← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 240 · 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 the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 81 (d) 90
  2. 2.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 9506 (c) 4753 (d) 4754
  3. 3.What is the sum of the first 11 terms of the AP 5, 11, 17, …? (a) 65 (b) 385 (c) 770 (d) 418
  4. 4.What is the missing term in the AP 7, 14, 21, ?, 35? (a) 27 (b) 35 (c) 29 (d) 28
  5. 5.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 56 (b) 98 (c) 13 (d) 49
  6. 6.What is the missing term in the AP 7, ?, 15, 19, 23? (a) 10 (b) 12 (c) 15 (d) 11
  7. 7.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 370 (b) 200 (c) 185 (d) 32
  8. 8.What is the sum of the first 5 terms of the AP 6, 11, 16, …? (a) 26 (b) 160 (c) 85 (d) 80
  9. 9.What is the sum of all the whole numbers from 1 to 100? (a) 5000 (b) 4950 (c) 5050 (d) 10100
  10. 10.What is the missing term in the AP 8, ?, 14, 17, 20? (a) 11 (b) 14 (c) 12 (d) 10
  11. 11.What is the sum of the first 6 terms of the AP 8, 14, 20, …? (a) 276 (b) 138 (c) 38 (d) 156
  12. 12.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 60 (b) 61 (c) 14 (d) 120
  13. 13.What is the sum of all the whole numbers from 1 to 22? (a) 253 (b) 506 (c) 242 (d) 231
  14. 14.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 69 (b) 19 (c) 78 (d) 138
  15. 15.What is the missing term in the AP 8, 14, ?, 26, 32? (a) 19 (b) 20 (c) 26 (d) 21
  16. 16.What is the sum of all the whole numbers from 1 to 60? (a) 1770 (b) 1800 (c) 1830 (d) 3660
  17. 17.What is the 14th term of the AP 8, 11, 14, 17, …? (a) 39 (b) 50 (c) 42 (d) 47
  18. 18.What is the sum of the first 12 terms of the AP 8, 13, 18, …? (a) 852 (b) 63 (c) 456 (d) 426
  19. 19.What is the missing term in the AP 17, 23, 29, ?, 41? (a) 35 (b) 41 (c) 36 (d) 34
  20. 20.What is the 34th term of the AP 2, 5, 8, 11, …? (a) 104 (b) 99 (c) 101 (d) 102
  21. 21.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 600 (c) 576 (d) 47
  22. 22.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 55 (c) 812 (d) 784
  23. 23.What is the 21st term of the AP 15, 24, 33, 42, …? (a) 195 (b) 204 (c) 189 (d) 180
  24. 24.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 126 (b) 11 (c) 63 (d) 64
  25. 25.What is the 13th term of the AP 4, 13, 22, 31, …? (a) 112 (b) 121 (c) 117 (d) 108
  26. 26.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 70 (c) 40 (d) 35
  27. 27.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 330 (b) 166 (c) 20 (d) 165
  28. 28.What is the sum of all the whole numbers from 1 to 41? (a) 861 (b) 1722 (c) 862 (d) 820
  29. 29.What is the 27th term of the AP 12, 21, 30, 39, …? (a) 234 (b) 246 (c) 255 (d) 243
  30. 30.What is the sum of all the whole numbers from 1 to 44? (a) 990 (b) 946 (c) 968 (d) 1980
  31. 31.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 242 (b) 121 (c) 132 (d) 21
  32. 32.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 15 (c) 30 (d) 9
  33. 33.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 32 (b) 132 (c) 117 (d) 234
  34. 34.What is the 26th term of the AP 7, 10, 13, 16, …? (a) 85 (b) 75 (c) 78 (d) 82
  35. 35.What is the 35th term of the AP 19, 21, 23, 25, …? (a) 70 (b) 89 (c) 87 (d) 68
  36. 36.What is the sum of the first 7 terms of the AP 7, 13, 19, …? (a) 196 (b) 43 (c) 350 (d) 175
  37. 37.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 378 (c) 392 (d) 406
  38. 38.What is the missing term in the AP 12, ?, 20, 24, 28? (a) 20 (b) 17 (c) 15 (d) 16
  39. 39.Which term of the AP 7, 13, 19, 25, … is 103? (a) 16th (b) 17th (c) 19th (d) 18th
  40. 40.What is the 38th term of the AP 15, 23, 31, 39, …? (a) 304 (b) 311 (c) 319 (d) 296

Answer key

  1. 81
  2. 4753
  3. 385
  4. 28
  5. 49
  6. 11
  7. 185
  8. 80
  9. 5050
  10. 11
  11. 138
  12. 60
  13. 253
  14. 69
  15. 20
  16. 1830
  17. 47
  18. 426
  19. 35
  20. 101
  21. 576
  22. 784
  23. 195
  24. 63
  25. 112
  26. 35
  27. 165
  28. 861
  29. 246
  30. 990
  31. 121
  32. 25
  33. 117
  34. 82
  35. 87
  36. 175
  37. 406
  38. 16
  39. 17th
  40. 311

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