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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 714 · 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 15, 18, 21, ?, 27? (a) 25 (b) 24 (c) 27 (d) 23
  2. 2.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 56 (d) 49
  3. 3.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 84 (b) 72 (c) 22 (d) 144
  4. 4.What is the 17th term of the AP 6, 10, 14, 18, …? (a) 64 (b) 74 (c) 68 (d) 70
  5. 5.What is the 15th term of the AP 5, 8, 11, 14, …? (a) 42 (b) 47 (c) 45 (d) 50
  6. 6.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 21 (d) 42
  7. 7.What is the 24th term of the AP 9, 16, 23, 30, …? (a) 170 (b) 161 (c) 177 (d) 168
  8. 8.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 228 (b) 114 (c) 29 (d) 126
  9. 9.Which term of the AP 4, 10, 16, 22, … is 184? (a) 30th (b) 32nd (c) 31st (d) 33rd
  10. 10.What is the 26th term of the AP 16, 23, 30, 37, …? (a) 198 (b) 191 (c) 175 (d) 182
  11. 11.What is the sum of the first 10 terms of the AP 9, 14, 19, …? (a) 340 (b) 54 (c) 630 (d) 315
  12. 12.What is the sum of all the whole numbers from 1 to 88? (a) 7832 (b) 3872 (c) 3828 (d) 3916
  13. 13.What is the sum of all the whole numbers from 1 to 61? (a) 1830 (b) 1891 (c) 1892 (d) 3782
  14. 14.What is the 20th term of the AP 14, 20, 26, 32, …? (a) 128 (b) 134 (c) 120 (d) 114
  15. 15.What is the sum of the first 6 terms of the AP 9, 10, 11, …? (a) 72 (b) 14 (c) 69 (d) 138
  16. 16.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 21 (c) 121 (d) 132
  17. 17.What is the 27th term of the AP 6, 10, 14, 18, …? (a) 104 (b) 114 (c) 110 (d) 108
  18. 18.What is the missing term in the AP 11, 16, 21, ?, 31? (a) 25 (b) 26 (c) 27 (d) 31
  19. 19.What is the missing term in the AP 19, ?, 37, 46, 55? (a) 27 (b) 37 (c) 28 (d) 29
  20. 20.What is the missing term in the AP 4, 10, ?, 22, 28? (a) 22 (b) 16 (c) 15 (d) 17
  21. 21.What is the missing term in the AP 11, 14, 17, ?, 23? (a) 21 (b) 23 (c) 20 (d) 19
  22. 22.Which term of the AP 17, 19, 21, 23, … is 31? (a) 9th (b) 7th (c) 10th (d) 8th
  23. 23.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 140 (b) 24 (c) 75 (d) 70
  24. 24.What is the 18th term of the AP 3, 10, 17, 24, …? (a) 129 (b) 122 (c) 119 (d) 126
  25. 25.What is the sum of all the whole numbers from 1 to 14? (a) 105 (b) 210 (c) 91 (d) 98
  26. 26.Which term of the AP 4, 8, 12, 16, … is 160? (a) 42nd (b) 41st (c) 39th (d) 40th
  27. 27.Which term of the AP 12, 14, 16, 18, … is 52? (a) 22nd (b) 26th (c) 21st (d) 20th
  28. 28.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 378 (c) 729 (d) 756
  29. 29.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 30 (b) 16 (c) 5 (d) 15
  30. 30.What is the missing term in the AP 1, 5, 9, ?, 17? (a) 14 (b) 12 (c) 17 (d) 13
  31. 31.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 784 (d) 406
  32. 32.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 2070 (c) 1035 (d) 1036
  33. 33.Which term of the AP 11, 15, 19, 23, … is 71? (a) 17th (b) 15th (c) 16th (d) 18th
  34. 34.Which term of the AP 1, 3, 5, 7, … is 79? (a) 42nd (b) 41st (c) 40th (d) 39th
  35. 35.What is the missing term in the AP 8, 13, 18, ?, 28? (a) 28 (b) 22 (c) 23 (d) 24
  36. 36.What is the 31st term of the AP 3, 6, 9, 12, …? (a) 90 (b) 93 (c) 94 (d) 96
  37. 37.What is the missing term in the AP 12, ?, 26, 33, 40? (a) 26 (b) 20 (c) 19 (d) 18
  38. 38.Which term of the AP 1, 6, 11, 16, … is 141? (a) 30th (b) 28th (c) 29th (d) 31st
  39. 39.What is the 17th term of the AP 6, 9, 12, 15, …? (a) 54 (b) 51 (c) 57 (d) 48
  40. 40.What is the sum of all the whole numbers from 1 to 66? (a) 4422 (b) 2178 (c) 2145 (d) 2211

Answer key

  1. 24
  2. 49
  3. 72
  4. 70
  5. 47
  6. 36
  7. 170
  8. 114
  9. 31st
  10. 191
  11. 315
  12. 3916
  13. 1891
  14. 128
  15. 69
  16. 121
  17. 110
  18. 26
  19. 28
  20. 16
  21. 20
  22. 8th
  23. 70
  24. 122
  25. 105
  26. 40th
  27. 21st
  28. 729
  29. 15
  30. 13
  31. 784
  32. 1035
  33. 16th
  34. 40th
  35. 23
  36. 93
  37. 19
  38. 29th
  39. 54
  40. 2211

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