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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 537 · 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 24th term of the AP 2, 7, 12, 17, …? (a) 115 (b) 120 (c) 122 (d) 117
  2. 2.What is the 16th term of the AP 4, 7, 10, 13, …? (a) 48 (b) 45 (c) 52 (d) 49
  3. 3.What is the 29th term of the AP 17, 25, 33, 41, …? (a) 224 (b) 241 (c) 249 (d) 232
  4. 4.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 11 (c) 42 (d) 36
  5. 5.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 26 (b) 140 (c) 70 (d) 85
  6. 6.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 300 (c) 600 (d) 576
  7. 7.What is the 30th term of the AP 10, 18, 26, 34, …? (a) 232 (b) 242 (c) 240 (d) 250
  8. 8.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 182 (c) 169 (d) 91
  9. 9.What is the 21st term of the AP 8, 10, 12, 14, …? (a) 40 (b) 42 (c) 50 (d) 48
  10. 10.What is the 37th term of the AP 6, 8, 10, 12, …? (a) 80 (b) 78 (c) 74 (d) 72
  11. 11.What is the 10th term of the AP 12, 14, 16, 18, …? (a) 20 (b) 32 (c) 18 (d) 30
  12. 12.What is the missing term in the AP 9, 13, ?, 21, 25? (a) 18 (b) 17 (c) 16 (d) 21
  13. 13.What is the sum of all the whole numbers from 1 to 42? (a) 861 (b) 903 (c) 1806 (d) 882
  14. 14.What is the sum of all the whole numbers from 1 to 93? (a) 8742 (b) 4278 (c) 4372 (d) 4371
  15. 15.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 384 (b) 54 (c) 408 (d) 768
  16. 16.What is the sum of all the whole numbers from 1 to 36? (a) 666 (b) 648 (c) 1332 (d) 630
  17. 17.What is the missing term in the AP 7, ?, 13, 16, 19? (a) 11 (b) 13 (c) 10 (d) 9
  18. 18.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 435 (c) 841 (d) 57
  19. 19.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 497 (c) 992 (d) 496
  20. 20.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 240 (d) 225
  21. 21.Which term of the AP 7, 14, 21, 28, … is 266? (a) 38th (b) 39th (c) 40th (d) 37th
  22. 22.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 108 (b) 112 (c) 17 (d) 216
  23. 23.What is the missing term in the AP 20, 29, ?, 47, 56? (a) 47 (b) 37 (c) 38 (d) 39
  24. 24.What is the 39th term of the AP 2, 6, 10, 14, …? (a) 156 (b) 158 (c) 152 (d) 154
  25. 25.What is the missing term in the AP 3, 12, ?, 30, 39? (a) 30 (b) 22 (c) 21 (d) 20
  26. 26.What is the sum of all the whole numbers from 1 to 80? (a) 3200 (b) 3160 (c) 6480 (d) 3240
  27. 27.What is the sum of the first 5 terms of the AP 9, 14, 19, …? (a) 190 (b) 29 (c) 100 (d) 95
  28. 28.Which term of the AP 11, 19, 27, 35, … is 323? (a) 40th (b) 41st (c) 42nd (d) 39th
  29. 29.What is the 36th term of the AP 3, 9, 15, 21, …? (a) 216 (b) 219 (c) 210 (d) 213
  30. 30.What is the sum of all the whole numbers from 1 to 54? (a) 2970 (b) 1458 (c) 1485 (d) 1431
  31. 31.What is the sum of all the whole numbers from 1 to 61? (a) 3782 (b) 1830 (c) 1891 (d) 1892
  32. 32.Which term of the AP 16, 18, 20, 22, … is 44? (a) 22nd (b) 16th (c) 14th (d) 15th
  33. 33.What is the 15th term of the AP 14, 16, 18, 20, …? (a) 44 (b) 42 (c) 30 (d) 28
  34. 34.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 324 (b) 168 (c) 19 (d) 162
  35. 35.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 28 (d) 13
  36. 36.What is the 39th term of the AP 11, 13, 15, 17, …? (a) 87 (b) 78 (c) 89 (d) 76
  37. 37.What is the missing term in the AP 4, 6, 8, ?, 12? (a) 12 (b) 11 (c) 9 (d) 10
  38. 38.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 342 (d) 324
  39. 39.What is the 33rd term of the AP 14, 22, 30, 38, …? (a) 264 (b) 278 (c) 270 (d) 256
  40. 40.What is the 32nd term of the AP 3, 10, 17, 24, …? (a) 224 (b) 217 (c) 227 (d) 220

Answer key

  1. 117
  2. 49
  3. 241
  4. 36
  5. 70
  6. 576
  7. 242
  8. 169
  9. 48
  10. 78
  11. 30
  12. 17
  13. 903
  14. 4371
  15. 384
  16. 666
  17. 10
  18. 841
  19. 496
  20. 225
  21. 38th
  22. 108
  23. 38
  24. 154
  25. 21
  26. 3240
  27. 95
  28. 40th
  29. 213
  30. 1485
  31. 1891
  32. 15th
  33. 42
  34. 162
  35. 49
  36. 87
  37. 10
  38. 324
  39. 270
  40. 220

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