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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 335 · 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 15th term of the AP 1, 5, 9, 13, …? (a) 60 (b) 56 (c) 57 (d) 61
  2. 2.What is the sum of all the whole numbers from 1 to 95? (a) 9120 (b) 4465 (c) 4560 (d) 4561
  3. 3.What is the 21st term of the AP 12, 20, 28, 36, …? (a) 172 (b) 168 (c) 160 (d) 180
  4. 4.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 900 (c) 465 (d) 59
  5. 5.What is the 38th term of the AP 16, 19, 22, 25, …? (a) 111 (b) 127 (c) 114 (d) 130
  6. 6.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 406 (d) 784
  7. 7.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 342 (d) 324
  8. 8.What is the 11th term of the AP 14, 22, 30, 38, …? (a) 94 (b) 102 (c) 88 (d) 80
  9. 9.What is the 18th term of the AP 13, 19, 25, 31, …? (a) 102 (b) 121 (c) 108 (d) 115
  10. 10.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 128 (b) 120 (c) 240 (d) 22
  11. 11.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 272 (b) 248 (c) 496 (d) 52
  12. 12.Which term of the AP 5, 8, 11, 14, … is 122? (a) 41st (b) 42nd (c) 40th (d) 39th
  13. 13.What is the sum of all the whole numbers from 1 to 14? (a) 91 (b) 98 (c) 210 (d) 105
  14. 14.What is the 12th term of the AP 6, 11, 16, 21, …? (a) 55 (b) 66 (c) 61 (d) 60
  15. 15.What is the 19th term of the AP 7, 11, 15, 19, …? (a) 76 (b) 79 (c) 72 (d) 83
  16. 16.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 26 (b) 81 (c) 162 (d) 96
  17. 17.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 2016 (c) 4160 (d) 2080
  18. 18.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 99 (b) 198 (c) 29 (d) 114
  19. 19.What is the 30th term of the AP 5, 8, 11, 14, …? (a) 92 (b) 90 (c) 87 (d) 95
  20. 20.What is the 24th term of the AP 4, 8, 12, 16, …? (a) 100 (b) 92 (c) 97 (d) 96
  21. 21.Which term of the AP 1, 7, 13, 19, … is 97? (a) 18th (b) 17th (c) 16th (d) 19th
  22. 22.What is the 18th term of the AP 11, 14, 17, 20, …? (a) 51 (b) 62 (c) 54 (d) 65
  23. 23.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 130 (b) 65 (c) 70 (d) 23
  24. 24.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 66 (c) 132 (d) 121
  25. 25.What is the 27th term of the AP 2, 5, 8, 11, …? (a) 81 (b) 78 (c) 83 (d) 80
  26. 26.What is the sum of the first 8 terms of the AP 6, 7, 8, …? (a) 80 (b) 13 (c) 152 (d) 76
  27. 27.What is the sum of the first 9 terms of the AP 6, 10, 14, …? (a) 216 (b) 38 (c) 198 (d) 396
  28. 28.Which term of the AP 8, 14, 20, 26, … is 134? (a) 21st (b) 24th (c) 23rd (d) 22nd
  29. 29.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 100 (b) 50 (c) 18 (d) 60
  30. 30.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 70 (b) 9 (c) 36 (d) 35
  31. 31.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 756 (c) 53 (d) 729
  32. 32.What is the 19th term of the AP 6, 10, 14, 18, …? (a) 82 (b) 76 (c) 78 (d) 72
  33. 33.Which term of the AP 1, 7, 13, 19, … is 73? (a) 12th (b) 13th (c) 15th (d) 14th
  34. 34.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2145 (c) 2146 (d) 2080
  35. 35.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 105 (c) 27 (d) 210
  36. 36.What is the missing term in the AP 3, 8, 13, ?, 23? (a) 18 (b) 23 (c) 17 (d) 19
  37. 37.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 2017 (c) 2016 (d) 1953
  38. 38.What is the sum of the first 9 terms of the AP 7, 12, 17, …? (a) 248 (b) 243 (c) 47 (d) 486
  39. 39.Which term of the AP 7, 16, 25, 34, … is 313? (a) 35th (b) 37th (c) 34th (d) 36th
  40. 40.What is the 17th term of the AP 12, 17, 22, 27, …? (a) 97 (b) 85 (c) 80 (d) 92

Answer key

  1. 57
  2. 4560
  3. 172
  4. 900
  5. 127
  6. 784
  7. 324
  8. 94
  9. 115
  10. 120
  11. 248
  12. 40th
  13. 105
  14. 61
  15. 79
  16. 81
  17. 2080
  18. 99
  19. 92
  20. 96
  21. 17th
  22. 62
  23. 65
  24. 121
  25. 80
  26. 76
  27. 198
  28. 22nd
  29. 50
  30. 35
  31. 729
  32. 78
  33. 13th
  34. 2145
  35. 196
  36. 18
  37. 2016
  38. 243
  39. 35th
  40. 92

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