← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 456 · 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 the first 10 terms of the AP 2, 4, 6, …? (a) 120 (b) 220 (c) 20 (d) 110
  2. 2.What is the missing term in the AP 13, ?, 23, 28, 33? (a) 18 (b) 19 (c) 23 (d) 17
  3. 3.What is the 28th term of the AP 16, 18, 20, 22, …? (a) 54 (b) 70 (c) 72 (d) 56
  4. 4.What is the 19th term of the AP 11, 20, 29, 38, …? (a) 171 (b) 173 (c) 182 (d) 162
  5. 5.Which term of the AP 17, 25, 33, 41, … is 265? (a) 34th (b) 31st (c) 33rd (d) 32nd
  6. 6.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 182 (b) 94 (c) 22 (d) 91
  7. 7.What is the 32nd term of the AP 2, 10, 18, 26, …? (a) 258 (b) 248 (c) 250 (d) 256
  8. 8.What is the 18th term of the AP 11, 15, 19, 23, …? (a) 79 (b) 83 (c) 68 (d) 72
  9. 9.Which term of the AP 8, 12, 16, 20, … is 148? (a) 35th (b) 37th (c) 38th (d) 36th
  10. 10.What is the missing term in the AP 18, ?, 26, 30, 34? (a) 26 (b) 23 (c) 22 (d) 21
  11. 11.Which term of the AP 7, 10, 13, 16, … is 103? (a) 34th (b) 35th (c) 33rd (d) 32nd
  12. 12.What is the 16th term of the AP 2, 11, 20, 29, …? (a) 144 (b) 146 (c) 135 (d) 137
  13. 13.What is the missing term in the AP 11, ?, 25, 32, 39? (a) 25 (b) 17 (c) 19 (d) 18
  14. 14.Which term of the AP 1, 7, 13, 19, … is 49? (a) 10th (b) 9th (c) 8th (d) 11th
  15. 15.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 344 (b) 192 (c) 172 (d) 39
  16. 16.Which term of the AP 12, 19, 26, 33, … is 173? (a) 26th (b) 24th (c) 25th (d) 23rd
  17. 17.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 186 (b) 28 (c) 93 (d) 108
  18. 18.Which term of the AP 12, 17, 22, 27, … is 77? (a) 15th (b) 13th (c) 16th (d) 14th
  19. 19.What is the 35th term of the AP 15, 21, 27, 33, …? (a) 204 (b) 210 (c) 219 (d) 225
  20. 20.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 441 (c) 462 (d) 231
  21. 21.What is the sum of all the whole numbers from 1 to 22? (a) 242 (b) 231 (c) 506 (d) 253
  22. 22.What is the sum of the first 9 terms of the AP 6, 8, 10, …? (a) 252 (b) 22 (c) 126 (d) 135
  23. 23.What is the 15th term of the AP 13, 21, 29, 37, …? (a) 133 (b) 120 (c) 125 (d) 112
  24. 24.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 2016 (c) 4160 (d) 2080
  25. 25.What is the missing term in the AP 8, 13, 18, ?, 28? (a) 28 (b) 22 (c) 24 (d) 23
  26. 26.What is the 26th term of the AP 12, 21, 30, 39, …? (a) 246 (b) 225 (c) 237 (d) 234
  27. 27.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 90 (b) 170 (c) 85 (d) 13
  28. 28.What is the 27th term of the AP 17, 24, 31, 38, …? (a) 206 (b) 189 (c) 199 (d) 182
  29. 29.What is the missing term in the AP 18, 25, 32, ?, 46? (a) 39 (b) 46 (c) 38 (d) 40
  30. 30.What is the sum of the first 6 terms of the AP 10, 11, 12, …? (a) 75 (b) 15 (c) 150 (d) 78
  31. 31.What is the sum of all the whole numbers from 1 to 21? (a) 462 (b) 232 (c) 210 (d) 231
  32. 32.What is the sum of all the whole numbers from 1 to 85? (a) 3655 (b) 7310 (c) 3656 (d) 3570
  33. 33.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 246 (b) 123 (c) 33 (d) 138
  34. 34.What is the missing term in the AP 8, 17, ?, 35, 44? (a) 26 (b) 27 (c) 25 (d) 35
  35. 35.What is the sum of all the whole numbers from 1 to 19? (a) 190 (b) 191 (c) 171 (d) 380
  36. 36.What is the sum of all the whole numbers from 1 to 69? (a) 2346 (b) 2416 (c) 2415 (d) 4830
  37. 37.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 16 (b) 108 (c) 109 (d) 216
  38. 38.What is the 18th term of the AP 8, 14, 20, 26, …? (a) 110 (b) 108 (c) 102 (d) 116
  39. 39.What is the sum of the first 7 terms of the AP 9, 13, 17, …? (a) 33 (b) 147 (c) 294 (d) 161
  40. 40.Which term of the AP 12, 16, 20, 24, … is 148? (a) 35th (b) 36th (c) 37th (d) 34th

Answer key

  1. 110
  2. 18
  3. 70
  4. 173
  5. 32nd
  6. 91
  7. 250
  8. 79
  9. 36th
  10. 22
  11. 33rd
  12. 137
  13. 18
  14. 9th
  15. 172
  16. 24th
  17. 93
  18. 14th
  19. 219
  20. 441
  21. 253
  22. 126
  23. 125
  24. 2080
  25. 23
  26. 237
  27. 85
  28. 199
  29. 39
  30. 75
  31. 231
  32. 3655
  33. 123
  34. 26
  35. 190
  36. 2415
  37. 108
  38. 110
  39. 147
  40. 35th

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