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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 763 · 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 the first 8 terms of the AP 5, 11, 17, …? (a) 47 (b) 416 (c) 232 (d) 208
  2. 2.What is the sum of all the whole numbers from 1 to 25? (a) 325 (b) 650 (c) 326 (d) 300
  3. 3.What is the sum of all the whole numbers from 1 to 34? (a) 561 (b) 578 (c) 1190 (d) 595
  4. 4.What is the 10th term of the AP 1, 4, 7, 10, …? (a) 31 (b) 28 (c) 27 (d) 30
  5. 5.What is the 15th term of the AP 19, 23, 27, 31, …? (a) 60 (b) 56 (c) 75 (d) 79
  6. 6.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 60 (b) 120 (c) 66 (d) 15
  7. 7.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 65 (b) 55 (c) 110 (d) 19
  8. 8.What is the 31st term of the AP 5, 14, 23, 32, …? (a) 275 (b) 284 (c) 279 (d) 270
  9. 9.Which term of the AP 5, 9, 13, 17, … is 69? (a) 16th (b) 17th (c) 18th (d) 19th
  10. 10.Which term of the AP 16, 18, 20, 22, … is 90? (a) 39th (b) 38th (c) 37th (d) 45th
  11. 11.What is the 14th term of the AP 17, 20, 23, 26, …? (a) 59 (b) 39 (c) 42 (d) 56
  12. 12.What is the 37th term of the AP 19, 21, 23, 25, …? (a) 93 (b) 74 (c) 91 (d) 72
  13. 13.What is the missing term in the AP 5, 10, ?, 20, 25? (a) 16 (b) 14 (c) 20 (d) 15
  14. 14.What is the 10th term of the AP 13, 21, 29, 37, …? (a) 93 (b) 85 (c) 72 (d) 80
  15. 15.Which term of the AP 3, 8, 13, 18, … is 48? (a) 11th (b) 9th (c) 10th (d) 12th
  16. 16.What is the 35th term of the AP 20, 29, 38, 47, …? (a) 335 (b) 315 (c) 306 (d) 326
  17. 17.What is the missing term in the AP 14, 23, ?, 41, 50? (a) 33 (b) 41 (c) 31 (d) 32
  18. 18.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 136 (c) 256 (d) 31
  19. 19.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 96 (b) 24 (c) 84 (d) 168
  20. 20.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 133 (b) 28 (c) 136 (d) 266
  21. 21.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 289 (d) 306
  22. 22.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1682 (c) 1711 (d) 1653
  23. 23.What is the missing term in the AP 8, 14, ?, 26, 32? (a) 19 (b) 26 (c) 21 (d) 20
  24. 24.What is the sum of the first 10 terms of the AP 5, 11, 17, …? (a) 320 (b) 640 (c) 59 (d) 350
  25. 25.What is the 10th term of the AP 7, 10, 13, 16, …? (a) 37 (b) 34 (c) 30 (d) 27
  26. 26.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 96 (b) 81 (c) 26 (d) 162
  27. 27.What is the sum of all the whole numbers from 1 to 30? (a) 435 (b) 930 (c) 450 (d) 465
  28. 28.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 330 (b) 57 (c) 300 (d) 600
  29. 29.What is the missing term in the AP 9, 17, ?, 33, 41? (a) 33 (b) 26 (c) 24 (d) 25
  30. 30.What is the 14th term of the AP 17, 21, 25, 29, …? (a) 69 (b) 73 (c) 52 (d) 56
  31. 31.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 36 (c) 42 (d) 11
  32. 32.What is the sum of all the whole numbers from 1 to 53? (a) 1432 (b) 2862 (c) 1431 (d) 1378
  33. 33.What is the sum of the first 10 terms of the AP 3, 4, 5, …? (a) 150 (b) 75 (c) 80 (d) 12
  34. 34.What is the sum of all the whole numbers from 1 to 65? (a) 4290 (b) 2080 (c) 2146 (d) 2145
  35. 35.What is the 38th term of the AP 11, 13, 15, 17, …? (a) 85 (b) 74 (c) 87 (d) 76
  36. 36.What is the 15th term of the AP 13, 15, 17, 19, …? (a) 28 (b) 30 (c) 41 (d) 43
  37. 37.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 756 (c) 378 (d) 53
  38. 38.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 276 (c) 529 (d) 552
  39. 39.What is the missing term in the AP 20, 22, 24, ?, 28? (a) 28 (b) 27 (c) 25 (d) 26
  40. 40.Which term of the AP 1, 9, 17, 25, … is 249? (a) 33rd (b) 34th (c) 31st (d) 32nd

Answer key

  1. 208
  2. 325
  3. 595
  4. 28
  5. 75
  6. 60
  7. 55
  8. 275
  9. 17th
  10. 38th
  11. 56
  12. 91
  13. 15
  14. 85
  15. 10th
  16. 326
  17. 32
  18. 256
  19. 84
  20. 133
  21. 289
  22. 1711
  23. 20
  24. 320
  25. 34
  26. 81
  27. 465
  28. 300
  29. 25
  30. 69
  31. 36
  32. 1431
  33. 75
  34. 2145
  35. 85
  36. 41
  37. 729
  38. 529
  39. 26
  40. 32nd

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