← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 914 · 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 missing term in the AP 4, 9, 14, ?, 24? (a) 18 (b) 24 (c) 19 (d) 20
  2. 2.What is the sum of all the whole numbers from 1 to 50? (a) 1225 (b) 2550 (c) 1250 (d) 1275
  3. 3.What is the 37th term of the AP 17, 19, 21, 23, …? (a) 91 (b) 74 (c) 89 (d) 72
  4. 4.Which term of the AP 2, 6, 10, 14, … is 138? (a) 36th (b) 34th (c) 35th (d) 37th
  5. 5.What is the 28th term of the AP 3, 8, 13, 18, …? (a) 143 (b) 140 (c) 135 (d) 138
  6. 6.What is the missing term in the AP 19, ?, 33, 40, 47? (a) 27 (b) 25 (c) 26 (d) 33
  7. 7.What is the sum of all the whole numbers from 1 to 13? (a) 78 (b) 91 (c) 92 (d) 182
  8. 8.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 31 (c) 136 (d) 256
  9. 9.What is the 19th term of the AP 18, 27, 36, 45, …? (a) 189 (b) 171 (c) 180 (d) 162
  10. 10.What is the missing term in the AP 1, 4, 7, ?, 13? (a) 11 (b) 9 (c) 13 (d) 10
  11. 11.What is the sum of all the whole numbers from 1 to 74? (a) 5550 (b) 2775 (c) 2701 (d) 2738
  12. 12.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 380 (d) 361
  13. 13.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 400 (c) 420 (d) 39
  14. 14.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 306 (c) 153 (d) 154
  15. 15.What is the 39th term of the AP 12, 20, 28, 36, …? (a) 316 (b) 304 (c) 312 (d) 324
  16. 16.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 144 (b) 80 (c) 72 (d) 16
  17. 17.What is the 25th term of the AP 20, 22, 24, 26, …? (a) 70 (b) 50 (c) 48 (d) 68
  18. 18.What is the missing term in the AP 19, 27, 35, ?, 51? (a) 51 (b) 42 (c) 44 (d) 43
  19. 19.Which term of the AP 19, 28, 37, 46, … is 262? (a) 30th (b) 28th (c) 29th (d) 27th
  20. 20.Which term of the AP 10, 13, 16, 19, … is 82? (a) 26th (b) 24th (c) 25th (d) 27th
  21. 21.Which term of the AP 19, 22, 25, 28, … is 121? (a) 36th (b) 34th (c) 37th (d) 35th
  22. 22.What is the 33rd term of the AP 4, 6, 8, 10, …? (a) 64 (b) 66 (c) 70 (d) 68
  23. 23.What is the 14th term of the AP 10, 13, 16, 19, …? (a) 49 (b) 52 (c) 39 (d) 42
  24. 24.What is the 33rd term of the AP 19, 25, 31, 37, …? (a) 217 (b) 198 (c) 211 (d) 192
  25. 25.Which term of the AP 18, 24, 30, 36, … is 108? (a) 15th (b) 17th (c) 16th (d) 18th
  26. 26.Which term of the AP 15, 18, 21, 24, … is 39? (a) 10th (b) 13th (c) 8th (d) 9th
  27. 27.Which term of the AP 9, 12, 15, 18, … is 96? (a) 29th (b) 31st (c) 32nd (d) 30th
  28. 28.What is the sum of all the whole numbers from 1 to 34? (a) 561 (b) 1190 (c) 595 (d) 578
  29. 29.Which term of the AP 15, 21, 27, 33, … is 57? (a) 10th (b) 7th (c) 9th (d) 8th
  30. 30.Which term of the AP 17, 20, 23, 26, … is 62? (a) 18th (b) 15th (c) 17th (d) 16th
  31. 31.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 22 (b) 84 (c) 144 (d) 72
  32. 32.What is the 37th term of the AP 17, 21, 25, 29, …? (a) 148 (b) 161 (c) 165 (d) 144
  33. 33.Which term of the AP 5, 8, 11, 14, … is 89? (a) 30th (b) 31st (c) 29th (d) 28th
  34. 34.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 900 (c) 465 (d) 59
  35. 35.Which term of the AP 6, 11, 16, 21, … is 96? (a) 20th (b) 19th (c) 21st (d) 18th
  36. 36.What is the sum of all the whole numbers from 1 to 75? (a) 2850 (b) 5700 (c) 2851 (d) 2775
  37. 37.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 81 (d) 90
  38. 38.What is the missing term in the AP 18, ?, 36, 45, 54? (a) 26 (b) 28 (c) 36 (d) 27
  39. 39.What is the 38th term of the AP 8, 15, 22, 29, …? (a) 274 (b) 267 (c) 266 (d) 259
  40. 40.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 41 (d) 441

Answer key

  1. 19
  2. 1275
  3. 89
  4. 35th
  5. 138
  6. 26
  7. 91
  8. 256
  9. 180
  10. 10
  11. 2775
  12. 361
  13. 400
  14. 153
  15. 316
  16. 72
  17. 68
  18. 43
  19. 28th
  20. 25th
  21. 35th
  22. 68
  23. 49
  24. 211
  25. 16th
  26. 9th
  27. 30th
  28. 595
  29. 8th
  30. 16th
  31. 72
  32. 161
  33. 29th
  34. 900
  35. 19th
  36. 2850
  37. 81
  38. 27
  39. 267
  40. 441

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