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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 529 · 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 34th term of the AP 11, 16, 21, 26, …? (a) 165 (b) 170 (c) 176 (d) 181
  2. 2.Which term of the AP 1, 6, 11, 16, … is 106? (a) 23rd (b) 22nd (c) 21st (d) 24th
  3. 3.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 40 (b) 8 (c) 72 (d) 36
  4. 4.What is the 21st term of the AP 17, 19, 21, 23, …? (a) 42 (b) 40 (c) 59 (d) 57
  5. 5.What is the 30th term of the AP 1, 3, 5, 7, …? (a) 58 (b) 59 (c) 61 (d) 60
  6. 6.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 595 (c) 1260 (d) 630
  7. 7.What is the 14th term of the AP 15, 20, 25, 30, …? (a) 65 (b) 70 (c) 80 (d) 85
  8. 8.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 325 (c) 49 (d) 650
  9. 9.What is the 30th term of the AP 9, 13, 17, 21, …? (a) 125 (b) 129 (c) 120 (d) 116
  10. 10.What is the 23rd term of the AP 14, 17, 20, 23, …? (a) 83 (b) 69 (c) 80 (d) 66
  11. 11.What is the missing term in the AP 16, 21, 26, ?, 36? (a) 32 (b) 36 (c) 30 (d) 31
  12. 12.What is the 22nd term of the AP 8, 10, 12, 14, …? (a) 44 (b) 42 (c) 52 (d) 50
  13. 13.What is the missing term in the AP 10, 17, 24, ?, 38? (a) 38 (b) 31 (c) 32 (d) 30
  14. 14.What is the 11th term of the AP 18, 23, 28, 33, …? (a) 50 (b) 73 (c) 68 (d) 55
  15. 15.What is the sum of the first 8 terms of the AP 7, 13, 19, …? (a) 224 (b) 248 (c) 49 (d) 448
  16. 16.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 5852 (c) 2888 (d) 2926
  17. 17.What is the missing term in the AP 11, 14, ?, 20, 23? (a) 20 (b) 16 (c) 17 (d) 18
  18. 18.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 63 (b) 120 (c) 60 (d) 18
  19. 19.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 29 (b) 133 (c) 238 (d) 119
  20. 20.What is the sum of the first 12 terms of the AP 8, 12, 16, …? (a) 360 (b) 52 (c) 720 (d) 384
  21. 21.What is the sum of the first 11 terms of the AP 5, 11, 17, …? (a) 770 (b) 65 (c) 418 (d) 385
  22. 22.What is the 15th term of the AP 19, 25, 31, 37, …? (a) 109 (b) 84 (c) 90 (d) 103
  23. 23.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 930 (c) 900 (d) 59
  24. 24.What is the sum of the first 8 terms of the AP 5, 10, 15, …? (a) 180 (b) 40 (c) 200 (d) 360
  25. 25.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 870 (c) 841 (d) 435
  26. 26.Which term of the AP 20, 29, 38, 47, … is 119? (a) 13th (b) 11th (c) 14th (d) 12th
  27. 27.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 153 (c) 33 (d) 289
  28. 28.What is the 38th term of the AP 20, 29, 38, 47, …? (a) 333 (b) 353 (c) 362 (d) 342
  29. 29.What is the missing term in the AP 18, ?, 34, 42, 50? (a) 27 (b) 25 (c) 34 (d) 26
  30. 30.What is the 34th term of the AP 18, 22, 26, 30, …? (a) 132 (b) 150 (c) 136 (d) 154
  31. 31.Which term of the AP 12, 19, 26, 33, … is 194? (a) 27th (b) 29th (c) 28th (d) 26th
  32. 32.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 1953 (c) 3906 (d) 1891
  33. 33.What is the sum of all the whole numbers from 1 to 97? (a) 4753 (b) 4754 (c) 4656 (d) 9506
  34. 34.What is the sum of all the whole numbers from 1 to 28? (a) 378 (b) 812 (c) 392 (d) 406
  35. 35.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 26 (b) 122 (c) 119 (d) 238
  36. 36.Which term of the AP 11, 20, 29, 38, … is 254? (a) 29th (b) 27th (c) 28th (d) 30th
  37. 37.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 70 (c) 35 (d) 40
  38. 38.What is the sum of the first 9 terms of the AP 9, 12, 15, …? (a) 378 (b) 33 (c) 192 (d) 189
  39. 39.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 105 (d) 210
  40. 40.What is the sum of all the whole numbers from 1 to 20? (a) 420 (b) 190 (c) 200 (d) 210

Answer key

  1. 176
  2. 22nd
  3. 36
  4. 57
  5. 59
  6. 630
  7. 80
  8. 625
  9. 125
  10. 80
  11. 31
  12. 50
  13. 31
  14. 68
  15. 224
  16. 2926
  17. 17
  18. 60
  19. 119
  20. 360
  21. 385
  22. 103
  23. 900
  24. 180
  25. 841
  26. 12th
  27. 289
  28. 353
  29. 26
  30. 150
  31. 27th
  32. 1953
  33. 4753
  34. 406
  35. 119
  36. 28th
  37. 35
  38. 189
  39. 196
  40. 210

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