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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 10 · 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 10, 17, 24, ?, 38? (a) 30 (b) 31 (c) 38 (d) 32
  2. 2.What is the sum of the first 8 terms of the AP 5, 6, 7, …? (a) 72 (b) 68 (c) 12 (d) 136
  3. 3.What is the missing term in the AP 15, 17, 19, ?, 23? (a) 22 (b) 23 (c) 21 (d) 20
  4. 4.What is the sum of the first 6 terms of the AP 10, 16, 22, …? (a) 150 (b) 168 (c) 300 (d) 40
  5. 5.What is the sum of all the whole numbers from 1 to 89? (a) 4005 (b) 3916 (c) 4006 (d) 8010
  6. 6.What is the 27th term of the AP 17, 26, 35, 44, …? (a) 234 (b) 243 (c) 260 (d) 251
  7. 7.What is the missing term in the AP 5, 13, ?, 29, 37? (a) 21 (b) 20 (c) 29 (d) 22
  8. 8.What is the missing term in the AP 11, 17, 23, ?, 35? (a) 30 (b) 29 (c) 35 (d) 28
  9. 9.What is the sum of the first 9 terms of the AP 6, 10, 14, …? (a) 198 (b) 396 (c) 216 (d) 38
  10. 10.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 1035 (c) 1036 (d) 2070
  11. 11.What is the 21st term of the AP 7, 15, 23, 31, …? (a) 175 (b) 168 (c) 167 (d) 160
  12. 12.What is the sum of the first 8 terms of the AP 3, 4, 5, …? (a) 10 (b) 52 (c) 56 (d) 104
  13. 13.What is the 34th term of the AP 5, 14, 23, 32, …? (a) 302 (b) 297 (c) 306 (d) 311
  14. 14.What is the missing term in the AP 10, 16, ?, 28, 34? (a) 21 (b) 22 (c) 23 (d) 28
  15. 15.Which term of the AP 4, 7, 10, 13, … is 67? (a) 24th (b) 22nd (c) 21st (d) 23rd
  16. 16.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 242 (b) 16 (c) 121 (d) 122
  17. 17.Which term of the AP 5, 11, 17, 23, … is 131? (a) 21st (b) 24th (c) 23rd (d) 22nd
  18. 18.What is the missing term in the AP 1, 7, 13, ?, 25? (a) 20 (b) 19 (c) 25 (d) 18
  19. 19.What is the 14th term of the AP 9, 16, 23, 30, …? (a) 98 (b) 91 (c) 107 (d) 100
  20. 20.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 145 (b) 290 (c) 150 (d) 19
  21. 21.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 96 (b) 176 (c) 88 (d) 18
  22. 22.What is the sum of all the whole numbers from 1 to 41? (a) 1722 (b) 861 (c) 820 (d) 862
  23. 23.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 66 (d) 132
  24. 24.What is the 33rd term of the AP 2, 8, 14, 20, …? (a) 192 (b) 198 (c) 200 (d) 194
  25. 25.What is the 16th term of the AP 18, 22, 26, 30, …? (a) 64 (b) 82 (c) 78 (d) 60
  26. 26.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 1260 (c) 631 (d) 595
  27. 27.Which term of the AP 13, 15, 17, 19, … is 63? (a) 25th (b) 27th (c) 28th (d) 26th
  28. 28.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 15 (c) 72 (d) 36
  29. 29.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 3 (b) 5 (c) 2 (d) 4
  30. 30.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 96 (b) 184 (c) 92 (d) 15
  31. 31.What is the 30th term of the AP 2, 5, 8, 11, …? (a) 92 (b) 87 (c) 90 (d) 89
  32. 32.What is the missing term in the AP 18, 21, 24, ?, 30? (a) 28 (b) 26 (c) 27 (d) 30
  33. 33.What is the 22nd term of the AP 20, 23, 26, 29, …? (a) 86 (b) 63 (c) 83 (d) 66
  34. 34.What is the 21st term of the AP 2, 9, 16, 23, …? (a) 149 (b) 140 (c) 142 (d) 147
  35. 35.What is the 10th term of the AP 6, 10, 14, 18, …? (a) 40 (b) 36 (c) 42 (d) 46
  36. 36.Which term of the AP 1, 5, 9, 13, … is 157? (a) 39th (b) 42nd (c) 40th (d) 41st
  37. 37.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 11 (c) 36 (d) 42
  38. 38.What is the sum of the first 7 terms of the AP 4, 5, 6, …? (a) 10 (b) 49 (c) 50 (d) 98
  39. 39.What is the missing term in the AP 20, ?, 26, 29, 32? (a) 26 (b) 22 (c) 24 (d) 23
  40. 40.What is the missing term in the AP 5, 13, 21, ?, 37? (a) 28 (b) 30 (c) 37 (d) 29

Answer key

  1. 31
  2. 68
  3. 21
  4. 150
  5. 4005
  6. 251
  7. 21
  8. 29
  9. 198
  10. 1035
  11. 167
  12. 52
  13. 302
  14. 22
  15. 22nd
  16. 121
  17. 22nd
  18. 19
  19. 100
  20. 145
  21. 88
  22. 861
  23. 121
  24. 194
  25. 78
  26. 630
  27. 26th
  28. 64
  29. 3
  30. 92
  31. 89
  32. 27
  33. 83
  34. 142
  35. 42
  36. 40th
  37. 36
  38. 49
  39. 23
  40. 29

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