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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 116 · 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 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 324 (c) 342 (d) 171
  2. 2.What is the sum of the first 7 terms of the AP 9, 14, 19, …? (a) 39 (b) 168 (c) 336 (d) 173
  3. 3.What is the missing term in the AP 8, 17, 26, ?, 44? (a) 36 (b) 34 (c) 44 (d) 35
  4. 4.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 625 (d) 650
  5. 5.What is the sum of all the whole numbers from 1 to 50? (a) 1225 (b) 1275 (c) 2550 (d) 1250
  6. 6.What is the 25th term of the AP 14, 16, 18, 20, …? (a) 48 (b) 50 (c) 64 (d) 62
  7. 7.What is the 16th term of the AP 13, 22, 31, 40, …? (a) 157 (b) 148 (c) 135 (d) 144
  8. 8.What is the sum of all the whole numbers from 1 to 78? (a) 6162 (b) 3042 (c) 3003 (d) 3081
  9. 9.Which term of the AP 16, 19, 22, 25, … is 85? (a) 23rd (b) 24th (c) 26th (d) 25th
  10. 10.What is the missing term in the AP 8, 16, ?, 32, 40? (a) 25 (b) 24 (c) 23 (d) 32
  11. 11.What is the 18th term of the AP 9, 12, 15, 18, …? (a) 51 (b) 60 (c) 54 (d) 63
  12. 12.What is the missing term in the AP 2, ?, 12, 17, 22? (a) 12 (b) 6 (c) 7 (d) 8
  13. 13.What is the sum of all the whole numbers from 1 to 46? (a) 1035 (b) 2162 (c) 1081 (d) 1058
  14. 14.What is the 21st term of the AP 4, 6, 8, 10, …? (a) 44 (b) 46 (c) 40 (d) 42
  15. 15.Which term of the AP 19, 28, 37, 46, … is 172? (a) 17th (b) 20th (c) 19th (d) 18th
  16. 16.What is the sum of all the whole numbers from 1 to 83? (a) 3487 (b) 3403 (c) 3486 (d) 6972
  17. 17.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 756 (c) 729 (d) 53
  18. 18.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 275 (b) 540 (c) 50 (d) 270
  19. 19.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 47 (b) 270 (c) 245 (d) 490
  20. 20.What is the missing term in the AP 19, ?, 31, 37, 43? (a) 24 (b) 31 (c) 25 (d) 26
  21. 21.What is the 25th term of the AP 11, 18, 25, 32, …? (a) 168 (b) 186 (c) 175 (d) 179
  22. 22.What is the 27th term of the AP 12, 14, 16, 18, …? (a) 54 (b) 52 (c) 66 (d) 64
  23. 23.What is the sum of the first 12 terms of the AP 3, 9, 15, …? (a) 69 (b) 468 (c) 864 (d) 432
  24. 24.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 81 (c) 90 (d) 45
  25. 25.What is the 33rd term of the AP 5, 10, 15, 20, …? (a) 166 (b) 170 (c) 165 (d) 160
  26. 26.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 71 (b) 13 (c) 70 (d) 140
  27. 27.What is the sum of the first 7 terms of the AP 1, 7, 13, …? (a) 266 (b) 133 (c) 37 (d) 154
  28. 28.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 100 (c) 110 (d) 19
  29. 29.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 36 (c) 64 (d) 15
  30. 30.Which term of the AP 11, 14, 17, 20, … is 128? (a) 41st (b) 42nd (c) 39th (d) 40th
  31. 31.What is the 26th term of the AP 19, 26, 33, 40, …? (a) 175 (b) 182 (c) 201 (d) 194
  32. 32.What is the missing term in the AP 7, 13, 19, ?, 31? (a) 26 (b) 24 (c) 31 (d) 25
  33. 33.What is the sum of all the whole numbers from 1 to 62? (a) 1953 (b) 1922 (c) 1891 (d) 3906
  34. 34.What is the sum of all the whole numbers from 1 to 79? (a) 3161 (b) 6320 (c) 3160 (d) 3081
  35. 35.What is the 33rd term of the AP 4, 13, 22, 31, …? (a) 301 (b) 288 (c) 297 (d) 292
  36. 36.What is the 24th term of the AP 6, 9, 12, 15, …? (a) 72 (b) 78 (c) 69 (d) 75
  37. 37.What is the 29th term of the AP 5, 11, 17, 23, …? (a) 174 (b) 179 (c) 173 (d) 168
  38. 38.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 42 (b) 11 (c) 72 (d) 36
  39. 39.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 429 (b) 858 (c) 69 (d) 462
  40. 40.What is the 22nd term of the AP 20, 26, 32, 38, …? (a) 132 (b) 146 (c) 126 (d) 152

Answer key

  1. 324
  2. 168
  3. 35
  4. 625
  5. 1275
  6. 62
  7. 148
  8. 3081
  9. 24th
  10. 24
  11. 60
  12. 7
  13. 1081
  14. 44
  15. 18th
  16. 3486
  17. 729
  18. 270
  19. 245
  20. 25
  21. 179
  22. 64
  23. 432
  24. 81
  25. 165
  26. 70
  27. 133
  28. 100
  29. 64
  30. 40th
  31. 194
  32. 25
  33. 1953
  34. 3160
  35. 292
  36. 75
  37. 173
  38. 36
  39. 429
  40. 146

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