← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 668 · 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 21st term of the AP 6, 14, 22, 30, …? (a) 168 (b) 160 (c) 174 (d) 166
  2. 2.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 72 (b) 504 (c) 468 (d) 936
  3. 3.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 50 (b) 25 (c) 26 (d) 7
  4. 4.What is the 30th term of the AP 10, 16, 22, 28, …? (a) 190 (b) 174 (c) 184 (d) 180
  5. 5.What is the sum of all the whole numbers from 1 to 51? (a) 1326 (b) 1327 (c) 2652 (d) 1275
  6. 6.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 676 (d) 702
  7. 7.What is the missing term in the AP 5, ?, 9, 11, 13? (a) 7 (b) 9 (c) 8 (d) 6
  8. 8.What is the missing term in the AP 11, 14, 17, ?, 23? (a) 23 (b) 19 (c) 21 (d) 20
  9. 9.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 441 (c) 462 (d) 41
  10. 10.What is the 11th term of the AP 12, 19, 26, 33, …? (a) 89 (b) 82 (c) 77 (d) 70
  11. 11.What is the 11th term of the AP 14, 18, 22, 26, …? (a) 58 (b) 54 (c) 44 (d) 40
  12. 12.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 220 (b) 20 (c) 120 (d) 110
  13. 13.What is the missing term in the AP 2, 11, 20, ?, 38? (a) 38 (b) 29 (c) 28 (d) 30
  14. 14.What is the sum of all the whole numbers from 1 to 23? (a) 277 (b) 253 (c) 276 (d) 552
  15. 15.What is the sum of all the whole numbers from 1 to 38? (a) 722 (b) 741 (c) 703 (d) 1482
  16. 16.What is the sum of the first 8 terms of the AP 7, 12, 17, …? (a) 216 (b) 42 (c) 392 (d) 196
  17. 17.What is the sum of all the whole numbers from 1 to 45? (a) 1036 (b) 990 (c) 1035 (d) 2070
  18. 18.What is the 25th term of the AP 9, 14, 19, 24, …? (a) 125 (b) 129 (c) 120 (d) 134
  19. 19.What is the sum of all the whole numbers from 1 to 50? (a) 1250 (b) 1275 (c) 2550 (d) 1225
  20. 20.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 35 (b) 36 (c) 9 (d) 70
  21. 21.What is the missing term in the AP 13, 17, ?, 25, 29? (a) 22 (b) 20 (c) 25 (d) 21
  22. 22.What is the 33rd term of the AP 18, 22, 26, 30, …? (a) 150 (b) 128 (c) 132 (d) 146
  23. 23.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 176 (b) 352 (c) 26 (d) 187
  24. 24.What is the 21st term of the AP 9, 12, 15, 18, …? (a) 63 (b) 60 (c) 69 (d) 72
  25. 25.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 80 (b) 45 (c) 12 (d) 40
  26. 26.What is the 20th term of the AP 6, 9, 12, 15, …? (a) 60 (b) 63 (c) 57 (d) 66
  27. 27.What is the 18th term of the AP 7, 9, 11, 13, …? (a) 43 (b) 34 (c) 36 (d) 41
  28. 28.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 78 (b) 132 (c) 66 (d) 21
  29. 29.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 90 (b) 85 (c) 13 (d) 170
  30. 30.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 256 (c) 31 (d) 272
  31. 31.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 39 (c) 210 (d) 420
  32. 32.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 184 (b) 92 (c) 96 (d) 15
  33. 33.What is the 18th term of the AP 10, 12, 14, 16, …? (a) 46 (b) 34 (c) 36 (d) 44
  34. 34.What is the 33rd term of the AP 17, 25, 33, 41, …? (a) 264 (b) 256 (c) 281 (d) 273
  35. 35.What is the 40th term of the AP 13, 19, 25, 31, …? (a) 240 (b) 247 (c) 253 (d) 234
  36. 36.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 196 (b) 112 (c) 26 (d) 98
  37. 37.What is the 22nd term of the AP 9, 17, 25, 33, …? (a) 168 (b) 177 (c) 185 (d) 176
  38. 38.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 29 (c) 225 (d) 120
  39. 39.Which term of the AP 16, 19, 22, 25, … is 118? (a) 34th (b) 36th (c) 35th (d) 37th
  40. 40.What is the sum of the first 12 terms of the AP 1, 4, 7, …? (a) 420 (b) 228 (c) 210 (d) 34

Answer key

  1. 166
  2. 468
  3. 25
  4. 184
  5. 1326
  6. 676
  7. 7
  8. 20
  9. 441
  10. 82
  11. 54
  12. 110
  13. 29
  14. 276
  15. 741
  16. 196
  17. 1035
  18. 129
  19. 1275
  20. 35
  21. 21
  22. 146
  23. 176
  24. 69
  25. 40
  26. 63
  27. 41
  28. 66
  29. 85
  30. 256
  31. 400
  32. 92
  33. 44
  34. 273
  35. 247
  36. 98
  37. 177
  38. 225
  39. 35th
  40. 210

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