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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 586 · 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 38th term of the AP 19, 25, 31, 37, …? (a) 228 (b) 241 (c) 222 (d) 247
  2. 2.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 30 (b) 54 (c) 27 (d) 7
  3. 3.What is the missing term in the AP 10, ?, 24, 31, 38? (a) 17 (b) 16 (c) 24 (d) 18
  4. 4.Which term of the AP 7, 11, 15, 19, … is 103? (a) 25th (b) 24th (c) 26th (d) 27th
  5. 5.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 24 (b) 75 (c) 140 (d) 70
  6. 6.What is the missing term in the AP 4, 8, ?, 16, 20? (a) 13 (b) 11 (c) 12 (d) 16
  7. 7.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 64 (c) 15 (d) 72
  8. 8.What is the 17th term of the AP 2, 5, 8, 11, …? (a) 50 (b) 51 (c) 48 (d) 53
  9. 9.What is the sum of the first 9 terms of the AP 2, 5, 8, …? (a) 129 (b) 126 (c) 26 (d) 252
  10. 10.What is the sum of all the whole numbers from 1 to 61? (a) 1891 (b) 1892 (c) 3782 (d) 1830
  11. 11.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 123 (b) 138 (c) 246 (d) 33
  12. 12.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 252 (b) 126 (c) 33 (d) 131
  13. 13.Which term of the AP 5, 11, 17, 23, … is 71? (a) 13th (b) 11th (c) 12th (d) 14th
  14. 14.What is the missing term in the AP 10, 18, 26, ?, 42? (a) 33 (b) 34 (c) 35 (d) 42
  15. 15.Which term of the AP 2, 9, 16, 23, … is 149? (a) 22nd (b) 24th (c) 23rd (d) 21st
  16. 16.What is the 40th term of the AP 16, 20, 24, 28, …? (a) 176 (b) 156 (c) 172 (d) 160
  17. 17.What is the 24th term of the AP 14, 23, 32, 41, …? (a) 207 (b) 221 (c) 230 (d) 216
  18. 18.What is the sum of the first 8 terms of the AP 1, 6, 11, …? (a) 296 (b) 36 (c) 168 (d) 148
  19. 19.Which term of the AP 7, 12, 17, 22, … is 52? (a) 11th (b) 9th (c) 12th (d) 10th
  20. 20.What is the 13th term of the AP 10, 18, 26, 34, …? (a) 104 (b) 114 (c) 96 (d) 106
  21. 21.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 91 (c) 25 (d) 169
  22. 22.What is the 19th term of the AP 13, 22, 31, 40, …? (a) 171 (b) 175 (c) 184 (d) 162
  23. 23.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 2926 (c) 2888 (d) 5852
  24. 24.What is the missing term in the AP 1, 8, ?, 22, 29? (a) 14 (b) 22 (c) 15 (d) 16
  25. 25.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 35 (b) 240 (c) 222 (d) 444
  26. 26.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 30 (d) 25
  27. 27.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 276 (c) 45 (d) 529
  28. 28.What is the sum of all the whole numbers from 1 to 21? (a) 232 (b) 231 (c) 210 (d) 462
  29. 29.What is the sum of all the whole numbers from 1 to 47? (a) 1129 (b) 1128 (c) 1081 (d) 2256
  30. 30.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 30 (b) 31 (c) 60 (d) 8
  31. 31.What is the sum of all the whole numbers from 1 to 55? (a) 1540 (b) 1485 (c) 1541 (d) 3080
  32. 32.What is the 38th term of the AP 10, 17, 24, 31, …? (a) 269 (b) 259 (c) 266 (d) 276
  33. 33.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 57 (c) 841 (d) 435
  34. 34.What is the missing term in the AP 19, 22, ?, 28, 31? (a) 28 (b) 24 (c) 26 (d) 25
  35. 35.What is the sum of all the whole numbers from 1 to 38? (a) 741 (b) 703 (c) 1482 (d) 722
  36. 36.What is the 20th term of the AP 16, 18, 20, 22, …? (a) 38 (b) 40 (c) 54 (d) 56
  37. 37.What is the missing term in the AP 20, 22, 24, ?, 28? (a) 28 (b) 25 (c) 26 (d) 27
  38. 38.What is the 37th term of the AP 2, 6, 10, 14, …? (a) 150 (b) 148 (c) 144 (d) 146
  39. 39.What is the sum of all the whole numbers from 1 to 98? (a) 9702 (b) 4802 (c) 4753 (d) 4851
  40. 40.What is the 28th term of the AP 7, 9, 11, 13, …? (a) 54 (b) 56 (c) 63 (d) 61

Answer key

  1. 241
  2. 27
  3. 17
  4. 25th
  5. 70
  6. 12
  7. 64
  8. 50
  9. 126
  10. 1891
  11. 123
  12. 126
  13. 12th
  14. 34
  15. 22nd
  16. 172
  17. 221
  18. 148
  19. 10th
  20. 106
  21. 169
  22. 175
  23. 2926
  24. 15
  25. 222
  26. 25
  27. 529
  28. 231
  29. 1128
  30. 30
  31. 1540
  32. 269
  33. 841
  34. 25
  35. 741
  36. 54
  37. 26
  38. 146
  39. 4851
  40. 61

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