← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 417 · 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 19, 25, ?, 37, 43? (a) 30 (b) 32 (c) 37 (d) 31
  2. 2.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 9506 (c) 4753 (d) 4754
  3. 3.Which term of the AP 9, 14, 19, 24, … is 79? (a) 17th (b) 14th (c) 16th (d) 15th
  4. 4.What is the sum of all the whole numbers from 1 to 75? (a) 2850 (b) 5700 (c) 2775 (d) 2851
  5. 5.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 841 (c) 870 (d) 435
  6. 6.What is the sum of all the whole numbers from 1 to 55? (a) 3080 (b) 1485 (c) 1540 (d) 1541
  7. 7.What is the sum of the first 11 terms of the AP 6, 10, 14, …? (a) 572 (b) 46 (c) 308 (d) 286
  8. 8.What is the sum of all the whole numbers from 1 to 83? (a) 6972 (b) 3403 (c) 3486 (d) 3487
  9. 9.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 360 (b) 198 (c) 36 (d) 180
  10. 10.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 990 (c) 2070 (d) 1035
  11. 11.What is the 16th term of the AP 6, 10, 14, 18, …? (a) 66 (b) 70 (c) 64 (d) 60
  12. 12.What is the sum of the first 10 terms of the AP 10, 16, 22, …? (a) 740 (b) 64 (c) 370 (d) 400
  13. 13.What is the missing term in the AP 19, 27, 35, ?, 51? (a) 51 (b) 44 (c) 43 (d) 42
  14. 14.What is the 23rd term of the AP 6, 12, 18, 24, …? (a) 144 (b) 139 (c) 138 (d) 132
  15. 15.What is the 34th term of the AP 11, 17, 23, 29, …? (a) 215 (b) 209 (c) 204 (d) 198
  16. 16.What is the 34th term of the AP 17, 23, 29, 35, …? (a) 204 (b) 198 (c) 221 (d) 215
  17. 17.What is the sum of the first 11 terms of the AP 5, 9, 13, …? (a) 45 (b) 297 (c) 550 (d) 275
  18. 18.What is the missing term in the AP 15, ?, 19, 21, 23? (a) 18 (b) 17 (c) 16 (d) 19
  19. 19.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 200 (b) 176 (c) 43 (d) 352
  20. 20.What is the 10th term of the AP 6, 14, 22, 30, …? (a) 78 (b) 86 (c) 72 (d) 80
  21. 21.What is the 11th term of the AP 17, 19, 21, 23, …? (a) 39 (b) 37 (c) 22 (d) 20
  22. 22.Which term of the AP 2, 5, 8, 11, … is 116? (a) 41st (b) 38th (c) 39th (d) 40th
  23. 23.What is the sum of the first 6 terms of the AP 5, 9, 13, …? (a) 102 (b) 180 (c) 90 (d) 25
  24. 24.What is the sum of all the whole numbers from 1 to 69? (a) 4830 (b) 2416 (c) 2346 (d) 2415
  25. 25.Which term of the AP 13, 20, 27, 34, … is 258? (a) 36th (b) 37th (c) 38th (d) 35th
  26. 26.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 99 (b) 24 (c) 198 (d) 108
  27. 27.What is the 35th term of the AP 5, 7, 9, 11, …? (a) 73 (b) 70 (c) 75 (d) 68
  28. 28.Which term of the AP 6, 8, 10, 12, … is 58? (a) 26th (b) 29th (c) 27th (d) 28th
  29. 29.What is the 16th term of the AP 11, 14, 17, 20, …? (a) 56 (b) 48 (c) 59 (d) 45
  30. 30.What is the missing term in the AP 17, 19, ?, 23, 25? (a) 23 (b) 22 (c) 21 (d) 20
  31. 31.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 210 (c) 420 (d) 400
  32. 32.What is the 17th term of the AP 9, 18, 27, 36, …? (a) 162 (b) 144 (c) 154 (d) 153
  33. 33.What is the 18th term of the AP 2, 11, 20, 29, …? (a) 153 (b) 155 (c) 164 (d) 162
  34. 34.What is the sum of all the whole numbers from 1 to 34? (a) 1190 (b) 595 (c) 578 (d) 561
  35. 35.What is the 25th term of the AP 19, 23, 27, 31, …? (a) 96 (b) 100 (c) 119 (d) 115
  36. 36.What is the 35th term of the AP 20, 29, 38, 47, …? (a) 315 (b) 306 (c) 335 (d) 326
  37. 37.Which term of the AP 16, 18, 20, 22, … is 66? (a) 27th (b) 25th (c) 33rd (d) 26th
  38. 38.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 55 (b) 54 (c) 10 (d) 108
  39. 39.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 60 (b) 57 (c) 12 (d) 114
  40. 40.What is the sum of all the whole numbers from 1 to 47? (a) 1128 (b) 2256 (c) 1081 (d) 1129

Answer key

  1. 31
  2. 4753
  3. 15th
  4. 2850
  5. 841
  6. 1540
  7. 286
  8. 3486
  9. 180
  10. 1035
  11. 66
  12. 370
  13. 43
  14. 138
  15. 209
  16. 215
  17. 275
  18. 17
  19. 176
  20. 78
  21. 37
  22. 39th
  23. 90
  24. 2415
  25. 36th
  26. 99
  27. 73
  28. 27th
  29. 56
  30. 21
  31. 400
  32. 153
  33. 155
  34. 595
  35. 115
  36. 326
  37. 26th
  38. 54
  39. 57
  40. 1128

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