← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 426 · 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 8, ?, 20, 26, 32? (a) 15 (b) 14 (c) 13 (d) 20
  2. 2.What is the 24th term of the AP 5, 11, 17, 23, …? (a) 143 (b) 138 (c) 144 (d) 149
  3. 3.What is the sum of the first 10 terms of the AP 9, 13, 17, …? (a) 540 (b) 270 (c) 290 (d) 45
  4. 4.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 306 (b) 42 (c) 324 (d) 612
  5. 5.What is the 17th term of the AP 17, 25, 33, 41, …? (a) 128 (b) 153 (c) 145 (d) 136
  6. 6.What is the 13th term of the AP 11, 18, 25, 32, …? (a) 91 (b) 102 (c) 84 (d) 95
  7. 7.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 240 (b) 450 (c) 225 (d) 36
  8. 8.What is the 25th term of the AP 5, 9, 13, 17, …? (a) 105 (b) 101 (c) 100 (d) 96
  9. 9.Which term of the AP 16, 25, 34, 43, … is 349? (a) 39th (b) 37th (c) 40th (d) 38th
  10. 10.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 28 (b) 108 (c) 216 (d) 120
  11. 11.What is the sum of all the whole numbers from 1 to 26? (a) 702 (b) 351 (c) 338 (d) 325
  12. 12.What is the 39th term of the AP 15, 19, 23, 27, …? (a) 171 (b) 156 (c) 167 (d) 152
  13. 13.What is the 18th term of the AP 3, 6, 9, 12, …? (a) 51 (b) 55 (c) 54 (d) 57
  14. 14.What is the 15th term of the AP 4, 9, 14, 19, …? (a) 75 (b) 70 (c) 74 (d) 79
  15. 15.Which term of the AP 5, 14, 23, 32, … is 311? (a) 34th (b) 36th (c) 37th (d) 35th
  16. 16.What is the 15th term of the AP 15, 22, 29, 36, …? (a) 98 (b) 113 (c) 105 (d) 120
  17. 17.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 64 (d) 72
  18. 18.What is the sum of all the whole numbers from 1 to 51? (a) 1327 (b) 2652 (c) 1275 (d) 1326
  19. 19.What is the 34th term of the AP 18, 25, 32, 39, …? (a) 256 (b) 238 (c) 231 (d) 249
  20. 20.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 324 (b) 162 (c) 180 (d) 34
  21. 21.What is the sum of all the whole numbers from 1 to 38? (a) 1482 (b) 722 (c) 741 (d) 703
  22. 22.What is the 24th term of the AP 2, 8, 14, 20, …? (a) 144 (b) 146 (c) 138 (d) 140
  23. 23.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 27 (c) 210 (d) 105
  24. 24.What is the missing term in the AP 11, 14, ?, 20, 23? (a) 17 (b) 16 (c) 20 (d) 18
  25. 25.What is the 40th term of the AP 11, 14, 17, 20, …? (a) 120 (b) 117 (c) 128 (d) 131
  26. 26.What is the missing term in the AP 12, 20, ?, 36, 44? (a) 29 (b) 27 (c) 28 (d) 36
  27. 27.What is the sum of all the whole numbers from 1 to 92? (a) 8556 (b) 4186 (c) 4278 (d) 4232
  28. 28.What is the 20th term of the AP 12, 21, 30, 39, …? (a) 180 (b) 183 (c) 171 (d) 192
  29. 29.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 102 (b) 204 (c) 120 (d) 32
  30. 30.What is the 20th term of the AP 2, 5, 8, 11, …? (a) 59 (b) 60 (c) 57 (d) 62
  31. 31.What is the missing term in the AP 1, ?, 13, 19, 25? (a) 7 (b) 8 (c) 13 (d) 6
  32. 32.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 8 (b) 36 (c) 35 (d) 70
  33. 33.What is the 15th term of the AP 1, 10, 19, 28, …? (a) 126 (b) 127 (c) 135 (d) 136
  34. 34.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 99 (b) 14 (c) 100 (d) 198
  35. 35.What is the 35th term of the AP 4, 11, 18, 25, …? (a) 249 (b) 245 (c) 238 (d) 242
  36. 36.Which term of the AP 1, 8, 15, 22, … is 225? (a) 35th (b) 32nd (c) 34th (d) 33rd
  37. 37.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 18 (b) 17 (c) 22 (d) 19
  38. 38.Which term of the AP 20, 27, 34, 41, … is 167? (a) 21st (b) 23rd (c) 24th (d) 22nd
  39. 39.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 81 (d) 45
  40. 40.What is the 38th term of the AP 15, 23, 31, 39, …? (a) 304 (b) 311 (c) 319 (d) 296

Answer key

  1. 14
  2. 143
  3. 270
  4. 306
  5. 145
  6. 95
  7. 225
  8. 101
  9. 38th
  10. 108
  11. 351
  12. 167
  13. 54
  14. 74
  15. 35th
  16. 113
  17. 64
  18. 1326
  19. 249
  20. 162
  21. 741
  22. 140
  23. 196
  24. 17
  25. 128
  26. 28
  27. 4278
  28. 183
  29. 102
  30. 59
  31. 7
  32. 35
  33. 127
  34. 99
  35. 242
  36. 33rd
  37. 18
  38. 22nd
  39. 81
  40. 311

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