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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 789 · 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 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 812 (d) 784
  2. 2.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 1035 (c) 2070 (d) 990
  3. 3.What is the missing term in the AP 2, 5, 8, ?, 14? (a) 10 (b) 14 (c) 11 (d) 12
  4. 4.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 90 (b) 17 (c) 162 (d) 81
  5. 5.What is the 34th term of the AP 16, 24, 32, 40, …? (a) 272 (b) 280 (c) 264 (d) 288
  6. 6.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 50 (b) 7 (c) 26 (d) 25
  7. 7.What is the 23rd term of the AP 3, 8, 13, 18, …? (a) 110 (b) 115 (c) 113 (d) 118
  8. 8.What is the 22nd term of the AP 13, 16, 19, 22, …? (a) 79 (b) 66 (c) 63 (d) 76
  9. 9.What is the sum of all the whole numbers from 1 to 86? (a) 3655 (b) 3698 (c) 7482 (d) 3741
  10. 10.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 286 (b) 143 (c) 144 (d) 18
  11. 11.What is the 38th term of the AP 5, 10, 15, 20, …? (a) 190 (b) 195 (c) 185 (d) 191
  12. 12.What is the sum of all the whole numbers from 1 to 43? (a) 947 (b) 903 (c) 946 (d) 1892
  13. 13.What is the 18th term of the AP 12, 14, 16, 18, …? (a) 46 (b) 34 (c) 48 (d) 36
  14. 14.What is the 28th term of the AP 1, 5, 9, 13, …? (a) 112 (b) 109 (c) 108 (d) 113
  15. 15.What is the missing term in the AP 13, 22, 31, ?, 49? (a) 40 (b) 41 (c) 49 (d) 39
  16. 16.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 120 (b) 240 (c) 130 (d) 21
  17. 17.Which term of the AP 14, 18, 22, 26, … is 162? (a) 37th (b) 40th (c) 38th (d) 39th
  18. 18.Which term of the AP 13, 17, 21, 25, … is 77? (a) 19th (b) 17th (c) 16th (d) 18th
  19. 19.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 180 (b) 20 (c) 90 (d) 96
  20. 20.What is the sum of all the whole numbers from 1 to 68? (a) 2278 (b) 4692 (c) 2312 (d) 2346
  21. 21.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 120 (b) 14 (c) 60 (d) 61
  22. 22.What is the sum of the first 11 terms of the AP 9, 14, 19, …? (a) 748 (b) 379 (c) 59 (d) 374
  23. 23.What is the 14th term of the AP 17, 21, 25, 29, …? (a) 52 (b) 56 (c) 69 (d) 73
  24. 24.What is the 16th term of the AP 8, 14, 20, 26, …? (a) 96 (b) 98 (c) 104 (d) 90
  25. 25.What is the 11th term of the AP 4, 7, 10, 13, …? (a) 30 (b) 34 (c) 37 (d) 33
  26. 26.What is the 21st term of the AP 18, 23, 28, 33, …? (a) 100 (b) 118 (c) 105 (d) 123
  27. 27.What is the 16th term of the AP 6, 10, 14, 18, …? (a) 70 (b) 60 (c) 64 (d) 66
  28. 28.Which term of the AP 4, 8, 12, 16, … is 48? (a) 13th (b) 14th (c) 11th (d) 12th
  29. 29.Which term of the AP 14, 20, 26, 32, … is 104? (a) 16th (b) 18th (c) 17th (d) 15th
  30. 30.What is the 40th term of the AP 5, 9, 13, 17, …? (a) 161 (b) 156 (c) 165 (d) 160
  31. 31.What is the 33rd term of the AP 2, 7, 12, 17, …? (a) 162 (b) 160 (c) 165 (d) 167
  32. 32.What is the 30th term of the AP 16, 20, 24, 28, …? (a) 136 (b) 116 (c) 120 (d) 132
  33. 33.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 105 (d) 210
  34. 34.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 324 (b) 34 (c) 180 (d) 162
  35. 35.Which term of the AP 20, 23, 26, 29, … is 80? (a) 23rd (b) 21st (c) 20th (d) 22nd
  36. 36.What is the 11th term of the AP 1, 10, 19, 28, …? (a) 91 (b) 100 (c) 90 (d) 99
  37. 37.What is the 23rd term of the AP 18, 24, 30, 36, …? (a) 138 (b) 132 (c) 150 (d) 156
  38. 38.What is the 32nd term of the AP 20, 26, 32, 38, …? (a) 212 (b) 192 (c) 186 (d) 206
  39. 39.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 90 (b) 150 (c) 75 (d) 27
  40. 40.What is the 17th term of the AP 8, 10, 12, 14, …? (a) 32 (b) 40 (c) 42 (d) 34

Answer key

  1. 784
  2. 1035
  3. 11
  4. 81
  5. 280
  6. 25
  7. 113
  8. 76
  9. 3741
  10. 143
  11. 190
  12. 946
  13. 46
  14. 109
  15. 40
  16. 120
  17. 38th
  18. 17th
  19. 90
  20. 2346
  21. 60
  22. 374
  23. 69
  24. 98
  25. 34
  26. 118
  27. 66
  28. 12th
  29. 16th
  30. 161
  31. 162
  32. 132
  33. 196
  34. 162
  35. 21st
  36. 91
  37. 150
  38. 206
  39. 75
  40. 40

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