← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 65 · 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 15th term of the AP 14, 19, 24, 29, …? (a) 75 (b) 70 (c) 84 (d) 89
  2. 2.What is the 11th term of the AP 5, 13, 21, 29, …? (a) 93 (b) 80 (c) 85 (d) 88
  3. 3.What is the sum of all the whole numbers from 1 to 38? (a) 703 (b) 722 (c) 1482 (d) 741
  4. 4.What is the sum of all the whole numbers from 1 to 86? (a) 3741 (b) 7482 (c) 3698 (d) 3655
  5. 5.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 144 (b) 80 (c) 72 (d) 16
  6. 6.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 231 (d) 441
  7. 7.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 14 (b) 43 (c) 40 (d) 80
  8. 8.What is the 15th term of the AP 15, 18, 21, 24, …? (a) 45 (b) 57 (c) 42 (d) 60
  9. 9.What is the 13th term of the AP 17, 21, 25, 29, …? (a) 48 (b) 52 (c) 69 (d) 65
  10. 10.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 28 (d) 13
  11. 11.What is the 40th term of the AP 1, 8, 15, 22, …? (a) 273 (b) 281 (c) 274 (d) 280
  12. 12.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 132 (b) 66 (c) 16 (d) 72
  13. 13.What is the 12th term of the AP 15, 24, 33, 42, …? (a) 108 (b) 99 (c) 114 (d) 123
  14. 14.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 3906 (c) 1953 (d) 1891
  15. 15.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 105 (c) 210 (d) 27
  16. 16.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 45 (b) 40 (c) 12 (d) 80
  17. 17.What is the sum of all the whole numbers from 1 to 26? (a) 702 (b) 351 (c) 338 (d) 325
  18. 18.What is the 12th term of the AP 9, 14, 19, 24, …? (a) 64 (b) 55 (c) 69 (d) 60
  19. 19.What is the sum of all the whole numbers from 1 to 11? (a) 66 (b) 55 (c) 67 (d) 132
  20. 20.What is the sum of the first 6 terms of the AP 3, 5, 7, …? (a) 48 (b) 54 (c) 13 (d) 96
  21. 21.What is the 17th term of the AP 20, 27, 34, 41, …? (a) 139 (b) 112 (c) 119 (d) 132
  22. 22.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 312 (b) 41 (c) 294 (d) 588
  23. 23.What is the 11th term of the AP 15, 18, 21, 24, …? (a) 33 (b) 48 (c) 45 (d) 30
  24. 24.What is the missing term in the AP 3, 10, ?, 24, 31? (a) 18 (b) 17 (c) 16 (d) 24
  25. 25.What is the 17th term of the AP 13, 21, 29, 37, …? (a) 149 (b) 136 (c) 141 (d) 128
  26. 26.Which term of the AP 2, 10, 18, 26, … is 82? (a) 11th (b) 13th (c) 12th (d) 10th
  27. 27.What is the missing term in the AP 6, 12, 18, ?, 30? (a) 23 (b) 24 (c) 30 (d) 25
  28. 28.What is the sum of the first 11 terms of the AP 7, 9, 11, …? (a) 187 (b) 27 (c) 198 (d) 374
  29. 29.What is the sum of all the whole numbers from 1 to 44? (a) 946 (b) 990 (c) 1980 (d) 968
  30. 30.What is the sum of the first 6 terms of the AP 8, 10, 12, …? (a) 84 (b) 78 (c) 156 (d) 18
  31. 31.What is the missing term in the AP 4, ?, 12, 16, 20? (a) 7 (b) 9 (c) 8 (d) 12
  32. 32.What is the missing term in the AP 3, 12, ?, 30, 39? (a) 20 (b) 30 (c) 22 (d) 21
  33. 33.What is the 39th term of the AP 4, 9, 14, 19, …? (a) 199 (b) 190 (c) 195 (d) 194
  34. 34.What is the missing term in the AP 6, 15, ?, 33, 42? (a) 25 (b) 23 (c) 24 (d) 33
  35. 35.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 406 (c) 436 (d) 435
  36. 36.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 57 (b) 12 (c) 114 (d) 60
  37. 37.What is the 29th term of the AP 6, 14, 22, 30, …? (a) 230 (b) 238 (c) 224 (d) 232
  38. 38.Which term of the AP 11, 19, 27, 35, … is 227? (a) 30th (b) 29th (c) 28th (d) 27th
  39. 39.What is the missing term in the AP 1, 4, ?, 10, 13? (a) 7 (b) 6 (c) 8 (d) 10
  40. 40.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 11 (d) 36

Answer key

  1. 84
  2. 85
  3. 741
  4. 3741
  5. 72
  6. 441
  7. 40
  8. 57
  9. 65
  10. 49
  11. 274
  12. 66
  13. 114
  14. 1953
  15. 196
  16. 40
  17. 351
  18. 64
  19. 66
  20. 48
  21. 132
  22. 294
  23. 45
  24. 17
  25. 141
  26. 11th
  27. 24
  28. 187
  29. 990
  30. 78
  31. 8
  32. 21
  33. 194
  34. 24
  35. 435
  36. 57
  37. 230
  38. 28th
  39. 7
  40. 36

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