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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 455 · 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 sum of all the whole numbers from 1 to 45? (a) 1036 (b) 2070 (c) 990 (d) 1035
  2. 2.What is the sum of all the whole numbers from 1 to 40? (a) 800 (b) 1640 (c) 780 (d) 820
  3. 3.What is the 25th term of the AP 8, 12, 16, 20, …? (a) 100 (b) 108 (c) 96 (d) 104
  4. 4.What is the 30th term of the AP 12, 15, 18, 21, …? (a) 102 (b) 99 (c) 87 (d) 90
  5. 5.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 31 (b) 190 (c) 95 (d) 110
  6. 6.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 65 (b) 21 (c) 75 (d) 130
  7. 7.What is the missing term in the AP 9, ?, 21, 27, 33? (a) 16 (b) 14 (c) 15 (d) 21
  8. 8.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 21 (b) 20 (c) 40 (d) 6
  9. 9.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 2926 (c) 2888 (d) 5852
  10. 10.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 63 (b) 112 (c) 14 (d) 56
  11. 11.Which term of the AP 12, 15, 18, 21, … is 42? (a) 11th (b) 12th (c) 14th (d) 10th
  12. 12.What is the sum of the first 6 terms of the AP 8, 9, 10, …? (a) 126 (b) 66 (c) 63 (d) 13
  13. 13.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 184 (b) 336 (c) 35 (d) 168
  14. 14.What is the missing term in the AP 2, 8, 14, ?, 26? (a) 21 (b) 19 (c) 20 (d) 26
  15. 15.What is the sum of all the whole numbers from 1 to 61? (a) 1892 (b) 1891 (c) 3782 (d) 1830
  16. 16.What is the 17th term of the AP 3, 5, 7, 9, …? (a) 32 (b) 35 (c) 37 (d) 34
  17. 17.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 360 (b) 36 (c) 198 (d) 180
  18. 18.What is the 38th term of the AP 11, 19, 27, 35, …? (a) 304 (b) 307 (c) 296 (d) 315
  19. 19.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 625 (d) 650
  20. 20.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 11 (b) 51 (c) 54 (d) 102
  21. 21.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 676 (b) 702 (c) 51 (d) 351
  22. 22.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 16 (b) 60 (c) 65 (d) 120
  23. 23.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 352 (b) 192 (c) 176 (d) 36
  24. 24.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 7 (b) 4 (c) 6 (d) 5
  25. 25.Which term of the AP 14, 18, 22, 26, … is 70? (a) 17th (b) 16th (c) 15th (d) 14th
  26. 26.What is the 22nd term of the AP 2, 6, 10, 14, …? (a) 90 (b) 84 (c) 86 (d) 88
  27. 27.What is the missing term in the AP 12, 19, 26, ?, 40? (a) 40 (b) 32 (c) 33 (d) 34
  28. 28.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 204 (b) 102 (c) 27 (d) 114
  29. 29.What is the missing term in the AP 6, 13, ?, 27, 34? (a) 21 (b) 27 (c) 20 (d) 19
  30. 30.What is the missing term in the AP 4, 7, ?, 13, 16? (a) 10 (b) 13 (c) 11 (d) 9
  31. 31.What is the 11th term of the AP 2, 4, 6, 8, …? (a) 24 (b) 23 (c) 22 (d) 20
  32. 32.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 55 (b) 19 (c) 65 (d) 110
  33. 33.What is the 22nd term of the AP 13, 17, 21, 25, …? (a) 101 (b) 84 (c) 88 (d) 97
  34. 34.What is the 34th term of the AP 14, 21, 28, 35, …? (a) 245 (b) 252 (c) 231 (d) 238
  35. 35.Which term of the AP 17, 24, 31, 38, … is 185? (a) 25th (b) 26th (c) 27th (d) 24th
  36. 36.What is the 12th term of the AP 3, 5, 7, 9, …? (a) 22 (b) 27 (c) 24 (d) 25
  37. 37.What is the 15th term of the AP 20, 28, 36, 44, …? (a) 112 (b) 140 (c) 120 (d) 132
  38. 38.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 132 (d) 66
  39. 39.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 119 (b) 32 (c) 124 (d) 238
  40. 40.Which term of the AP 7, 14, 21, 28, … is 84? (a) 11th (b) 14th (c) 13th (d) 12th

Answer key

  1. 1035
  2. 820
  3. 104
  4. 99
  5. 95
  6. 65
  7. 15
  8. 20
  9. 2926
  10. 56
  11. 11th
  12. 63
  13. 168
  14. 20
  15. 1891
  16. 35
  17. 180
  18. 307
  19. 625
  20. 51
  21. 676
  22. 60
  23. 176
  24. 5
  25. 15th
  26. 86
  27. 33
  28. 102
  29. 20
  30. 10
  31. 22
  32. 55
  33. 97
  34. 245
  35. 25th
  36. 25
  37. 132
  38. 121
  39. 119
  40. 12th

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