← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 218 · 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 35th term of the AP 3, 7, 11, 15, …? (a) 136 (b) 139 (c) 143 (d) 140
  2. 2.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 15 (c) 36 (d) 72
  3. 3.What is the sum of the first 5 terms of the AP 1, 3, 5, …? (a) 9 (b) 50 (c) 25 (d) 30
  4. 4.Which term of the AP 15, 22, 29, 36, … is 78? (a) 11th (b) 12th (c) 10th (d) 9th
  5. 5.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 31 (b) 60 (c) 30 (d) 8
  6. 6.What is the 18th term of the AP 17, 22, 27, 32, …? (a) 85 (b) 107 (c) 102 (d) 90
  7. 7.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 5 (b) 6 (c) 4 (d) 7
  8. 8.What is the 31st term of the AP 12, 15, 18, 21, …? (a) 90 (b) 102 (c) 93 (d) 105
  9. 9.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 88 (b) 160 (c) 80 (d) 17
  10. 10.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 162 (b) 26 (c) 96 (d) 81
  11. 11.Which term of the AP 17, 25, 33, 41, … is 73? (a) 9th (b) 10th (c) 7th (d) 8th
  12. 12.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 168 (b) 147 (c) 294 (d) 39
  13. 13.What is the 21st term of the AP 7, 11, 15, 19, …? (a) 84 (b) 80 (c) 87 (d) 91
  14. 14.What is the missing term in the AP 2, ?, 12, 17, 22? (a) 12 (b) 8 (c) 7 (d) 6
  15. 15.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 19 (c) 55 (d) 100
  16. 16.What is the sum of the first 8 terms of the AP 2, 5, 8, …? (a) 200 (b) 112 (c) 100 (d) 23
  17. 17.What is the 31st term of the AP 2, 8, 14, 20, …? (a) 188 (b) 182 (c) 180 (d) 186
  18. 18.What is the 18th term of the AP 8, 10, 12, 14, …? (a) 44 (b) 34 (c) 42 (d) 36
  19. 19.Which term of the AP 19, 22, 25, 28, … is 52? (a) 14th (b) 11th (c) 12th (d) 13th
  20. 20.Which term of the AP 7, 10, 13, 16, … is 55? (a) 18th (b) 17th (c) 19th (d) 16th
  21. 21.What is the 34th term of the AP 12, 19, 26, 33, …? (a) 250 (b) 238 (c) 231 (d) 243
  22. 22.What is the sum of all the whole numbers from 1 to 22? (a) 506 (b) 242 (c) 231 (d) 253
  23. 23.What is the 34th term of the AP 18, 26, 34, 42, …? (a) 264 (b) 272 (c) 290 (d) 282
  24. 24.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 66 (c) 21 (d) 132
  25. 25.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 235 (b) 470 (c) 260 (d) 46
  26. 26.What is the 28th term of the AP 2, 8, 14, 20, …? (a) 162 (b) 164 (c) 170 (d) 168
  27. 27.What is the 36th term of the AP 6, 13, 20, 27, …? (a) 258 (b) 245 (c) 251 (d) 252
  28. 28.What is the 29th term of the AP 7, 14, 21, 28, …? (a) 210 (b) 203 (c) 196 (d) 204
  29. 29.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 240 (b) 51 (c) 264 (d) 480
  30. 30.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 266 (b) 133 (c) 37 (d) 154
  31. 31.What is the sum of all the whole numbers from 1 to 20? (a) 200 (b) 420 (c) 210 (d) 190
  32. 32.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 38 (b) 35 (c) 13 (d) 70
  33. 33.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 156 (d) 144
  34. 34.Which term of the AP 2, 7, 12, 17, … is 57? (a) 14th (b) 13th (c) 11th (d) 12th
  35. 35.What is the 38th term of the AP 18, 20, 22, 24, …? (a) 92 (b) 76 (c) 74 (d) 94
  36. 36.What is the sum of all the whole numbers from 1 to 87? (a) 3828 (b) 7656 (c) 3741 (d) 3829
  37. 37.What is the missing term in the AP 11, ?, 21, 26, 31? (a) 21 (b) 15 (c) 16 (d) 17
  38. 38.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 29 (b) 133 (c) 238 (d) 119
  39. 39.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 216 (b) 28 (c) 120 (d) 108
  40. 40.What is the 14th term of the AP 12, 16, 20, 24, …? (a) 56 (b) 52 (c) 64 (d) 68

Answer key

  1. 139
  2. 64
  3. 25
  4. 10th
  5. 30
  6. 102
  7. 5
  8. 102
  9. 80
  10. 81
  11. 8th
  12. 147
  13. 87
  14. 7
  15. 100
  16. 100
  17. 182
  18. 42
  19. 12th
  20. 17th
  21. 243
  22. 253
  23. 282
  24. 121
  25. 235
  26. 164
  27. 251
  28. 203
  29. 240
  30. 133
  31. 210
  32. 35
  33. 144
  34. 12th
  35. 92
  36. 3828
  37. 16
  38. 119
  39. 108
  40. 64

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