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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 998 · 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 12, ?, 20, 24, 28? (a) 20 (b) 15 (c) 17 (d) 16
  2. 2.What is the 23rd term of the AP 11, 15, 19, 23, …? (a) 92 (b) 99 (c) 103 (d) 88
  3. 3.What is the 22nd term of the AP 15, 17, 19, 21, …? (a) 44 (b) 57 (c) 42 (d) 59
  4. 4.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 15 (b) 90 (c) 48 (d) 45
  5. 5.What is the 21st term of the AP 17, 26, 35, 44, …? (a) 206 (b) 189 (c) 180 (d) 197
  6. 6.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 31 (b) 350 (c) 175 (d) 190
  7. 7.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 154 (b) 286 (c) 23 (d) 143
  8. 8.Which term of the AP 19, 24, 29, 34, … is 209? (a) 38th (b) 41st (c) 40th (d) 39th
  9. 9.What is the 37th term of the AP 3, 11, 19, 27, …? (a) 299 (b) 296 (c) 288 (d) 291
  10. 10.What is the sum of the first 11 terms of the AP 1, 5, 9, …? (a) 253 (b) 231 (c) 41 (d) 462
  11. 11.What is the sum of the first 12 terms of the AP 2, 6, 10, …? (a) 312 (b) 288 (c) 46 (d) 576
  12. 12.What is the 34th term of the AP 7, 9, 11, 13, …? (a) 75 (b) 66 (c) 73 (d) 68
  13. 13.What is the sum of the first 10 terms of the AP 3, 8, 13, …? (a) 255 (b) 48 (c) 510 (d) 280
  14. 14.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 19 (b) 110 (c) 100 (d) 200
  15. 15.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 108 (b) 192 (c) 26 (d) 96
  16. 16.What is the 12th term of the AP 20, 26, 32, 38, …? (a) 66 (b) 92 (c) 72 (d) 86
  17. 17.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 41 (c) 441 (d) 462
  18. 18.What is the 23rd term of the AP 12, 19, 26, 33, …? (a) 173 (b) 166 (c) 154 (d) 161
  19. 19.What is the sum of the first 6 terms of the AP 1, 4, 7, …? (a) 16 (b) 60 (c) 51 (d) 102
  20. 20.What is the 10th term of the AP 5, 8, 11, 14, …? (a) 30 (b) 27 (c) 35 (d) 32
  21. 21.What is the missing term in the AP 16, 24, 32, ?, 48? (a) 39 (b) 48 (c) 41 (d) 40
  22. 22.What is the 15th term of the AP 6, 12, 18, 24, …? (a) 90 (b) 96 (c) 91 (d) 84
  23. 23.What is the missing term in the AP 12, 15, ?, 21, 24? (a) 19 (b) 17 (c) 18 (d) 21
  24. 24.Which term of the AP 12, 14, 16, 18, … is 42? (a) 15th (b) 16th (c) 17th (d) 21st
  25. 25.What is the 15th term of the AP 11, 14, 17, 20, …? (a) 53 (b) 45 (c) 56 (d) 42
  26. 26.What is the 16th term of the AP 4, 6, 8, 10, …? (a) 36 (b) 34 (c) 32 (d) 30
  27. 27.What is the 14th term of the AP 13, 15, 17, 19, …? (a) 28 (b) 39 (c) 26 (d) 41
  28. 28.What is the 11th term of the AP 3, 11, 19, 27, …? (a) 88 (b) 91 (c) 80 (d) 83
  29. 29.What is the 39th term of the AP 10, 15, 20, 25, …? (a) 195 (b) 200 (c) 205 (d) 190
  30. 30.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 342 (c) 35 (d) 171
  31. 31.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 40 (b) 41 (c) 10 (d) 80
  32. 32.What is the sum of all the whole numbers from 1 to 98? (a) 9702 (b) 4753 (c) 4851 (d) 4802
  33. 33.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 42 (b) 336 (c) 189 (d) 168
  34. 34.Which term of the AP 7, 13, 19, 25, … is 145? (a) 23rd (b) 26th (c) 24th (d) 25th
  35. 35.What is the missing term in the AP 19, 23, ?, 31, 35? (a) 26 (b) 28 (c) 31 (d) 27
  36. 36.What is the 32nd term of the AP 18, 21, 24, 27, …? (a) 96 (b) 93 (c) 111 (d) 114
  37. 37.What is the sum of all the whole numbers from 1 to 69? (a) 2346 (b) 4830 (c) 2416 (d) 2415
  38. 38.Which term of the AP 11, 16, 21, 26, … is 131? (a) 27th (b) 24th (c) 25th (d) 26th
  39. 39.What is the sum of all the whole numbers from 1 to 93? (a) 4371 (b) 8742 (c) 4372 (d) 4278
  40. 40.What is the 10th term of the AP 5, 10, 15, 20, …? (a) 51 (b) 45 (c) 50 (d) 55

Answer key

  1. 16
  2. 99
  3. 57
  4. 45
  5. 197
  6. 175
  7. 143
  8. 39th
  9. 291
  10. 231
  11. 288
  12. 73
  13. 255
  14. 100
  15. 96
  16. 86
  17. 441
  18. 166
  19. 51
  20. 32
  21. 40
  22. 90
  23. 18
  24. 16th
  25. 53
  26. 34
  27. 39
  28. 83
  29. 200
  30. 324
  31. 40
  32. 4851
  33. 168
  34. 24th
  35. 27
  36. 111
  37. 2415
  38. 25th
  39. 4371
  40. 50

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