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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 624 · 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 100? (a) 5050 (b) 10100 (c) 4950 (d) 5000
  2. 2.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 29 (c) 225 (d) 120
  3. 3.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 384 (b) 45 (c) 216 (d) 192
  4. 4.What is the 17th term of the AP 9, 17, 25, 33, …? (a) 136 (b) 137 (c) 145 (d) 128
  5. 5.Which term of the AP 17, 23, 29, 35, … is 185? (a) 28th (b) 29th (c) 30th (d) 31st
  6. 6.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 26 (b) 7 (c) 25 (d) 50
  7. 7.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 224 (b) 112 (c) 31 (d) 117
  8. 8.What is the sum of the first 9 terms of the AP 2, 8, 14, …? (a) 468 (b) 261 (c) 50 (d) 234
  9. 9.What is the sum of the first 9 terms of the AP 8, 12, 16, …? (a) 234 (b) 40 (c) 216 (d) 432
  10. 10.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 414 (b) 828 (c) 62 (d) 444
  11. 11.What is the 24th term of the AP 18, 22, 26, 30, …? (a) 92 (b) 114 (c) 96 (d) 110
  12. 12.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 31 (c) 136 (d) 272
  13. 13.What is the missing term in the AP 19, ?, 37, 46, 55? (a) 29 (b) 37 (c) 28 (d) 27
  14. 14.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 435 (c) 436 (d) 406
  15. 15.Which term of the AP 10, 12, 14, 16, … is 36? (a) 18th (b) 13th (c) 15th (d) 14th
  16. 16.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 130 (b) 23 (c) 70 (d) 65
  17. 17.What is the missing term in the AP 2, 11, 20, ?, 38? (a) 30 (b) 29 (c) 28 (d) 38
  18. 18.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 841 (c) 435 (d) 57
  19. 19.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 72 (d) 64
  20. 20.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 154 (b) 77 (c) 80 (d) 20
  21. 21.What is the 35th term of the AP 17, 22, 27, 32, …? (a) 187 (b) 192 (c) 175 (d) 170
  22. 22.What is the sum of the first 8 terms of the AP 9, 14, 19, …? (a) 232 (b) 424 (c) 212 (d) 44
  23. 23.What is the missing term in the AP 16, 21, ?, 31, 36? (a) 25 (b) 31 (c) 26 (d) 27
  24. 24.What is the missing term in the AP 8, ?, 22, 29, 36? (a) 16 (b) 22 (c) 15 (d) 14
  25. 25.What is the sum of the first 8 terms of the AP 8, 12, 16, …? (a) 192 (b) 36 (c) 352 (d) 176
  26. 26.What is the 23rd term of the AP 5, 8, 11, 14, …? (a) 74 (b) 66 (c) 69 (d) 71
  27. 27.Which term of the AP 16, 21, 26, 31, … is 196? (a) 38th (b) 39th (c) 36th (d) 37th
  28. 28.What is the missing term in the AP 19, ?, 35, 43, 51? (a) 27 (b) 26 (c) 35 (d) 28
  29. 29.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 300 (c) 576 (d) 600
  30. 30.What is the missing term in the AP 3, 7, 11, ?, 19? (a) 19 (b) 16 (c) 14 (d) 15
  31. 31.What is the 16th term of the AP 7, 12, 17, 22, …? (a) 82 (b) 87 (c) 75 (d) 80
  32. 32.What is the missing term in the AP 20, 23, 26, ?, 32? (a) 28 (b) 30 (c) 32 (d) 29
  33. 33.What is the missing term in the AP 14, 18, 22, ?, 30? (a) 25 (b) 26 (c) 27 (d) 30
  34. 34.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 114 (b) 31 (c) 192 (d) 96
  35. 35.What is the 25th term of the AP 15, 24, 33, 42, …? (a) 225 (b) 216 (c) 240 (d) 231
  36. 36.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 300 (b) 324 (c) 600 (d) 47
  37. 37.What is the sum of the first 7 terms of the AP 10, 15, 20, …? (a) 350 (b) 180 (c) 175 (d) 40
  38. 38.What is the 14th term of the AP 12, 17, 22, 27, …? (a) 82 (b) 65 (c) 70 (d) 77
  39. 39.What is the 20th term of the AP 6, 11, 16, 21, …? (a) 95 (b) 100 (c) 101 (d) 106
  40. 40.Which term of the AP 18, 26, 34, 42, … is 82? (a) 8th (b) 9th (c) 11th (d) 10th

Answer key

  1. 5050
  2. 225
  3. 192
  4. 137
  5. 29th
  6. 25
  7. 112
  8. 234
  9. 216
  10. 414
  11. 110
  12. 256
  13. 28
  14. 435
  15. 14th
  16. 65
  17. 29
  18. 841
  19. 64
  20. 77
  21. 187
  22. 212
  23. 26
  24. 15
  25. 176
  26. 71
  27. 37th
  28. 27
  29. 576
  30. 15
  31. 82
  32. 29
  33. 26
  34. 96
  35. 231
  36. 300
  37. 175
  38. 77
  39. 101
  40. 9th

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