← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 451 · 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 all the whole numbers from 1 to 51? (a) 1327 (b) 1326 (c) 2652 (d) 1275
  2. 2.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 55 (c) 812 (d) 406
  3. 3.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 108 (b) 60 (c) 14 (d) 54
  4. 4.What is the 21st term of the AP 4, 13, 22, 31, …? (a) 189 (b) 193 (c) 184 (d) 180
  5. 5.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 80 (b) 150 (c) 75 (d) 12
  6. 6.What is the sum of all the whole numbers from 1 to 92? (a) 4278 (b) 4186 (c) 4232 (d) 8556
  7. 7.What is the sum of all the whole numbers from 1 to 64? (a) 2080 (b) 2048 (c) 2016 (d) 4160
  8. 8.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 7140 (c) 3570 (d) 3486
  9. 9.What is the missing term in the AP 19, 28, 37, ?, 55? (a) 46 (b) 45 (c) 47 (d) 55
  10. 10.What is the 32nd term of the AP 17, 21, 25, 29, …? (a) 128 (b) 141 (c) 145 (d) 124
  11. 11.What is the 33rd term of the AP 1, 9, 17, 25, …? (a) 256 (b) 264 (c) 265 (d) 257
  12. 12.What is the 35th term of the AP 9, 11, 13, 15, …? (a) 68 (b) 79 (c) 77 (d) 70
  13. 13.Which term of the AP 12, 15, 18, 21, … is 36? (a) 10th (b) 12th (c) 9th (d) 8th
  14. 14.What is the missing term in the AP 14, ?, 24, 29, 34? (a) 19 (b) 20 (c) 24 (d) 18
  15. 15.Which term of the AP 8, 15, 22, 29, … is 281? (a) 39th (b) 41st (c) 42nd (d) 40th
  16. 16.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 45 (c) 110 (d) 55
  17. 17.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 32 (b) 117 (c) 132 (d) 234
  18. 18.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 90 (b) 13 (c) 50 (d) 45
  19. 19.Which term of the AP 14, 21, 28, 35, … is 175? (a) 23rd (b) 26th (c) 25th (d) 24th
  20. 20.What is the 20th term of the AP 19, 25, 31, 37, …? (a) 139 (b) 133 (c) 120 (d) 114
  21. 21.What is the 34th term of the AP 20, 22, 24, 26, …? (a) 68 (b) 86 (c) 88 (d) 66
  22. 22.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 96 (b) 90 (c) 20 (d) 180
  23. 23.What is the sum of the first 11 terms of the AP 5, 8, 11, …? (a) 223 (b) 35 (c) 440 (d) 220
  24. 24.What is the sum of all the whole numbers from 1 to 12? (a) 156 (b) 78 (c) 72 (d) 66
  25. 25.Which term of the AP 17, 26, 35, 44, … is 341? (a) 37th (b) 36th (c) 39th (d) 38th
  26. 26.What is the 30th term of the AP 6, 8, 10, 12, …? (a) 64 (b) 58 (c) 66 (d) 60
  27. 27.What is the 26th term of the AP 7, 11, 15, 19, …? (a) 107 (b) 100 (c) 111 (d) 104
  28. 28.What is the sum of the first 12 terms of the AP 5, 7, 9, …? (a) 384 (b) 27 (c) 204 (d) 192
  29. 29.What is the missing term in the AP 14, 18, 22, ?, 30? (a) 27 (b) 26 (c) 25 (d) 30
  30. 30.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 19 (b) 84 (c) 168 (d) 90
  31. 31.What is the 12th term of the AP 13, 22, 31, 40, …? (a) 121 (b) 108 (c) 112 (d) 99
  32. 32.What is the missing term in the AP 9, ?, 27, 36, 45? (a) 19 (b) 18 (c) 27 (d) 17
  33. 33.What is the missing term in the AP 20, 25, ?, 35, 40? (a) 35 (b) 29 (c) 30 (d) 31
  34. 34.What is the missing term in the AP 3, 12, ?, 30, 39? (a) 21 (b) 20 (c) 22 (d) 30
  35. 35.What is the sum of all the whole numbers from 1 to 58? (a) 1653 (b) 3422 (c) 1682 (d) 1711
  36. 36.What is the 13th term of the AP 10, 13, 16, 19, …? (a) 46 (b) 39 (c) 36 (d) 49
  37. 37.What is the 33rd term of the AP 12, 20, 28, 36, …? (a) 264 (b) 256 (c) 276 (d) 268
  38. 38.What is the sum of the first 5 terms of the AP 8, 12, 16, …? (a) 160 (b) 24 (c) 80 (d) 90
  39. 39.Which term of the AP 13, 18, 23, 28, … is 203? (a) 40th (b) 39th (c) 41st (d) 38th
  40. 40.What is the sum of the first 10 terms of the AP 4, 9, 14, …? (a) 265 (b) 49 (c) 530 (d) 290

Answer key

  1. 1326
  2. 784
  3. 54
  4. 184
  5. 75
  6. 4278
  7. 2080
  8. 3570
  9. 46
  10. 141
  11. 257
  12. 77
  13. 9th
  14. 19
  15. 40th
  16. 55
  17. 117
  18. 45
  19. 24th
  20. 133
  21. 86
  22. 90
  23. 220
  24. 78
  25. 37th
  26. 64
  27. 107
  28. 192
  29. 26
  30. 84
  31. 112
  32. 18
  33. 30
  34. 21
  35. 1711
  36. 46
  37. 268
  38. 80
  39. 39th
  40. 265

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