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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 718 · 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 5, 12, ?, 26, 33? (a) 19 (b) 20 (c) 18 (d) 26
  2. 2.Which term of the AP 16, 19, 22, 25, … is 109? (a) 33rd (b) 32nd (c) 34th (d) 31st
  3. 3.What is the 30th term of the AP 5, 11, 17, 23, …? (a) 185 (b) 174 (c) 180 (d) 179
  4. 4.Which term of the AP 14, 17, 20, 23, … is 119? (a) 36th (b) 38th (c) 35th (d) 37th
  5. 5.What is the 13th term of the AP 19, 21, 23, 25, …? (a) 24 (b) 45 (c) 26 (d) 43
  6. 6.What is the sum of the first 6 terms of the AP 2, 6, 10, …? (a) 84 (b) 22 (c) 144 (d) 72
  7. 7.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 60 (b) 108 (c) 54 (d) 14
  8. 8.What is the 15th term of the AP 4, 8, 12, 16, …? (a) 64 (b) 60 (c) 56 (d) 61
  9. 9.What is the sum of the first 9 terms of the AP 10, 16, 22, …? (a) 612 (b) 333 (c) 58 (d) 306
  10. 10.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 13 (d) 28
  11. 11.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 17 (b) 88 (c) 80 (d) 160
  12. 12.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 240 (c) 120 (d) 225
  13. 13.What is the 12th term of the AP 15, 17, 19, 21, …? (a) 39 (b) 24 (c) 37 (d) 22
  14. 14.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 552 (c) 276 (d) 45
  15. 15.What is the sum of all the whole numbers from 1 to 99? (a) 4950 (b) 9900 (c) 4851 (d) 4951
  16. 16.Which term of the AP 13, 20, 27, 34, … is 167? (a) 23rd (b) 24th (c) 22nd (d) 25th
  17. 17.What is the 28th term of the AP 9, 18, 27, 36, …? (a) 243 (b) 252 (c) 253 (d) 261
  18. 18.What is the 30th term of the AP 2, 9, 16, 23, …? (a) 212 (b) 210 (c) 203 (d) 205
  19. 19.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 13 (b) 70 (c) 35 (d) 38
  20. 20.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 154 (b) 19 (c) 155 (d) 308
  21. 21.What is the missing term in the AP 7, ?, 21, 28, 35? (a) 21 (b) 15 (c) 13 (d) 14
  22. 22.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 41 (b) 294 (c) 312 (d) 588
  23. 23.Which term of the AP 19, 21, 23, 25, … is 43? (a) 12th (b) 14th (c) 13th (d) 15th
  24. 24.What is the sum of all the whole numbers from 1 to 16? (a) 272 (b) 136 (c) 120 (d) 128
  25. 25.What is the 12th term of the AP 20, 25, 30, 35, …? (a) 55 (b) 75 (c) 80 (d) 60
  26. 26.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 21 (b) 24 (c) 6 (d) 42
  27. 27.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 1035 (c) 2070 (d) 1036
  28. 28.What is the sum of the first 7 terms of the AP 9, 12, 15, …? (a) 252 (b) 27 (c) 129 (d) 126
  29. 29.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 166 (b) 165 (c) 20 (d) 330
  30. 30.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 210 (c) 420 (d) 400
  31. 31.What is the 26th term of the AP 10, 15, 20, 25, …? (a) 130 (b) 125 (c) 140 (d) 135
  32. 32.What is the 11th term of the AP 1, 7, 13, 19, …? (a) 60 (b) 67 (c) 66 (d) 61
  33. 33.What is the sum of all the whole numbers from 1 to 37? (a) 1406 (b) 666 (c) 703 (d) 704
  34. 34.What is the missing term in the AP 6, 15, 24, ?, 42? (a) 33 (b) 42 (c) 34 (d) 32
  35. 35.What is the missing term in the AP 16, 21, ?, 31, 36? (a) 31 (b) 25 (c) 27 (d) 26
  36. 36.What is the sum of the first 8 terms of the AP 4, 10, 16, …? (a) 200 (b) 46 (c) 224 (d) 400
  37. 37.What is the 17th term of the AP 13, 15, 17, 19, …? (a) 47 (b) 45 (c) 34 (d) 32
  38. 38.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 36 (c) 21 (d) 42
  39. 39.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 784 (c) 55 (d) 812
  40. 40.What is the 24th term of the AP 10, 18, 26, 34, …? (a) 202 (b) 192 (c) 184 (d) 194

Answer key

  1. 19
  2. 32nd
  3. 179
  4. 36th
  5. 43
  6. 72
  7. 54
  8. 60
  9. 306
  10. 49
  11. 80
  12. 225
  13. 37
  14. 529
  15. 4950
  16. 23rd
  17. 252
  18. 205
  19. 35
  20. 154
  21. 14
  22. 294
  23. 13th
  24. 136
  25. 75
  26. 21
  27. 1035
  28. 126
  29. 165
  30. 400
  31. 135
  32. 61
  33. 703
  34. 33
  35. 26
  36. 200
  37. 45
  38. 36
  39. 784
  40. 194

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