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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 854 · 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 22nd term of the AP 1, 8, 15, 22, …? (a) 148 (b) 155 (c) 147 (d) 154
  2. 2.What is the 18th term of the AP 14, 19, 24, 29, …? (a) 104 (b) 85 (c) 90 (d) 99
  3. 3.What is the 18th term of the AP 5, 11, 17, 23, …? (a) 102 (b) 107 (c) 113 (d) 108
  4. 4.What is the 34th term of the AP 4, 7, 10, 13, …? (a) 106 (b) 99 (c) 103 (d) 102
  5. 5.Which term of the AP 4, 7, 10, 13, … is 34? (a) 12th (b) 13th (c) 11th (d) 10th
  6. 6.What is the sum of the first 9 terms of the AP 4, 10, 16, …? (a) 279 (b) 52 (c) 504 (d) 252
  7. 7.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 462 (c) 231 (d) 41
  8. 8.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 324 (b) 165 (c) 162 (d) 30
  9. 9.What is the 21st term of the AP 16, 21, 26, 31, …? (a) 116 (b) 105 (c) 121 (d) 100
  10. 10.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 184 (b) 200 (c) 368 (d) 37
  11. 11.Which term of the AP 3, 7, 11, 15, … is 55? (a) 16th (b) 15th (c) 14th (d) 13th
  12. 12.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 290 (b) 145 (c) 19 (d) 150
  13. 13.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 72 (c) 64 (d) 15
  14. 14.What is the 16th term of the AP 1, 8, 15, 22, …? (a) 105 (b) 113 (c) 112 (d) 106
  15. 15.What is the missing term in the AP 13, 19, 25, ?, 37? (a) 32 (b) 31 (c) 37 (d) 30
  16. 16.What is the 33rd term of the AP 10, 16, 22, 28, …? (a) 198 (b) 208 (c) 192 (d) 202
  17. 17.Which term of the AP 14, 17, 20, 23, … is 131? (a) 42nd (b) 40th (c) 39th (d) 41st
  18. 18.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 300 (c) 47 (d) 576
  19. 19.What is the 14th term of the AP 19, 21, 23, 25, …? (a) 47 (b) 28 (c) 26 (d) 45
  20. 20.What is the 14th term of the AP 19, 26, 33, 40, …? (a) 117 (b) 98 (c) 91 (d) 110
  21. 21.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 31 (b) 136 (c) 256 (d) 272
  22. 22.Which term of the AP 17, 24, 31, 38, … is 290? (a) 39th (b) 40th (c) 41st (d) 42nd
  23. 23.Which term of the AP 6, 12, 18, 24, … is 132? (a) 21st (b) 22nd (c) 24th (d) 23rd
  24. 24.What is the 25th term of the AP 17, 20, 23, 26, …? (a) 72 (b) 75 (c) 92 (d) 89
  25. 25.Which term of the AP 12, 19, 26, 33, … is 68? (a) 11th (b) 9th (c) 10th (d) 8th
  26. 26.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 110 (c) 19 (d) 55
  27. 27.What is the sum of all the whole numbers from 1 to 77? (a) 6006 (b) 3004 (c) 3003 (d) 2926
  28. 28.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 90 (b) 150 (c) 75 (d) 27
  29. 29.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 650 (c) 300 (d) 325
  30. 30.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 182 (d) 169
  31. 31.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 3486 (c) 7140 (d) 3570
  32. 32.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 30 (b) 10 (c) 60 (d) 35
  33. 33.What is the 23rd term of the AP 4, 11, 18, 25, …? (a) 158 (b) 161 (c) 154 (d) 165
  34. 34.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 25 (d) 15
  35. 35.What is the missing term in the AP 12, 18, 24, ?, 36? (a) 36 (b) 29 (c) 31 (d) 30
  36. 36.What is the 12th term of the AP 20, 23, 26, 29, …? (a) 33 (b) 36 (c) 53 (d) 56
  37. 37.What is the missing term in the AP 17, 20, ?, 26, 29? (a) 26 (b) 22 (c) 23 (d) 24
  38. 38.What is the 19th term of the AP 19, 21, 23, 25, …? (a) 36 (b) 55 (c) 38 (d) 57
  39. 39.What is the missing term in the AP 7, 9, ?, 13, 15? (a) 12 (b) 10 (c) 11 (d) 13
  40. 40.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 378 (c) 729 (d) 756

Answer key

  1. 148
  2. 99
  3. 107
  4. 103
  5. 11th
  6. 252
  7. 441
  8. 162
  9. 116
  10. 184
  11. 14th
  12. 145
  13. 64
  14. 106
  15. 31
  16. 202
  17. 40th
  18. 576
  19. 45
  20. 110
  21. 256
  22. 40th
  23. 22nd
  24. 89
  25. 9th
  26. 100
  27. 3003
  28. 75
  29. 325
  30. 169
  31. 3570
  32. 30
  33. 158
  34. 25
  35. 30
  36. 53
  37. 23
  38. 55
  39. 11
  40. 729

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