 6, 8, …? (a) 28 (b) 29 (c) 26 (d) 30
  12. 12.Which term of the AP 6, 9, 12, 15, … is 102? (a) 34th (b) 35th (c) 32nd (d) 33rd
  13. 13.What is the 12th term of the AP 19, 23, 27, 31, …? (a) 48 (b) 67 (c) 63 (d) 44
  14. 14.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 169 (c) 91 (d) 25
  15. 15.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 19 (b) 308 (c) 155 (d) 154
  16. 16.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 14 (b) 16 (c) 12 (d) 13
  17. 17.What is the sum of all the whole numbers from 1 to 59? (a) 1770 (b) 3540 (c) 1771 (d) 1711
  18. 18.What is the sum of all the whole numbers from 1 to 63? (a) 2017 (b) 2016 (c) 1953 (d) 4032
  19. 19.What is the sum of all the whole numbers from 1 to 37? (a) 703 (b) 1406 (c) 704 (d) 666
  20. 20.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 48 (b) 54 (c) 96 (d) 13
  21. 21.Which term of the AP 2, 4, 6, 8, … is 28? (a) 16th (b) 13th (c) 14th (d) 15th
  22. 22.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 308 (b) 154 (c) 24 (d) 165
  23. 23.What is the missing term in the AP 19, 23, 27, ?, 35? (a) 35 (b) 32 (c) 30 (d) 31
  24. 24.Which term of the AP 13, 15, 17, 19, … is 53? (a) 23rd (b) 20th (c) 21st (d) 22nd
  25. 25.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 78 (b) 17 (c) 72 (d) 144
  26. 26.What is the sum of the first 8 terms of the AP 10, 12, 14, …? (a) 272 (b) 136 (c) 144 (d) 24
  27. 27.Which term of the AP 6, 8, 10, 12, … is 72? (a) 33rd (b) 36th (c) 34th (d) 35th
  28. 28.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 36 (c) 42 (d) 21
  29. 29.What is the 14th term of the AP 3, 12, 21, 30, …? (a) 117 (b) 120 (c) 126 (d) 129
  30. 30.Which term of the AP 3, 5, 7, 9, … is 23? (a) 13th (b) 10th (c) 11th (d) 12th
  31. 31.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 24 (b) 160 (c) 300 (d) 150
  32. 32.What is the sum of the first 10 terms of the AP 7, 10, 13, …? (a) 34 (b) 220 (c) 205 (d) 410
  33. 33.What is the 23rd term of the AP 8, 14, 20, 26, …? (a) 146 (b) 132 (c) 140 (d) 138
  34. 34.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 14 (b) 78 (c) 154 (d) 77
  35. 35.What is the 31st term of the AP 5, 12, 19, 26, …? (a) 222 (b) 210 (c) 215 (d) 217
  36. 36.What is the sum of the first 10 terms of the AP 7, 12, 17, …? (a) 52 (b) 295 (c) 320 (d) 590
  37. 37.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 28 (c) 49 (d) 13
  38. 38.What is the 13th term of the AP 19, 24, 29, 34, …? (a) 84 (b) 60 (c) 65 (d) 79
  39. 39.What is the 39th term of the AP 14, 21, 28, 35, …? (a) 266 (b) 273 (c) 280 (d) 287
  40. 40.What is the sum of the first 5 terms of the AP 5, 10, 15, …? (a) 80 (b) 25 (c) 150 (d) 75

Answer key

  1. 62
  2. 20th
  3. 64
  4. 729
  5. 193
  6. 63
  7. 135
  8. 13
  9. 143
  10. 1596
  11. 28
  12. 33rd
  13. 63
  14. 169
  15. 154
  16. 13
  17. 1770
  18. 2016
  19. 703
  20. 48
  21. 14th
  22. 154
  23. 31
  24. 21st
  25. 72
  26. 136
  27. 34th
  28. 36
  29. 120
  30. 11th
  31. 150
  32. 205
  33. 140
  34. 77
  35. 215
  36. 295
  37. 49
  38. 79
  39. 280
  40. 75

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