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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 819 · 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 9, 10, 11, …? (a) 72 (b) 69 (c) 14 (d) 138
  2. 2.What is the missing term in the AP 20, 22, 24, ?, 28? (a) 28 (b) 26 (c) 25 (d) 27
  3. 3.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1682 (c) 1653 (d) 1711
  4. 4.What is the 37th term of the AP 19, 27, 35, 43, …? (a) 315 (b) 288 (c) 307 (d) 296
  5. 5.What is the 34th term of the AP 7, 13, 19, 25, …? (a) 211 (b) 205 (c) 198 (d) 204
  6. 6.Which term of the AP 5, 9, 13, 17, … is 33? (a) 8th (b) 10th (c) 7th (d) 9th
  7. 7.What is the 33rd term of the AP 9, 17, 25, 33, …? (a) 256 (b) 273 (c) 264 (d) 265
  8. 8.What is the sum of all the whole numbers from 1 to 44? (a) 1980 (b) 968 (c) 990 (d) 946
  9. 9.What is the sum of all the whole numbers from 1 to 24? (a) 600 (b) 276 (c) 288 (d) 300
  10. 10.What is the 35th term of the AP 3, 6, 9, 12, …? (a) 106 (b) 105 (c) 102 (d) 108
  11. 11.What is the 15th term of the AP 6, 13, 20, 27, …? (a) 111 (b) 104 (c) 105 (d) 98
  12. 12.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 56 (b) 580 (c) 320 (d) 290
  13. 13.What is the 22nd term of the AP 19, 27, 35, 43, …? (a) 176 (b) 187 (c) 195 (d) 168
  14. 14.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 40 (b) 8 (c) 72 (d) 36
  15. 15.What is the 29th term of the AP 5, 13, 21, 29, …? (a) 232 (b) 229 (c) 224 (d) 237
  16. 16.What is the 23rd term of the AP 12, 17, 22, 27, …? (a) 122 (b) 115 (c) 127 (d) 110
  17. 17.What is the 37th term of the AP 14, 17, 20, 23, …? (a) 108 (b) 111 (c) 125 (d) 122
  18. 18.What is the sum of all the whole numbers from 1 to 65? (a) 2146 (b) 2145 (c) 2080 (d) 4290
  19. 19.Which term of the AP 15, 18, 21, 24, … is 126? (a) 37th (b) 39th (c) 38th (d) 42nd
  20. 20.What is the 22nd term of the AP 6, 9, 12, 15, …? (a) 72 (b) 63 (c) 69 (d) 66
  21. 21.What is the missing term in the AP 9, 11, 13, ?, 17? (a) 16 (b) 17 (c) 14 (d) 15
  22. 22.What is the 25th term of the AP 15, 21, 27, 33, …? (a) 150 (b) 159 (c) 165 (d) 144
  23. 23.What is the missing term in the AP 13, 17, ?, 25, 29? (a) 25 (b) 21 (c) 20 (d) 22
  24. 24.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 13 (b) 12 (c) 16 (d) 14
  25. 25.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 280 (b) 55 (c) 310 (d) 560
  26. 26.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 21 (d) 36
  27. 27.What is the missing term in the AP 17, 20, 23, ?, 29? (a) 26 (b) 29 (c) 25 (d) 27
  28. 28.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 105 (b) 182 (c) 25 (d) 91
  29. 29.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 484 (c) 253 (d) 506
  30. 30.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 50 (b) 100 (c) 55 (d) 14
  31. 31.What is the missing term in the AP 1, 9, 17, ?, 33? (a) 24 (b) 26 (c) 25 (d) 33
  32. 32.Which term of the AP 5, 13, 21, 29, … is 285? (a) 37th (b) 35th (c) 38th (d) 36th
  33. 33.What is the 33rd term of the AP 1, 9, 17, 25, …? (a) 265 (b) 256 (c) 264 (d) 257
  34. 34.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 156 (c) 78 (d) 72
  35. 35.What is the missing term in the AP 3, ?, 21, 30, 39? (a) 21 (b) 11 (c) 12 (d) 13
  36. 36.What is the 22nd term of the AP 3, 10, 17, 24, …? (a) 147 (b) 154 (c) 157 (d) 150
  37. 37.What is the missing term in the AP 5, 9, 13, ?, 21? (a) 18 (b) 16 (c) 21 (d) 17
  38. 38.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 456 (b) 840 (c) 420 (d) 68
  39. 39.What is the sum of all the whole numbers from 1 to 42? (a) 903 (b) 1806 (c) 861 (d) 882
  40. 40.What is the 13th term of the AP 6, 8, 10, 12, …? (a) 24 (b) 32 (c) 30 (d) 26

Answer key

  1. 69
  2. 26
  3. 1711
  4. 307
  5. 205
  6. 8th
  7. 265
  8. 990
  9. 300
  10. 105
  11. 104
  12. 290
  13. 187
  14. 36
  15. 229
  16. 122
  17. 122
  18. 2145
  19. 38th
  20. 69
  21. 15
  22. 159
  23. 21
  24. 13
  25. 280
  26. 36
  27. 26
  28. 91
  29. 484
  30. 50
  31. 25
  32. 36th
  33. 257
  34. 78
  35. 12
  36. 150
  37. 17
  38. 420
  39. 903
  40. 30

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