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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 791 · 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 all the whole numbers from 1 to 39? (a) 741 (b) 780 (c) 1560 (d) 781
  2. 2.What is the missing term in the AP 14, 19, ?, 29, 34? (a) 23 (b) 25 (c) 29 (d) 24
  3. 3.Which term of the AP 17, 26, 35, 44, … is 125? (a) 13th (b) 15th (c) 12th (d) 14th
  4. 4.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 84 (b) 9 (c) 43 (d) 42
  5. 5.Which term of the AP 13, 15, 17, 19, … is 65? (a) 28th (b) 27th (c) 29th (d) 26th
  6. 6.What is the 16th term of the AP 17, 21, 25, 29, …? (a) 81 (b) 64 (c) 60 (d) 77
  7. 7.What is the 21st term of the AP 11, 13, 15, 17, …? (a) 53 (b) 42 (c) 51 (d) 40
  8. 8.What is the missing term in the AP 4, 9, ?, 19, 24? (a) 13 (b) 15 (c) 19 (d) 14
  9. 9.What is the sum of all the whole numbers from 1 to 87? (a) 3829 (b) 3741 (c) 7656 (d) 3828
  10. 10.What is the 18th term of the AP 4, 6, 8, 10, …? (a) 36 (b) 34 (c) 38 (d) 40
  11. 11.What is the 17th term of the AP 10, 13, 16, 19, …? (a) 58 (b) 61 (c) 51 (d) 48
  12. 12.What is the missing term in the AP 20, 23, ?, 29, 32? (a) 27 (b) 26 (c) 29 (d) 25
  13. 13.Which term of the AP 7, 11, 15, 19, … is 95? (a) 22nd (b) 24th (c) 23rd (d) 25th
  14. 14.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 68 (b) 840 (c) 456 (d) 420
  15. 15.What is the missing term in the AP 1, 4, 7, ?, 13? (a) 11 (b) 10 (c) 13 (d) 9
  16. 16.What is the 22nd term of the AP 2, 5, 8, 11, …? (a) 65 (b) 63 (c) 68 (d) 66
  17. 17.What is the 34th term of the AP 7, 10, 13, 16, …? (a) 99 (b) 106 (c) 102 (d) 109
  18. 18.What is the sum of all the whole numbers from 1 to 53? (a) 1432 (b) 1378 (c) 1431 (d) 2862
  19. 19.What is the 32nd term of the AP 3, 6, 9, 12, …? (a) 93 (b) 96 (c) 99 (d) 97
  20. 20.What is the 18th term of the AP 2, 8, 14, 20, …? (a) 102 (b) 110 (c) 104 (d) 108
  21. 21.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 109 (b) 216 (c) 108 (d) 16
  22. 22.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 42 (b) 242 (c) 484 (d) 264
  23. 23.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 13 (b) 49 (c) 56 (d) 98
  24. 24.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 625 (c) 49 (d) 325
  25. 25.What is the sum of all the whole numbers from 1 to 40? (a) 780 (b) 800 (c) 820 (d) 1640
  26. 26.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 210 (c) 39 (d) 420
  27. 27.What is the missing term in the AP 1, ?, 15, 22, 29? (a) 9 (b) 7 (c) 15 (d) 8
  28. 28.What is the missing term in the AP 11, 15, 19, ?, 27? (a) 27 (b) 23 (c) 22 (d) 24
  29. 29.What is the sum of all the whole numbers from 1 to 79? (a) 3161 (b) 3160 (c) 6320 (d) 3081
  30. 30.What is the sum of all the whole numbers from 1 to 43? (a) 903 (b) 947 (c) 946 (d) 1892
  31. 31.What is the 13th term of the AP 20, 27, 34, 41, …? (a) 111 (b) 84 (c) 91 (d) 104
  32. 32.What is the missing term in the AP 14, 23, 32, ?, 50? (a) 40 (b) 50 (c) 42 (d) 41
  33. 33.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 98 (b) 196 (c) 20 (d) 105
  34. 34.What is the missing term in the AP 18, 22, 26, ?, 34? (a) 31 (b) 34 (c) 30 (d) 29
  35. 35.What is the 24th term of the AP 6, 9, 12, 15, …? (a) 78 (b) 69 (c) 75 (d) 72
  36. 36.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 153 (c) 289 (d) 33
  37. 37.What is the sum of all the whole numbers from 1 to 61? (a) 1891 (b) 3782 (c) 1892 (d) 1830
  38. 38.Which term of the AP 20, 28, 36, 44, … is 148? (a) 17th (b) 18th (c) 19th (d) 16th
  39. 39.What is the 34th term of the AP 6, 8, 10, 12, …? (a) 68 (b) 74 (c) 66 (d) 72
  40. 40.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 406 (c) 784 (d) 55

Answer key

  1. 780
  2. 24
  3. 13th
  4. 42
  5. 27th
  6. 77
  7. 51
  8. 14
  9. 3828
  10. 38
  11. 58
  12. 26
  13. 23rd
  14. 420
  15. 10
  16. 65
  17. 106
  18. 1431
  19. 96
  20. 104
  21. 108
  22. 242
  23. 49
  24. 625
  25. 820
  26. 400
  27. 8
  28. 23
  29. 3160
  30. 946
  31. 104
  32. 41
  33. 98
  34. 30
  35. 75
  36. 289
  37. 1891
  38. 17th
  39. 72
  40. 784

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