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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 189 · 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 missing term in the AP 13, 19, ?, 31, 37? (a) 26 (b) 25 (c) 24 (d) 31
  2. 2.What is the 33rd term of the AP 8, 10, 12, 14, …? (a) 72 (b) 64 (c) 66 (d) 74
  3. 3.What is the 10th term of the AP 16, 18, 20, 22, …? (a) 18 (b) 34 (c) 36 (d) 20
  4. 4.What is the missing term in the AP 12, 15, 18, ?, 24? (a) 20 (b) 24 (c) 21 (d) 22
  5. 5.What is the sum of all the whole numbers from 1 to 47? (a) 1128 (b) 2256 (c) 1081 (d) 1129
  6. 6.What is the 27th term of the AP 4, 6, 8, 10, …? (a) 58 (b) 52 (c) 56 (d) 54
  7. 7.What is the 22nd term of the AP 11, 15, 19, 23, …? (a) 84 (b) 95 (c) 99 (d) 88
  8. 8.Which term of the AP 2, 10, 18, 26, … is 114? (a) 14th (b) 16th (c) 15th (d) 17th
  9. 9.What is the missing term in the AP 4, ?, 12, 16, 20? (a) 9 (b) 8 (c) 12 (d) 7
  10. 10.What is the 35th term of the AP 9, 16, 23, 30, …? (a) 245 (b) 247 (c) 238 (d) 254
  11. 11.What is the 14th term of the AP 12, 20, 28, 36, …? (a) 116 (b) 104 (c) 112 (d) 124
  12. 12.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 8 (b) 6 (c) 5 (d) 7
  13. 13.What is the sum of all the whole numbers from 1 to 82? (a) 3403 (b) 6806 (c) 3362 (d) 3321
  14. 14.Which term of the AP 9, 18, 27, 36, … is 225? (a) 24th (b) 26th (c) 27th (d) 25th
  15. 15.What is the sum of all the whole numbers from 1 to 59? (a) 1770 (b) 1771 (c) 1711 (d) 3540
  16. 16.What is the sum of all the whole numbers from 1 to 61? (a) 1830 (b) 1892 (c) 3782 (d) 1891
  17. 17.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 8 (b) 60 (c) 31 (d) 30
  18. 18.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 207 (b) 225 (c) 39 (d) 414
  19. 19.What is the missing term in the AP 4, 6, ?, 10, 12? (a) 10 (b) 7 (c) 8 (d) 9
  20. 20.Which term of the AP 14, 16, 18, 20, … is 42? (a) 14th (b) 15th (c) 21st (d) 16th
  21. 21.What is the missing term in the AP 4, ?, 18, 25, 32? (a) 11 (b) 12 (c) 10 (d) 18
  22. 22.What is the 31st term of the AP 4, 7, 10, 13, …? (a) 90 (b) 97 (c) 94 (d) 93
  23. 23.What is the sum of all the whole numbers from 1 to 72? (a) 2592 (b) 2628 (c) 2556 (d) 5256
  24. 24.What is the 35th term of the AP 16, 18, 20, 22, …? (a) 68 (b) 84 (c) 70 (d) 86
  25. 25.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100
  26. 26.Which term of the AP 9, 17, 25, 33, … is 257? (a) 33rd (b) 31st (c) 34th (d) 32nd
  27. 27.What is the 20th term of the AP 20, 29, 38, 47, …? (a) 191 (b) 200 (c) 171 (d) 180
  28. 28.What is the missing term in the AP 20, ?, 38, 47, 56? (a) 30 (b) 29 (c) 28 (d) 38
  29. 29.Which term of the AP 7, 14, 21, 28, … is 168? (a) 26th (b) 25th (c) 23rd (d) 24th
  30. 30.What is the 14th term of the AP 10, 12, 14, 16, …? (a) 38 (b) 36 (c) 26 (d) 28
  31. 31.What is the missing term in the AP 16, ?, 20, 22, 24? (a) 17 (b) 18 (c) 20 (d) 19
  32. 32.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 189 (b) 336 (c) 168 (d) 42
  33. 33.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 272 (d) 256
  34. 34.What is the 32nd term of the AP 13, 17, 21, 25, …? (a) 141 (b) 124 (c) 137 (d) 128
  35. 35.What is the 39th term of the AP 7, 11, 15, 19, …? (a) 156 (b) 163 (c) 152 (d) 159
  36. 36.What is the 40th term of the AP 12, 20, 28, 36, …? (a) 320 (b) 332 (c) 324 (d) 312
  37. 37.What is the sum of all the whole numbers from 1 to 100? (a) 5000 (b) 4950 (c) 10100 (d) 5050
  38. 38.What is the missing term in the AP 19, ?, 33, 40, 47? (a) 27 (b) 25 (c) 33 (d) 26
  39. 39.What is the sum of the first 8 terms of the AP 6, 9, 12, …? (a) 27 (b) 132 (c) 264 (d) 144
  40. 40.What is the sum of all the whole numbers from 1 to 99? (a) 4950 (b) 4851 (c) 9900 (d) 4951

Answer key

  1. 25
  2. 72
  3. 34
  4. 21
  5. 1128
  6. 56
  7. 95
  8. 15th
  9. 8
  10. 247
  11. 116
  12. 6
  13. 3403
  14. 25th
  15. 1770
  16. 1891
  17. 30
  18. 207
  19. 8
  20. 15th
  21. 11
  22. 94
  23. 2628
  24. 84
  25. 100
  26. 32nd
  27. 191
  28. 29
  29. 24th
  30. 36
  31. 18
  32. 168
  33. 256
  34. 137
  35. 159
  36. 324
  37. 5050
  38. 26
  39. 132
  40. 4950

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