← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 149 · 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 74? (a) 2775 (b) 5550 (c) 2701 (d) 2738
  2. 2.Which term of the AP 16, 24, 32, 40, … is 200? (a) 25th (b) 26th (c) 24th (d) 23rd
  3. 3.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 29 (c) 240 (d) 120
  4. 4.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 78 (c) 156 (d) 72
  5. 5.What is the 32nd term of the AP 17, 24, 31, 38, …? (a) 224 (b) 217 (c) 234 (d) 241
  6. 6.What is the 16th term of the AP 7, 16, 25, 34, …? (a) 142 (b) 151 (c) 144 (d) 135
  7. 7.What is the sum of all the whole numbers from 1 to 37? (a) 1406 (b) 703 (c) 666 (d) 704
  8. 8.What is the 38th term of the AP 13, 17, 21, 25, …? (a) 152 (b) 148 (c) 161 (d) 165
  9. 9.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 51 (b) 486 (c) 243 (d) 270
  10. 10.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 20 (b) 21 (c) 19 (d) 18
  11. 11.What is the sum of all the whole numbers from 1 to 78? (a) 3081 (b) 6162 (c) 3003 (d) 3042
  12. 12.What is the sum of all the whole numbers from 1 to 51? (a) 2652 (b) 1326 (c) 1275 (d) 1327
  13. 13.What is the 14th term of the AP 16, 20, 24, 28, …? (a) 52 (b) 56 (c) 72 (d) 68
  14. 14.What is the 25th term of the AP 3, 11, 19, 27, …? (a) 192 (b) 203 (c) 195 (d) 200
  15. 15.What is the sum of the first 10 terms of the AP 3, 6, 9, …? (a) 165 (b) 180 (c) 30 (d) 330
  16. 16.Which term of the AP 19, 26, 33, 40, … is 278? (a) 40th (b) 39th (c) 37th (d) 38th
  17. 17.What is the sum of the first 9 terms of the AP 4, 6, 8, …? (a) 117 (b) 20 (c) 108 (d) 216
  18. 18.What is the 22nd term of the AP 3, 11, 19, 27, …? (a) 179 (b) 168 (c) 176 (d) 171
  19. 19.What is the 27th term of the AP 15, 24, 33, 42, …? (a) 234 (b) 249 (c) 243 (d) 258
  20. 20.What is the 34th term of the AP 17, 19, 21, 23, …? (a) 85 (b) 66 (c) 83 (d) 68
  21. 21.What is the sum of the first 12 terms of the AP 8, 14, 20, …? (a) 984 (b) 74 (c) 492 (d) 528
  22. 22.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 112 (b) 105 (c) 21 (d) 210
  23. 23.What is the 34th term of the AP 12, 14, 16, 18, …? (a) 78 (b) 66 (c) 80 (d) 68
  24. 24.What is the sum of the first 10 terms of the AP 9, 15, 21, …? (a) 720 (b) 63 (c) 360 (d) 390
  25. 25.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 15 (b) 14 (c) 16 (d) 22
  26. 26.What is the sum of all the whole numbers from 1 to 83? (a) 3486 (b) 3403 (c) 3487 (d) 6972
  27. 27.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 9 (b) 78 (c) 42 (d) 39
  28. 28.What is the 28th term of the AP 17, 19, 21, 23, …? (a) 54 (b) 56 (c) 71 (d) 73
  29. 29.What is the 29th term of the AP 13, 20, 27, 34, …? (a) 196 (b) 209 (c) 203 (d) 216
  30. 30.What is the 12th term of the AP 4, 12, 20, 28, …? (a) 96 (b) 92 (c) 100 (d) 88
  31. 31.What is the 23rd term of the AP 2, 4, 6, 8, …? (a) 46 (b) 44 (c) 48 (d) 47
  32. 32.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 84 (b) 43 (c) 42 (d) 9
  33. 33.What is the 32nd term of the AP 14, 20, 26, 32, …? (a) 206 (b) 192 (c) 186 (d) 200
  34. 34.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 45 (c) 276 (d) 552
  35. 35.What is the sum of all the whole numbers from 1 to 64? (a) 2048 (b) 2016 (c) 4160 (d) 2080
  36. 36.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 500 (b) 270 (c) 43 (d) 250
  37. 37.What is the missing term in the AP 9, ?, 17, 21, 25? (a) 17 (b) 14 (c) 13 (d) 12
  38. 38.What is the sum of all the whole numbers from 1 to 46? (a) 1081 (b) 2162 (c) 1035 (d) 1058
  39. 39.What is the missing term in the AP 17, ?, 29, 35, 41? (a) 23 (b) 22 (c) 29 (d) 24
  40. 40.What is the sum of all the whole numbers from 1 to 43? (a) 947 (b) 1892 (c) 946 (d) 903

Answer key

  1. 2775
  2. 24th
  3. 225
  4. 78
  5. 234
  6. 142
  7. 703
  8. 161
  9. 243
  10. 19
  11. 3081
  12. 1326
  13. 68
  14. 195
  15. 165
  16. 38th
  17. 108
  18. 171
  19. 249
  20. 83
  21. 492
  22. 105
  23. 78
  24. 360
  25. 15
  26. 3486
  27. 39
  28. 71
  29. 209
  30. 92
  31. 46
  32. 42
  33. 200
  34. 529
  35. 2080
  36. 250
  37. 13
  38. 1081
  39. 23
  40. 946

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