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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 583 · 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.Which term of the AP 6, 9, 12, 15, … is 81? (a) 26th (b) 27th (c) 25th (d) 28th
  2. 2.What is the sum of the first 7 terms of the AP 5, 6, 7, …? (a) 112 (b) 11 (c) 56 (d) 57
  3. 3.What is the sum of all the whole numbers from 1 to 73? (a) 2628 (b) 2701 (c) 5402 (d) 2702
  4. 4.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 45 (d) 81
  5. 5.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 702 (c) 338 (d) 351
  6. 6.What is the 22nd term of the AP 7, 9, 11, 13, …? (a) 51 (b) 44 (c) 49 (d) 42
  7. 7.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 465 (c) 435 (d) 930
  8. 8.Which term of the AP 15, 17, 19, 21, … is 75? (a) 30th (b) 33rd (c) 32nd (d) 31st
  9. 9.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 37 (b) 189 (c) 378 (d) 207
  10. 10.What is the 22nd term of the AP 4, 8, 12, 16, …? (a) 89 (b) 84 (c) 92 (d) 88
  11. 11.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 506 (c) 242 (d) 253
  12. 12.What is the sum of all the whole numbers from 1 to 24? (a) 600 (b) 276 (c) 288 (d) 300
  13. 13.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 110 (c) 19 (d) 55
  14. 14.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 360 (b) 198 (c) 36 (d) 180
  15. 15.What is the 25th term of the AP 4, 6, 8, 10, …? (a) 48 (b) 54 (c) 50 (d) 52
  16. 16.Which term of the AP 3, 10, 17, 24, … is 171? (a) 26th (b) 27th (c) 24th (d) 25th
  17. 17.What is the sum of the first 12 terms of the AP 9, 14, 19, …? (a) 876 (b) 438 (c) 64 (d) 468
  18. 18.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 80 (b) 95 (c) 160 (d) 28
  19. 19.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 171 (c) 342 (d) 324
  20. 20.What is the sum of the first 9 terms of the AP 8, 14, 20, …? (a) 315 (b) 56 (c) 288 (d) 576
  21. 21.What is the missing term in the AP 3, 7, 11, ?, 19? (a) 19 (b) 16 (c) 15 (d) 14
  22. 22.What is the 38th term of the AP 13, 16, 19, 22, …? (a) 124 (b) 114 (c) 127 (d) 111
  23. 23.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 436 (c) 435 (d) 406
  24. 24.What is the 15th term of the AP 12, 16, 20, 24, …? (a) 72 (b) 68 (c) 60 (d) 56
  25. 25.What is the sum of the first 7 terms of the AP 10, 16, 22, …? (a) 392 (b) 46 (c) 217 (d) 196
  26. 26.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 11 (b) 36 (c) 72 (d) 42
  27. 27.What is the sum of all the whole numbers from 1 to 31? (a) 496 (b) 992 (c) 465 (d) 497
  28. 28.What is the 22nd term of the AP 1, 9, 17, 25, …? (a) 168 (b) 176 (c) 169 (d) 177
  29. 29.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 506 (c) 484 (d) 253
  30. 30.What is the 14th term of the AP 8, 10, 12, 14, …? (a) 28 (b) 26 (c) 36 (d) 34
  31. 31.What is the missing term in the AP 16, 21, ?, 31, 36? (a) 26 (b) 25 (c) 31 (d) 27
  32. 32.What is the 36th term of the AP 3, 6, 9, 12, …? (a) 105 (b) 111 (c) 109 (d) 108
  33. 33.What is the 11th term of the AP 8, 10, 12, 14, …? (a) 22 (b) 20 (c) 28 (d) 30
  34. 34.What is the 28th term of the AP 16, 19, 22, 25, …? (a) 97 (b) 84 (c) 100 (d) 81
  35. 35.What is the 14th term of the AP 17, 26, 35, 44, …? (a) 126 (b) 117 (c) 134 (d) 143
  36. 36.What is the sum of all the whole numbers from 1 to 61? (a) 1891 (b) 1892 (c) 1830 (d) 3782
  37. 37.What is the sum of all the whole numbers from 1 to 80? (a) 6480 (b) 3160 (c) 3200 (d) 3240
  38. 38.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 702 (c) 676 (d) 51
  39. 39.What is the missing term in the AP 4, 11, 18, ?, 32? (a) 25 (b) 32 (c) 24 (d) 26
  40. 40.Which term of the AP 17, 24, 31, 38, … is 129? (a) 17th (b) 18th (c) 16th (d) 19th

Answer key

  1. 26th
  2. 56
  3. 2701
  4. 81
  5. 351
  6. 49
  7. 465
  8. 31st
  9. 189
  10. 88
  11. 253
  12. 300
  13. 100
  14. 180
  15. 52
  16. 25th
  17. 438
  18. 80
  19. 324
  20. 288
  21. 15
  22. 124
  23. 435
  24. 68
  25. 196
  26. 36
  27. 496
  28. 169
  29. 484
  30. 34
  31. 26
  32. 108
  33. 28
  34. 97
  35. 134
  36. 1891
  37. 3240
  38. 676
  39. 25
  40. 17th

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