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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 842 · 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 1, 8, ?, 22, 29? (a) 16 (b) 22 (c) 14 (d) 15
  2. 2.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 166 (b) 330 (c) 20 (d) 165
  3. 3.What is the 27th term of the AP 4, 7, 10, 13, …? (a) 85 (b) 78 (c) 82 (d) 81
  4. 4.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 396 (b) 42 (c) 198 (d) 203
  5. 5.What is the 12th term of the AP 15, 22, 29, 36, …? (a) 77 (b) 99 (c) 84 (d) 92
  6. 6.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 154 (b) 80 (c) 20 (d) 77
  7. 7.What is the missing term in the AP 11, 20, ?, 38, 47? (a) 28 (b) 38 (c) 30 (d) 29
  8. 8.Which term of the AP 2, 4, 6, 8, … is 36? (a) 17th (b) 18th (c) 20th (d) 19th
  9. 9.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 144 (c) 78 (d) 23
  10. 10.What is the 19th term of the AP 18, 23, 28, 33, …? (a) 108 (b) 113 (c) 90 (d) 95
  11. 11.What is the 21st term of the AP 16, 22, 28, 34, …? (a) 136 (b) 142 (c) 120 (d) 126
  12. 12.What is the sum of all the whole numbers from 1 to 54? (a) 1485 (b) 1458 (c) 2970 (d) 1431
  13. 13.What is the missing term in the AP 8, 10, ?, 14, 16? (a) 12 (b) 14 (c) 13 (d) 11
  14. 14.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 540 (b) 504 (c) 75 (d) 1008
  15. 15.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 25 (d) 169
  16. 16.What is the sum of all the whole numbers from 1 to 47? (a) 2256 (b) 1081 (c) 1128 (d) 1129
  17. 17.What is the 13th term of the AP 1, 10, 19, 28, …? (a) 118 (b) 117 (c) 109 (d) 108
  18. 18.What is the sum of all the whole numbers from 1 to 32? (a) 1056 (b) 528 (c) 496 (d) 512
  19. 19.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 112 (b) 14 (c) 63 (d) 56
  20. 20.Which term of the AP 1, 4, 7, 10, … is 31? (a) 13th (b) 10th (c) 12th (d) 11th
  21. 21.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 600 (c) 576 (d) 300
  22. 22.What is the missing term in the AP 1, 10, 19, ?, 37? (a) 27 (b) 28 (c) 29 (d) 37
  23. 23.What is the sum of the first 9 terms of the AP 3, 8, 13, …? (a) 212 (b) 414 (c) 43 (d) 207
  24. 24.Which term of the AP 15, 19, 23, 27, … is 135? (a) 32nd (b) 31st (c) 33rd (d) 30th
  25. 25.What is the 36th term of the AP 14, 16, 18, 20, …? (a) 84 (b) 72 (c) 70 (d) 86
  26. 26.Which term of the AP 10, 15, 20, 25, … is 60? (a) 10th (b) 11th (c) 13th (d) 12th
  27. 27.What is the sum of all the whole numbers from 1 to 82? (a) 6806 (b) 3321 (c) 3403 (d) 3362
  28. 28.What is the 21st term of the AP 17, 25, 33, 41, …? (a) 168 (b) 185 (c) 160 (d) 177
  29. 29.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 240 (b) 480 (c) 42 (d) 260
  30. 30.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 21 (d) 121
  31. 31.What is the 24th term of the AP 4, 11, 18, 25, …? (a) 161 (b) 172 (c) 165 (d) 168
  32. 32.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 32 (b) 41 (c) 31 (d) 33
  33. 33.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 65 (b) 23 (c) 130 (d) 70
  34. 34.What is the 10th term of the AP 17, 19, 21, 23, …? (a) 20 (b) 37 (c) 35 (d) 18
  35. 35.What is the 16th term of the AP 12, 15, 18, 21, …? (a) 60 (b) 57 (c) 48 (d) 45
  36. 36.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 21 (d) 36
  37. 37.What is the sum of the first 9 terms of the AP 9, 12, 15, …? (a) 189 (b) 33 (c) 192 (d) 378
  38. 38.What is the 36th term of the AP 14, 21, 28, 35, …? (a) 245 (b) 259 (c) 252 (d) 266
  39. 39.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 28 (d) 49
  40. 40.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 625 (c) 49 (d) 325

Answer key

  1. 15
  2. 165
  3. 82
  4. 198
  5. 92
  6. 77
  7. 29
  8. 18th
  9. 144
  10. 108
  11. 136
  12. 1485
  13. 12
  14. 504
  15. 169
  16. 1128
  17. 109
  18. 528
  19. 56
  20. 11th
  21. 576
  22. 28
  23. 207
  24. 31st
  25. 84
  26. 11th
  27. 3403
  28. 177
  29. 240
  30. 121
  31. 165
  32. 32
  33. 65
  34. 35
  35. 57
  36. 36
  37. 189
  38. 259
  39. 49
  40. 625

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