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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 869 · 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, 7, ?, 19, 25? (a) 19 (b) 12 (c) 13 (d) 14
  2. 2.Which term of the AP 16, 24, 32, 40, … is 80? (a) 8th (b) 9th (c) 10th (d) 11th
  3. 3.Which term of the AP 11, 17, 23, 29, … is 191? (a) 31st (b) 33rd (c) 30th (d) 32nd
  4. 4.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 465 (c) 59 (d) 900
  5. 5.Which term of the AP 19, 22, 25, 28, … is 40? (a) 9th (b) 7th (c) 10th (d) 8th
  6. 6.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 49 (c) 56 (d) 13
  7. 7.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 55 (d) 100
  8. 8.What is the 35th term of the AP 10, 15, 20, 25, …? (a) 185 (b) 170 (c) 180 (d) 175
  9. 9.What is the 40th term of the AP 14, 16, 18, 20, …? (a) 94 (b) 92 (c) 80 (d) 78
  10. 10.What is the 29th term of the AP 3, 5, 7, 9, …? (a) 61 (b) 59 (c) 58 (d) 56
  11. 11.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 22 (b) 18 (c) 19 (d) 17
  12. 12.What is the 16th term of the AP 3, 10, 17, 24, …? (a) 108 (b) 105 (c) 112 (d) 115
  13. 13.What is the 39th term of the AP 20, 24, 28, 32, …? (a) 176 (b) 152 (c) 172 (d) 156
  14. 14.What is the sum of the first 7 terms of the AP 8, 12, 16, …? (a) 154 (b) 280 (c) 32 (d) 140
  15. 15.What is the 10th term of the AP 14, 17, 20, 23, …? (a) 44 (b) 27 (c) 41 (d) 30
  16. 16.What is the missing term in the AP 2, 9, ?, 23, 30? (a) 16 (b) 23 (c) 17 (d) 15
  17. 17.What is the 14th term of the AP 5, 7, 9, 11, …? (a) 31 (b) 26 (c) 28 (d) 33
  18. 18.What is the missing term in the AP 6, 11, ?, 21, 26? (a) 15 (b) 17 (c) 21 (d) 16
  19. 19.What is the sum of the first 11 terms of the AP 3, 8, 13, …? (a) 616 (b) 53 (c) 313 (d) 308
  20. 20.What is the sum of all the whole numbers from 1 to 56? (a) 1568 (b) 1540 (c) 3192 (d) 1596
  21. 21.Which term of the AP 5, 10, 15, 20, … is 50? (a) 12th (b) 10th (c) 11th (d) 9th
  22. 22.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 70 (b) 22 (c) 140 (d) 80
  23. 23.What is the 31st term of the AP 11, 16, 21, 26, …? (a) 150 (b) 166 (c) 155 (d) 161
  24. 24.What is the sum of the first 8 terms of the AP 3, 8, 13, …? (a) 328 (b) 184 (c) 38 (d) 164
  25. 25.What is the missing term in the AP 10, ?, 26, 34, 42? (a) 18 (b) 19 (c) 17 (d) 26
  26. 26.What is the 18th term of the AP 6, 12, 18, 24, …? (a) 114 (b) 108 (c) 109 (d) 102
  27. 27.What is the sum of all the whole numbers from 1 to 47? (a) 2256 (b) 1128 (c) 1081 (d) 1129
  28. 28.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 14 (b) 50 (c) 55 (d) 100
  29. 29.What is the 32nd term of the AP 18, 23, 28, 33, …? (a) 155 (b) 173 (c) 178 (d) 160
  30. 30.What is the sum of all the whole numbers from 1 to 26? (a) 351 (b) 338 (c) 702 (d) 325
  31. 31.What is the sum of all the whole numbers from 1 to 88? (a) 3828 (b) 3916 (c) 3872 (d) 7832
  32. 32.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 198 (b) 114 (c) 29 (d) 99
  33. 33.What is the 24th term of the AP 5, 7, 9, 11, …? (a) 46 (b) 53 (c) 51 (d) 48
  34. 34.What is the 12th term of the AP 17, 22, 27, 32, …? (a) 72 (b) 60 (c) 55 (d) 77
  35. 35.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 30 (b) 440 (c) 231 (d) 220
  36. 36.Which term of the AP 10, 18, 26, 34, … is 170? (a) 22nd (b) 20th (c) 21st (d) 23rd
  37. 37.What is the 18th term of the AP 16, 18, 20, 22, …? (a) 52 (b) 50 (c) 34 (d) 36
  38. 38.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 496 (c) 465 (d) 497
  39. 39.What is the sum of the first 7 terms of the AP 5, 7, 9, …? (a) 77 (b) 154 (c) 17 (d) 84
  40. 40.What is the sum of the first 5 terms of the AP 9, 10, 11, …? (a) 13 (b) 55 (c) 56 (d) 110

Answer key

  1. 13
  2. 9th
  3. 31st
  4. 900
  5. 8th
  6. 49
  7. 100
  8. 180
  9. 92
  10. 59
  11. 18
  12. 108
  13. 172
  14. 140
  15. 41
  16. 16
  17. 31
  18. 16
  19. 308
  20. 1596
  21. 10th
  22. 70
  23. 161
  24. 164
  25. 18
  26. 108
  27. 1128
  28. 50
  29. 173
  30. 351
  31. 3916
  32. 99
  33. 51
  34. 72
  35. 220
  36. 21st
  37. 50
  38. 496
  39. 77
  40. 55

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