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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 513 · 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 16, 18, 20, ?, 24? (a) 21 (b) 23 (c) 22 (d) 24
  2. 2.What is the missing term in the AP 10, ?, 28, 37, 46? (a) 20 (b) 19 (c) 28 (d) 18
  3. 3.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 400 (d) 39
  4. 4.What is the 30th term of the AP 19, 24, 29, 34, …? (a) 145 (b) 150 (c) 164 (d) 169
  5. 5.What is the missing term in the AP 13, 15, 17, ?, 21? (a) 21 (b) 19 (c) 18 (d) 20
  6. 6.Which term of the AP 2, 6, 10, 14, … is 82? (a) 21st (b) 20th (c) 23rd (d) 22nd
  7. 7.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 529 (c) 276 (d) 552
  8. 8.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 49 (b) 225 (c) 252 (d) 450
  9. 9.What is the missing term in the AP 12, ?, 28, 36, 44? (a) 21 (b) 28 (c) 19 (d) 20
  10. 10.What is the sum of the first 12 terms of the AP 1, 3, 5, …? (a) 23 (b) 288 (c) 156 (d) 144
  11. 11.What is the 40th term of the AP 6, 9, 12, 15, …? (a) 117 (b) 120 (c) 123 (d) 126
  12. 12.What is the 33rd term of the AP 4, 7, 10, 13, …? (a) 100 (b) 103 (c) 96 (d) 99
  13. 13.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 81 (c) 17 (d) 90
  14. 14.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 266 (b) 136 (c) 28 (d) 133
  15. 15.What is the 28th term of the AP 10, 13, 16, 19, …? (a) 91 (b) 84 (c) 94 (d) 81
  16. 16.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 42 (b) 39 (c) 9 (d) 78
  17. 17.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 625 (d) 650
  18. 18.What is the sum of all the whole numbers from 1 to 70? (a) 2485 (b) 2415 (c) 4970 (d) 2450
  19. 19.What is the sum of the first 8 terms of the AP 5, 6, 7, …? (a) 72 (b) 12 (c) 136 (d) 68
  20. 20.Which term of the AP 5, 11, 17, 23, … is 71? (a) 14th (b) 13th (c) 11th (d) 12th
  21. 21.What is the 37th term of the AP 10, 15, 20, 25, …? (a) 195 (b) 185 (c) 190 (d) 180
  22. 22.What is the 20th term of the AP 20, 26, 32, 38, …? (a) 120 (b) 140 (c) 134 (d) 114
  23. 23.What is the 40th term of the AP 12, 21, 30, 39, …? (a) 372 (b) 360 (c) 363 (d) 351
  24. 24.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 136 (b) 29 (c) 120 (d) 240
  25. 25.What is the 15th term of the AP 17, 19, 21, 23, …? (a) 47 (b) 45 (c) 28 (d) 30
  26. 26.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 66 (d) 132
  27. 27.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 9 (b) 46 (c) 45 (d) 90
  28. 28.What is the sum of all the whole numbers from 1 to 46? (a) 1058 (b) 1081 (c) 2162 (d) 1035
  29. 29.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 5852 (c) 2926 (d) 2888
  30. 30.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 110 (b) 190 (c) 31 (d) 95
  31. 31.What is the 28th term of the AP 6, 12, 18, 24, …? (a) 174 (b) 168 (c) 162 (d) 169
  32. 32.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 729 (c) 756 (d) 378
  33. 33.What is the 33rd term of the AP 15, 23, 31, 39, …? (a) 279 (b) 264 (c) 271 (d) 256
  34. 34.What is the 29th term of the AP 15, 21, 27, 33, …? (a) 174 (b) 189 (c) 183 (d) 168
  35. 35.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 169 (d) 25
  36. 36.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 5 (b) 4 (c) 6 (d) 3
  37. 37.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 15 (d) 30
  38. 38.What is the sum of the first 11 terms of the AP 8, 9, 10, …? (a) 144 (b) 18 (c) 143 (d) 286
  39. 39.What is the missing term in the AP 2, ?, 12, 17, 22? (a) 12 (b) 8 (c) 7 (d) 6
  40. 40.What is the 11th term of the AP 7, 14, 21, 28, …? (a) 70 (b) 77 (c) 78 (d) 84

Answer key

  1. 22
  2. 19
  3. 400
  4. 164
  5. 19
  6. 21st
  7. 529
  8. 225
  9. 20
  10. 144
  11. 123
  12. 100
  13. 81
  14. 133
  15. 91
  16. 39
  17. 625
  18. 2485
  19. 68
  20. 12th
  21. 190
  22. 134
  23. 363
  24. 120
  25. 45
  26. 121
  27. 45
  28. 1081
  29. 2926
  30. 95
  31. 168
  32. 729
  33. 271
  34. 183
  35. 169
  36. 4
  37. 25
  38. 143
  39. 7
  40. 77

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