← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 746 · 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 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 600 (c) 576 (d) 47
  2. 2.What is the missing term in the AP 5, 11, ?, 23, 29? (a) 16 (b) 17 (c) 23 (d) 18
  3. 3.What is the 33rd term of the AP 6, 8, 10, 12, …? (a) 64 (b) 66 (c) 72 (d) 70
  4. 4.What is the 10th term of the AP 16, 22, 28, 34, …? (a) 70 (b) 60 (c) 54 (d) 76
  5. 5.What is the 35th term of the AP 11, 18, 25, 32, …? (a) 256 (b) 245 (c) 249 (d) 238
  6. 6.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 156 (b) 23 (c) 288 (d) 144
  7. 7.Which term of the AP 10, 13, 16, 19, … is 58? (a) 16th (b) 19th (c) 17th (d) 18th
  8. 8.What is the 16th term of the AP 4, 10, 16, 22, …? (a) 90 (b) 100 (c) 94 (d) 96
  9. 9.What is the 33rd term of the AP 18, 26, 34, 42, …? (a) 274 (b) 282 (c) 256 (d) 264
  10. 10.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 650 (c) 325 (d) 49
  11. 11.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 28 (d) 49
  12. 12.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 702 (b) 676 (c) 51 (d) 351
  13. 13.What is the 27th term of the AP 15, 18, 21, 24, …? (a) 81 (b) 78 (c) 93 (d) 96
  14. 14.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 66 (b) 16 (c) 132 (d) 72
  15. 15.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 17 (b) 78 (c) 72 (d) 144
  16. 16.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 108 (b) 216 (c) 109 (d) 16
  17. 17.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 19 (b) 198 (c) 99 (d) 108
  18. 18.What is the 16th term of the AP 17, 25, 33, 41, …? (a) 120 (b) 145 (c) 128 (d) 137
  19. 19.What is the 27th term of the AP 3, 9, 15, 21, …? (a) 165 (b) 162 (c) 159 (d) 156
  20. 20.What is the 31st term of the AP 9, 15, 21, 27, …? (a) 189 (b) 195 (c) 186 (d) 180
  21. 21.What is the sum of the first 9 terms of the AP 2, 8, 14, …? (a) 50 (b) 468 (c) 261 (d) 234
  22. 22.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 110 (b) 15 (c) 111 (d) 220
  23. 23.What is the sum of all the whole numbers from 1 to 34? (a) 1190 (b) 595 (c) 561 (d) 578
  24. 24.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 145 (b) 28 (c) 290 (d) 160
  25. 25.Which term of the AP 3, 6, 9, 12, … is 48? (a) 18th (b) 16th (c) 17th (d) 15th
  26. 26.What is the sum of the first 12 terms of the AP 9, 12, 15, …? (a) 42 (b) 612 (c) 324 (d) 306
  27. 27.What is the missing term in the AP 1, ?, 19, 28, 37? (a) 19 (b) 9 (c) 10 (d) 11
  28. 28.Which term of the AP 11, 16, 21, 26, … is 56? (a) 9th (b) 12th (c) 11th (d) 10th
  29. 29.What is the 25th term of the AP 20, 29, 38, 47, …? (a) 216 (b) 225 (c) 245 (d) 236
  30. 30.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 110 (b) 220 (c) 120 (d) 20
  31. 31.Which term of the AP 5, 14, 23, 32, … is 338? (a) 39th (b) 37th (c) 40th (d) 38th
  32. 32.What is the 23rd term of the AP 17, 26, 35, 44, …? (a) 207 (b) 198 (c) 224 (d) 215
  33. 33.What is the 32nd term of the AP 12, 15, 18, 21, …? (a) 96 (b) 108 (c) 93 (d) 105
  34. 34.What is the 26th term of the AP 19, 28, 37, 46, …? (a) 234 (b) 244 (c) 253 (d) 225
  35. 35.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 36 (c) 21 (d) 42
  36. 36.What is the 39th term of the AP 7, 16, 25, 34, …? (a) 351 (b) 349 (c) 342 (d) 358
  37. 37.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 14 (b) 80 (c) 40 (d) 43
  38. 38.What is the 40th term of the AP 6, 15, 24, 33, …? (a) 366 (b) 360 (c) 357 (d) 351
  39. 39.What is the 34th term of the AP 18, 20, 22, 24, …? (a) 86 (b) 66 (c) 68 (d) 84
  40. 40.What is the 28th term of the AP 19, 21, 23, 25, …? (a) 75 (b) 73 (c) 54 (d) 56

Answer key

  1. 576
  2. 17
  3. 70
  4. 70
  5. 249
  6. 144
  7. 17th
  8. 94
  9. 274
  10. 625
  11. 49
  12. 676
  13. 93
  14. 66
  15. 72
  16. 108
  17. 99
  18. 137
  19. 159
  20. 189
  21. 234
  22. 110
  23. 595
  24. 145
  25. 16th
  26. 306
  27. 10
  28. 10th
  29. 236
  30. 110
  31. 38th
  32. 215
  33. 105
  34. 244
  35. 36
  36. 349
  37. 40
  38. 357
  39. 84
  40. 73

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