← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 357 · 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.Which term of the AP 2, 8, 14, 20, … is 206? (a) 35th (b) 36th (c) 34th (d) 37th
  2. 2.What is the missing term in the AP 5, 10, 15, ?, 25? (a) 19 (b) 20 (c) 25 (d) 21
  3. 3.Which term of the AP 9, 14, 19, 24, … is 119? (a) 25th (b) 24th (c) 23rd (d) 22nd
  4. 4.What is the 28th term of the AP 1, 6, 11, 16, …? (a) 141 (b) 136 (c) 135 (d) 140
  5. 5.What is the sum of all the whole numbers from 1 to 57? (a) 1654 (b) 3306 (c) 1596 (d) 1653
  6. 6.What is the 34th term of the AP 19, 22, 25, 28, …? (a) 102 (b) 99 (c) 121 (d) 118
  7. 7.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 44 (b) 182 (c) 364 (d) 203
  8. 8.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 465 (c) 59 (d) 930
  9. 9.What is the 18th term of the AP 8, 16, 24, 32, …? (a) 152 (b) 136 (c) 145 (d) 144
  10. 10.Which term of the AP 18, 27, 36, 45, … is 306? (a) 35th (b) 32nd (c) 33rd (d) 34th
  11. 11.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 552 (c) 276 (d) 529
  12. 12.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 406 (c) 812 (d) 378
  13. 13.What is the missing term in the AP 6, 8, ?, 12, 14? (a) 9 (b) 11 (c) 12 (d) 10
  14. 14.What is the 16th term of the AP 8, 10, 12, 14, …? (a) 38 (b) 30 (c) 32 (d) 40
  15. 15.What is the 11th term of the AP 14, 17, 20, 23, …? (a) 47 (b) 33 (c) 30 (d) 44
  16. 16.Which term of the AP 1, 4, 7, 10, … is 82? (a) 27th (b) 30th (c) 29th (d) 28th
  17. 17.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 14 (b) 43 (c) 40 (d) 80
  18. 18.What is the 40th term of the AP 13, 16, 19, 22, …? (a) 117 (b) 133 (c) 120 (d) 130
  19. 19.Which term of the AP 15, 21, 27, 33, … is 249? (a) 42nd (b) 39th (c) 41st (d) 40th
  20. 20.What is the 38th term of the AP 9, 11, 13, 15, …? (a) 83 (b) 85 (c) 74 (d) 76
  21. 21.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 324 (b) 171 (c) 26 (d) 162
  22. 22.What is the 35th term of the AP 6, 12, 18, 24, …? (a) 210 (b) 211 (c) 216 (d) 204
  23. 23.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 108 (b) 24 (c) 210 (d) 105
  24. 24.Which term of the AP 11, 14, 17, 20, … is 50? (a) 16th (b) 15th (c) 14th (d) 13th
  25. 25.What is the sum of all the whole numbers from 1 to 45? (a) 1035 (b) 2070 (c) 990 (d) 1036
  26. 26.What is the 22nd term of the AP 16, 20, 24, 28, …? (a) 84 (b) 88 (c) 104 (d) 100
  27. 27.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 19 (b) 65 (c) 130 (d) 68
  28. 28.What is the sum of all the whole numbers from 1 to 77? (a) 3003 (b) 2926 (c) 6006 (d) 3004
  29. 29.What is the 20th term of the AP 12, 18, 24, 30, …? (a) 114 (b) 126 (c) 132 (d) 120
  30. 30.What is the sum of the first 9 terms of the AP 5, 7, 9, …? (a) 117 (b) 21 (c) 234 (d) 126
  31. 31.What is the 12th term of the AP 1, 8, 15, 22, …? (a) 84 (b) 77 (c) 85 (d) 78
  32. 32.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 14 (b) 78 (c) 77 (d) 154
  33. 33.What is the 33rd term of the AP 14, 21, 28, 35, …? (a) 245 (b) 224 (c) 231 (d) 238
  34. 34.What is the 21st term of the AP 7, 10, 13, 16, …? (a) 60 (b) 63 (c) 70 (d) 67
  35. 35.What is the 19th term of the AP 18, 26, 34, 42, …? (a) 170 (b) 152 (c) 144 (d) 162
  36. 36.What is the 35th term of the AP 2, 9, 16, 23, …? (a) 240 (b) 247 (c) 238 (d) 245
  37. 37.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 400 (b) 370 (c) 64 (d) 740
  38. 38.What is the 27th term of the AP 7, 13, 19, 25, …? (a) 156 (b) 169 (c) 162 (d) 163
  39. 39.What is the 19th term of the AP 20, 26, 32, 38, …? (a) 134 (b) 114 (c) 108 (d) 128
  40. 40.What is the sum of the first 9 terms of the AP 9, 11, 13, …? (a) 25 (b) 162 (c) 306 (d) 153

Answer key

  1. 35th
  2. 20
  3. 23rd
  4. 136
  5. 1653
  6. 118
  7. 182
  8. 900
  9. 144
  10. 33rd
  11. 529
  12. 406
  13. 10
  14. 38
  15. 44
  16. 28th
  17. 40
  18. 130
  19. 40th
  20. 83
  21. 162
  22. 210
  23. 105
  24. 14th
  25. 1035
  26. 100
  27. 65
  28. 3003
  29. 126
  30. 117
  31. 78
  32. 77
  33. 238
  34. 67
  35. 162
  36. 240
  37. 370
  38. 163
  39. 128
  40. 153

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad