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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 999 · 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 31st term of the AP 5, 8, 11, 14, …? (a) 93 (b) 95 (c) 90 (d) 98
  2. 2.What is the 24th term of the AP 19, 27, 35, 43, …? (a) 203 (b) 184 (c) 211 (d) 192
  3. 3.What is the sum of the first 7 terms of the AP 2, 8, 14, …? (a) 38 (b) 280 (c) 140 (d) 161
  4. 4.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 114 (b) 99 (c) 29 (d) 198
  5. 5.What is the 18th term of the AP 3, 10, 17, 24, …? (a) 119 (b) 122 (c) 129 (d) 126
  6. 6.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 784 (d) 406
  7. 7.What is the 39th term of the AP 6, 10, 14, 18, …? (a) 156 (b) 158 (c) 162 (d) 152
  8. 8.What is the missing term in the AP 18, 20, ?, 24, 26? (a) 21 (b) 23 (c) 24 (d) 22
  9. 9.What is the 12th term of the AP 17, 26, 35, 44, …? (a) 125 (b) 108 (c) 116 (d) 99
  10. 10.What is the 12th term of the AP 7, 10, 13, 16, …? (a) 36 (b) 33 (c) 43 (d) 40
  11. 11.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 129 (b) 126 (c) 252 (d) 27
  12. 12.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 150 (b) 290 (c) 145 (d) 19
  13. 13.What is the sum of the first 10 terms of the AP 9, 13, 17, …? (a) 290 (b) 540 (c) 45 (d) 270
  14. 14.What is the 13th term of the AP 14, 20, 26, 32, …? (a) 92 (b) 72 (c) 78 (d) 86
  15. 15.What is the sum of the first 10 terms of the AP 1, 2, 3, …? (a) 10 (b) 55 (c) 60 (d) 110
  16. 16.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 170 (b) 85 (c) 25 (d) 95
  17. 17.Which term of the AP 20, 28, 36, 44, … is 76? (a) 9th (b) 8th (c) 10th (d) 7th
  18. 18.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 504 (b) 468 (c) 72 (d) 936
  19. 19.What is the missing term in the AP 8, 17, 26, ?, 44? (a) 34 (b) 35 (c) 36 (d) 44
  20. 20.What is the sum of all the whole numbers from 1 to 44? (a) 990 (b) 968 (c) 1980 (d) 946
  21. 21.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 78 (c) 72 (d) 156
  22. 22.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 1953 (c) 2016 (d) 2017
  23. 23.What is the 21st term of the AP 9, 17, 25, 33, …? (a) 177 (b) 160 (c) 168 (d) 169
  24. 24.What is the 18th term of the AP 7, 14, 21, 28, …? (a) 133 (b) 126 (c) 119 (d) 127
  25. 25.What is the sum of the first 10 terms of the AP 8, 9, 10, …? (a) 130 (b) 250 (c) 125 (d) 17
  26. 26.What is the missing term in the AP 9, 14, 19, ?, 29? (a) 25 (b) 23 (c) 29 (d) 24
  27. 27.What is the 20th term of the AP 17, 23, 29, 35, …? (a) 131 (b) 137 (c) 120 (d) 114
  28. 28.What is the sum of all the whole numbers from 1 to 67? (a) 4556 (b) 2278 (c) 2279 (d) 2211
  29. 29.What is the sum of all the whole numbers from 1 to 62? (a) 1953 (b) 1922 (c) 3906 (d) 1891
  30. 30.Which term of the AP 7, 9, 11, 13, … is 25? (a) 10th (b) 12th (c) 9th (d) 11th
  31. 31.What is the 34th term of the AP 16, 20, 24, 28, …? (a) 152 (b) 136 (c) 132 (d) 148
  32. 32.What is the sum of all the whole numbers from 1 to 30? (a) 435 (b) 465 (c) 930 (d) 450
  33. 33.Which term of the AP 6, 9, 12, 15, … is 93? (a) 32nd (b) 31st (c) 30th (d) 29th
  34. 34.What is the sum of the first 9 terms of the AP 7, 8, 9, …? (a) 100 (b) 15 (c) 198 (d) 99
  35. 35.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 100 (c) 110 (d) 55
  36. 36.What is the sum of the first 10 terms of the AP 6, 7, 8, …? (a) 15 (b) 105 (c) 110 (d) 210
  37. 37.What is the 34th term of the AP 15, 18, 21, 24, …? (a) 114 (b) 117 (c) 102 (d) 99
  38. 38.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 105 (c) 27 (d) 210
  39. 39.What is the missing term in the AP 6, 11, 16, ?, 26? (a) 22 (b) 21 (c) 20 (d) 26
  40. 40.Which term of the AP 5, 7, 9, 11, … is 69? (a) 33rd (b) 32nd (c) 35th (d) 34th

Answer key

  1. 95
  2. 203
  3. 140
  4. 99
  5. 122
  6. 784
  7. 158
  8. 22
  9. 116
  10. 40
  11. 126
  12. 145
  13. 270
  14. 86
  15. 55
  16. 85
  17. 8th
  18. 468
  19. 35
  20. 990
  21. 78
  22. 2016
  23. 169
  24. 126
  25. 125
  26. 24
  27. 131
  28. 2278
  29. 1953
  30. 10th
  31. 148
  32. 465
  33. 30th
  34. 99
  35. 100
  36. 105
  37. 114
  38. 196
  39. 21
  40. 33rd

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