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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 696 · 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 13, 22, 31, ?, 49? (a) 41 (b) 49 (c) 39 (d) 40
  2. 2.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 47 (c) 300 (d) 576
  3. 3.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 21 (b) 224 (c) 120 (d) 112
  4. 4.Which term of the AP 7, 10, 13, 16, … is 91? (a) 29th (b) 31st (c) 28th (d) 30th
  5. 5.What is the 33rd term of the AP 6, 8, 10, 12, …? (a) 70 (b) 66 (c) 64 (d) 72
  6. 6.What is the 14th term of the AP 20, 27, 34, 41, …? (a) 98 (b) 118 (c) 111 (d) 91
  7. 7.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 91 (b) 94 (c) 182 (d) 22
  8. 8.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 465 (c) 930 (d) 900
  9. 9.What is the 15th term of the AP 6, 9, 12, 15, …? (a) 45 (b) 48 (c) 42 (d) 51
  10. 10.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 11 (b) 120 (c) 60 (d) 64
  11. 11.What is the 37th term of the AP 16, 23, 30, 37, …? (a) 259 (b) 268 (c) 275 (d) 252
  12. 12.What is the sum of all the whole numbers from 1 to 57? (a) 1596 (b) 1653 (c) 1654 (d) 3306
  13. 13.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 15 (d) 30
  14. 14.What is the sum of all the whole numbers from 1 to 53? (a) 1432 (b) 2862 (c) 1431 (d) 1378
  15. 15.What is the missing term in the AP 15, 17, ?, 21, 23? (a) 20 (b) 18 (c) 19 (d) 21
  16. 16.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 30 (b) 120 (c) 105 (d) 210
  17. 17.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 540 (b) 39 (c) 288 (d) 270
  18. 18.Which term of the AP 20, 26, 32, 38, … is 218? (a) 35th (b) 36th (c) 33rd (d) 34th
  19. 19.What is the sum of all the whole numbers from 1 to 42? (a) 882 (b) 903 (c) 861 (d) 1806
  20. 20.What is the sum of the first 7 terms of the AP 1, 2, 3, …? (a) 29 (b) 7 (c) 28 (d) 56
  21. 21.What is the 10th term of the AP 13, 16, 19, 22, …? (a) 43 (b) 27 (c) 30 (d) 40
  22. 22.What is the sum of the first 11 terms of the AP 5, 8, 11, …? (a) 223 (b) 440 (c) 220 (d) 35
  23. 23.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 114 (b) 66 (c) 17 (d) 57
  24. 24.What is the sum of the first 12 terms of the AP 10, 14, 18, …? (a) 408 (b) 768 (c) 54 (d) 384
  25. 25.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 42 (b) 6 (c) 24 (d) 21
  26. 26.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 238 (b) 119 (c) 29 (d) 133
  27. 27.What is the missing term in the AP 1, 8, ?, 22, 29? (a) 16 (b) 15 (c) 22 (d) 14
  28. 28.Which term of the AP 7, 10, 13, 16, … is 37? (a) 10th (b) 13th (c) 12th (d) 11th
  29. 29.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 465 (c) 435 (d) 930
  30. 30.What is the missing term in the AP 12, ?, 26, 33, 40? (a) 18 (b) 26 (c) 19 (d) 20
  31. 31.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 100 (d) 19
  32. 32.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 14 (b) 50 (c) 100 (d) 55
  33. 33.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 43 (c) 506 (d) 253
  34. 34.What is the sum of the first 8 terms of the AP 10, 14, 18, …? (a) 192 (b) 384 (c) 208 (d) 38
  35. 35.What is the 38th term of the AP 13, 15, 17, 19, …? (a) 74 (b) 87 (c) 89 (d) 76
  36. 36.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 24 (b) 160 (c) 300 (d) 150
  37. 37.What is the sum of all the whole numbers from 1 to 73? (a) 5402 (b) 2701 (c) 2628 (d) 2702
  38. 38.Which term of the AP 7, 9, 11, 13, … is 45? (a) 22nd (b) 19th (c) 20th (d) 21st
  39. 39.Which term of the AP 6, 13, 20, 27, … is 244? (a) 36th (b) 35th (c) 34th (d) 37th
  40. 40.What is the sum of all the whole numbers from 1 to 96? (a) 4656 (b) 4560 (c) 4608 (d) 9312

Answer key

  1. 40
  2. 576
  3. 112
  4. 29th
  5. 70
  6. 111
  7. 91
  8. 900
  9. 48
  10. 60
  11. 268
  12. 1653
  13. 25
  14. 1431
  15. 19
  16. 105
  17. 270
  18. 34th
  19. 903
  20. 28
  21. 40
  22. 220
  23. 57
  24. 384
  25. 21
  26. 119
  27. 15
  28. 11th
  29. 465
  30. 19
  31. 100
  32. 50
  33. 484
  34. 192
  35. 87
  36. 150
  37. 2701
  38. 20th
  39. 35th
  40. 4656

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