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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 374 · 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 16th term of the AP 19, 25, 31, 37, …? (a) 109 (b) 90 (c) 96 (d) 115
  2. 2.What is the 10th term of the AP 15, 20, 25, 30, …? (a) 65 (b) 45 (c) 60 (d) 50
  3. 3.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 246 (b) 123 (c) 138 (d) 33
  4. 4.What is the sum of all the whole numbers from 1 to 18? (a) 171 (b) 342 (c) 162 (d) 153
  5. 5.What is the missing term in the AP 2, 9, ?, 23, 30? (a) 15 (b) 17 (c) 16 (d) 23
  6. 6.What is the missing term in the AP 6, ?, 20, 27, 34? (a) 13 (b) 14 (c) 20 (d) 12
  7. 7.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 15 (c) 25 (d) 30
  8. 8.Which term of the AP 10, 14, 18, 22, … is 70? (a) 15th (b) 18th (c) 17th (d) 16th
  9. 9.What is the 24th term of the AP 4, 7, 10, 13, …? (a) 72 (b) 73 (c) 76 (d) 69
  10. 10.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 325 (c) 625 (d) 49
  11. 11.What is the 27th term of the AP 6, 12, 18, 24, …? (a) 163 (b) 156 (c) 162 (d) 168
  12. 12.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 325 (c) 650 (d) 300
  13. 13.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 21 (b) 18 (c) 20 (d) 19
  14. 14.What is the sum of all the whole numbers from 1 to 31? (a) 496 (b) 497 (c) 992 (d) 465
  15. 15.What is the missing term in the AP 2, 7, ?, 17, 22? (a) 11 (b) 13 (c) 12 (d) 17
  16. 16.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 90 (b) 48 (c) 45 (d) 15
  17. 17.What is the sum of the first 8 terms of the AP 9, 11, 13, …? (a) 256 (b) 23 (c) 136 (d) 128
  18. 18.What is the sum of the first 5 terms of the AP 4, 8, 12, …? (a) 20 (b) 70 (c) 120 (d) 60
  19. 19.What is the missing term in the AP 16, 19, 22, ?, 28? (a) 24 (b) 25 (c) 28 (d) 26
  20. 20.What is the missing term in the AP 10, 18, ?, 34, 42? (a) 26 (b) 27 (c) 34 (d) 25
  21. 21.Which term of the AP 12, 15, 18, 21, … is 105? (a) 33rd (b) 32nd (c) 31st (d) 35th
  22. 22.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 11 (c) 36 (d) 21
  23. 23.What is the sum of the first 10 terms of the AP 7, 12, 17, …? (a) 590 (b) 320 (c) 52 (d) 295
  24. 24.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 841 (d) 870
  25. 25.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 240 (c) 120 (d) 225
  26. 26.What is the 27th term of the AP 16, 23, 30, 37, …? (a) 182 (b) 198 (c) 189 (d) 205
  27. 27.What is the 33rd term of the AP 12, 14, 16, 18, …? (a) 78 (b) 64 (c) 76 (d) 66
  28. 28.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 342 (d) 324
  29. 29.What is the 20th term of the AP 17, 23, 29, 35, …? (a) 137 (b) 131 (c) 120 (d) 114
  30. 30.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 165 (b) 20 (c) 166 (d) 330
  31. 31.What is the 27th term of the AP 20, 25, 30, 35, …? (a) 130 (b) 135 (c) 155 (d) 150
  32. 32.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 19 (b) 130 (c) 68 (d) 65
  33. 33.What is the 19th term of the AP 2, 9, 16, 23, …? (a) 128 (b) 135 (c) 126 (d) 133
  34. 34.What is the 17th term of the AP 9, 11, 13, 15, …? (a) 34 (b) 43 (c) 32 (d) 41
  35. 35.What is the missing term in the AP 2, 7, 12, ?, 22? (a) 22 (b) 16 (c) 18 (d) 17
  36. 36.What is the sum of the first 12 terms of the AP 9, 14, 19, …? (a) 468 (b) 438 (c) 64 (d) 876
  37. 37.What is the missing term in the AP 13, 19, ?, 31, 37? (a) 24 (b) 26 (c) 25 (d) 31
  38. 38.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 60 (b) 110 (c) 55 (d) 15
  39. 39.What is the 35th term of the AP 1, 10, 19, 28, …? (a) 315 (b) 316 (c) 307 (d) 306
  40. 40.What is the sum of all the whole numbers from 1 to 34? (a) 1190 (b) 561 (c) 595 (d) 578

Answer key

  1. 109
  2. 60
  3. 123
  4. 171
  5. 16
  6. 13
  7. 25
  8. 16th
  9. 73
  10. 625
  11. 162
  12. 325
  13. 19
  14. 496
  15. 12
  16. 45
  17. 128
  18. 60
  19. 25
  20. 26
  21. 32nd
  22. 36
  23. 295
  24. 841
  25. 225
  26. 198
  27. 76
  28. 324
  29. 131
  30. 165
  31. 150
  32. 65
  33. 128
  34. 41
  35. 17
  36. 438
  37. 25
  38. 55
  39. 307
  40. 595

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