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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 928 · 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 8 terms of the AP 6, 10, 14, …? (a) 176 (b) 160 (c) 320 (d) 34
  2. 2.Which term of the AP 17, 25, 33, 41, … is 201? (a) 23rd (b) 24th (c) 26th (d) 25th
  3. 3.What is the missing term in the AP 18, 20, 22, ?, 26? (a) 24 (b) 23 (c) 25 (d) 26
  4. 4.What is the 31st term of the AP 4, 10, 16, 22, …? (a) 190 (b) 180 (c) 186 (d) 184
  5. 5.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 24 (b) 108 (c) 120 (d) 216
  6. 6.What is the 31st term of the AP 14, 17, 20, 23, …? (a) 107 (b) 90 (c) 93 (d) 104
  7. 7.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 19 (b) 100 (c) 110 (d) 200
  8. 8.What is the missing term in the AP 14, 18, 22, ?, 30? (a) 30 (b) 27 (c) 25 (d) 26
  9. 9.What is the missing term in the AP 12, ?, 30, 39, 48? (a) 22 (b) 20 (c) 30 (d) 21
  10. 10.What is the 11th term of the AP 20, 22, 24, 26, …? (a) 42 (b) 40 (c) 20 (d) 22
  11. 11.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 276 (c) 529 (d) 552
  12. 12.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 336 (b) 312 (c) 48 (d) 624
  13. 13.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 85 (b) 80 (c) 26 (d) 160
  14. 14.What is the missing term in the AP 7, ?, 17, 22, 27? (a) 13 (b) 17 (c) 12 (d) 11
  15. 15.What is the sum of the first 9 terms of the AP 9, 11, 13, …? (a) 306 (b) 162 (c) 153 (d) 25
  16. 16.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 6 (b) 21 (c) 42 (d) 24
  17. 17.What is the 28th term of the AP 4, 11, 18, 25, …? (a) 196 (b) 200 (c) 189 (d) 193
  18. 18.What is the missing term in the AP 4, ?, 22, 31, 40? (a) 12 (b) 13 (c) 14 (d) 22
  19. 19.What is the 18th term of the AP 1, 3, 5, 7, …? (a) 34 (b) 36 (c) 35 (d) 37
  20. 20.What is the 31st term of the AP 10, 13, 16, 19, …? (a) 103 (b) 93 (c) 100 (d) 90
  21. 21.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 196 (b) 98 (c) 112 (d) 26
  22. 22.What is the sum of all the whole numbers from 1 to 38? (a) 1482 (b) 703 (c) 722 (d) 741
  23. 23.What is the 25th term of the AP 18, 23, 28, 33, …? (a) 120 (b) 143 (c) 138 (d) 125
  24. 24.What is the 16th term of the AP 4, 9, 14, 19, …? (a) 84 (b) 79 (c) 80 (d) 75
  25. 25.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 35 (c) 171 (d) 324
  26. 26.Which term of the AP 5, 11, 17, 23, … is 59? (a) 11th (b) 9th (c) 12th (d) 10th
  27. 27.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 7 (b) 4 (c) 5 (d) 3
  28. 28.What is the missing term in the AP 4, 10, ?, 22, 28? (a) 17 (b) 22 (c) 15 (d) 16
  29. 29.What is the sum of the first 9 terms of the AP 5, 8, 11, …? (a) 29 (b) 306 (c) 153 (d) 156
  30. 30.What is the 12th term of the AP 15, 24, 33, 42, …? (a) 108 (b) 123 (c) 114 (d) 99
  31. 31.What is the 35th term of the AP 18, 22, 26, 30, …? (a) 158 (b) 154 (c) 136 (d) 140
  32. 32.What is the missing term in the AP 5, 11, 17, ?, 29? (a) 24 (b) 22 (c) 29 (d) 23
  33. 33.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 110 (b) 55 (c) 13 (d) 56
  34. 34.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 29 (c) 120 (d) 225
  35. 35.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 56 (d) 28
  36. 36.What is the sum of the first 8 terms of the AP 1, 6, 11, …? (a) 168 (b) 296 (c) 36 (d) 148
  37. 37.What is the missing term in the AP 6, 8, 10, ?, 14? (a) 13 (b) 11 (c) 14 (d) 12
  38. 38.What is the 14th term of the AP 4, 9, 14, 19, …? (a) 70 (b) 69 (c) 65 (d) 74
  39. 39.What is the 31st term of the AP 20, 25, 30, 35, …? (a) 150 (b) 155 (c) 170 (d) 175
  40. 40.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 256 (c) 136 (d) 272

Answer key

  1. 160
  2. 24th
  3. 24
  4. 184
  5. 108
  6. 104
  7. 100
  8. 26
  9. 21
  10. 40
  11. 529
  12. 312
  13. 80
  14. 12
  15. 153
  16. 21
  17. 193
  18. 13
  19. 35
  20. 100
  21. 98
  22. 741
  23. 138
  24. 79
  25. 324
  26. 10th
  27. 4
  28. 16
  29. 153
  30. 114
  31. 154
  32. 23
  33. 55
  34. 225
  35. 49
  36. 148
  37. 12
  38. 69
  39. 170
  40. 256

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