← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 751 · 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 10th term of the AP 6, 15, 24, 33, …? (a) 90 (b) 96 (c) 87 (d) 81
  2. 2.What is the 27th term of the AP 20, 25, 30, 35, …? (a) 155 (b) 135 (c) 130 (d) 150
  3. 3.What is the sum of all the whole numbers from 1 to 88? (a) 3872 (b) 3916 (c) 3828 (d) 7832
  4. 4.What is the 25th term of the AP 14, 18, 22, 26, …? (a) 96 (b) 110 (c) 100 (d) 114
  5. 5.Which term of the AP 4, 9, 14, 19, … is 134? (a) 26th (b) 29th (c) 27th (d) 28th
  6. 6.Which term of the AP 5, 9, 13, 17, … is 133? (a) 34th (b) 35th (c) 33rd (d) 32nd
  7. 7.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 900 (c) 465 (d) 930
  8. 8.What is the sum of all the whole numbers from 1 to 50? (a) 1250 (b) 1275 (c) 1225 (d) 2550
  9. 9.What is the 32nd term of the AP 7, 14, 21, 28, …? (a) 225 (b) 224 (c) 231 (d) 217
  10. 10.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 90 (b) 84 (c) 168 (d) 19
  11. 11.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 95 (b) 28 (c) 80 (d) 160
  12. 12.What is the missing term in the AP 14, 21, ?, 35, 42? (a) 35 (b) 28 (c) 29 (d) 27
  13. 13.What is the sum of the first 11 terms of the AP 9, 11, 13, …? (a) 29 (b) 418 (c) 220 (d) 209
  14. 14.What is the sum of the first 5 terms of the AP 10, 14, 18, …? (a) 100 (b) 26 (c) 90 (d) 180
  15. 15.Which term of the AP 3, 11, 19, 27, … is 67? (a) 11th (b) 9th (c) 10th (d) 8th
  16. 16.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 361 (d) 380
  17. 17.What is the 14th term of the AP 7, 11, 15, 19, …? (a) 52 (b) 63 (c) 56 (d) 59
  18. 18.What is the 21st term of the AP 13, 17, 21, 25, …? (a) 84 (b) 97 (c) 80 (d) 93
  19. 19.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 144 (d) 156
  20. 20.What is the 11th term of the AP 14, 17, 20, 23, …? (a) 47 (b) 44 (c) 33 (d) 30
  21. 21.What is the sum of all the whole numbers from 1 to 29? (a) 435 (b) 436 (c) 870 (d) 406
  22. 22.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 30 (d) 25
  23. 23.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 29 (c) 120 (d) 240
  24. 24.What is the missing term in the AP 1, 6, 11, ?, 21? (a) 16 (b) 17 (c) 21 (d) 15
  25. 25.What is the 29th term of the AP 3, 9, 15, 21, …? (a) 177 (b) 174 (c) 171 (d) 168
  26. 26.What is the sum of all the whole numbers from 1 to 57? (a) 1596 (b) 1654 (c) 3306 (d) 1653
  27. 27.What is the 38th term of the AP 7, 9, 11, 13, …? (a) 83 (b) 74 (c) 81 (d) 76
  28. 28.What is the missing term in the AP 6, 11, 16, ?, 26? (a) 20 (b) 26 (c) 22 (d) 21
  29. 29.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 4754 (c) 9506 (d) 4753
  30. 30.What is the 29th term of the AP 15, 21, 27, 33, …? (a) 189 (b) 168 (c) 174 (d) 183
  31. 31.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 88 (b) 14 (c) 84 (d) 168
  32. 32.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 189 (b) 210 (c) 45 (d) 378
  33. 33.Which term of the AP 6, 13, 20, 27, … is 195? (a) 27th (b) 28th (c) 29th (d) 30th
  34. 34.What is the sum of the first 11 terms of the AP 4, 9, 14, …? (a) 319 (b) 638 (c) 54 (d) 324
  35. 35.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 270 (b) 138 (c) 27 (d) 135
  36. 36.What is the sum of the first 9 terms of the AP 9, 10, 11, …? (a) 234 (b) 17 (c) 118 (d) 117
  37. 37.What is the 18th term of the AP 4, 9, 14, 19, …? (a) 85 (b) 94 (c) 89 (d) 90
  38. 38.What is the missing term in the AP 17, 24, 31, ?, 45? (a) 39 (b) 45 (c) 38 (d) 37
  39. 39.Which term of the AP 18, 24, 30, 36, … is 240? (a) 38th (b) 37th (c) 39th (d) 40th
  40. 40.What is the 10th term of the AP 13, 20, 27, 34, …? (a) 63 (b) 76 (c) 83 (d) 70

Answer key

  1. 87
  2. 150
  3. 3916
  4. 110
  5. 27th
  6. 33rd
  7. 900
  8. 1275
  9. 224
  10. 84
  11. 80
  12. 28
  13. 209
  14. 90
  15. 9th
  16. 361
  17. 59
  18. 93
  19. 144
  20. 44
  21. 435
  22. 25
  23. 225
  24. 16
  25. 171
  26. 1653
  27. 81
  28. 21
  29. 4753
  30. 183
  31. 84
  32. 189
  33. 28th
  34. 319
  35. 135
  36. 117
  37. 89
  38. 38
  39. 38th
  40. 76

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