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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 125 · 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 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 105 (c) 27 (d) 196
  2. 2.What is the sum of all the whole numbers from 1 to 67? (a) 2278 (b) 2211 (c) 4556 (d) 2279
  3. 3.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 120 (c) 240 (d) 225
  4. 4.What is the sum of all the whole numbers from 1 to 100? (a) 10100 (b) 5050 (c) 4950 (d) 5000
  5. 5.What is the 13th term of the AP 5, 14, 23, 32, …? (a) 122 (b) 113 (c) 117 (d) 108
  6. 6.What is the 12th term of the AP 4, 10, 16, 22, …? (a) 76 (b) 70 (c) 72 (d) 66
  7. 7.What is the 16th term of the AP 10, 16, 22, 28, …? (a) 90 (b) 96 (c) 106 (d) 100
  8. 8.What is the sum of all the whole numbers from 1 to 17? (a) 153 (b) 154 (c) 136 (d) 306
  9. 9.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 25 (c) 91 (d) 169
  10. 10.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 600 (c) 47 (d) 300
  11. 11.What is the missing term in the AP 2, ?, 12, 17, 22? (a) 8 (b) 6 (c) 7 (d) 12
  12. 12.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 14 (b) 180 (c) 91 (d) 90
  13. 13.What is the 34th term of the AP 16, 19, 22, 25, …? (a) 115 (b) 118 (c) 102 (d) 99
  14. 14.Which term of the AP 9, 16, 23, 30, … is 247? (a) 34th (b) 37th (c) 35th (d) 36th
  15. 15.Which term of the AP 3, 8, 13, 18, … is 63? (a) 15th (b) 12th (c) 14th (d) 13th
  16. 16.What is the 31st term of the AP 20, 22, 24, 26, …? (a) 82 (b) 80 (c) 60 (d) 62
  17. 17.What is the sum of the first 9 terms of the AP 8, 14, 20, …? (a) 315 (b) 56 (c) 288 (d) 576
  18. 18.What is the missing term in the AP 11, 15, ?, 23, 27? (a) 19 (b) 23 (c) 20 (d) 18
  19. 19.What is the 38th term of the AP 9, 14, 19, 24, …? (a) 194 (b) 185 (c) 199 (d) 190
  20. 20.Which term of the AP 15, 23, 31, 39, … is 303? (a) 37th (b) 39th (c) 38th (d) 36th
  21. 21.What is the 21st term of the AP 18, 20, 22, 24, …? (a) 42 (b) 60 (c) 40 (d) 58
  22. 22.What is the sum of all the whole numbers from 1 to 10? (a) 45 (b) 55 (c) 110 (d) 50
  23. 23.What is the missing term in the AP 9, ?, 17, 21, 25? (a) 14 (b) 12 (c) 17 (d) 13
  24. 24.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 13 (b) 70 (c) 38 (d) 35
  25. 25.What is the missing term in the AP 12, 20, 28, ?, 44? (a) 36 (b) 37 (c) 35 (d) 44
  26. 26.What is the missing term in the AP 5, 12, 19, ?, 33? (a) 33 (b) 25 (c) 26 (d) 27
  27. 27.What is the sum of all the whole numbers from 1 to 93? (a) 8742 (b) 4278 (c) 4371 (d) 4372
  28. 28.What is the 15th term of the AP 14, 20, 26, 32, …? (a) 90 (b) 98 (c) 84 (d) 104
  29. 29.What is the 38th term of the AP 15, 24, 33, 42, …? (a) 357 (b) 333 (c) 342 (d) 348
  30. 30.What is the 14th term of the AP 3, 9, 15, 21, …? (a) 84 (b) 78 (c) 81 (d) 87
  31. 31.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 27 (b) 138 (c) 270 (d) 135
  32. 32.Which term of the AP 20, 25, 30, 35, … is 70? (a) 11th (b) 10th (c) 14th (d) 12th
  33. 33.What is the sum of the first 9 terms of the AP 3, 9, 15, …? (a) 270 (b) 243 (c) 51 (d) 486
  34. 34.What is the missing term in the AP 13, 15, ?, 19, 21? (a) 16 (b) 19 (c) 18 (d) 17
  35. 35.What is the missing term in the AP 15, 23, ?, 39, 47? (a) 30 (b) 39 (c) 32 (d) 31
  36. 36.What is the 28th term of the AP 4, 10, 16, 22, …? (a) 172 (b) 162 (c) 168 (d) 166
  37. 37.Which term of the AP 5, 14, 23, 32, … is 347? (a) 38th (b) 40th (c) 39th (d) 41st
  38. 38.Which term of the AP 9, 12, 15, 18, … is 114? (a) 38th (b) 37th (c) 35th (d) 36th
  39. 39.What is the 13th term of the AP 9, 16, 23, 30, …? (a) 100 (b) 93 (c) 84 (d) 91
  40. 40.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 35 (b) 70 (c) 40 (d) 11

Answer key

  1. 196
  2. 2278
  3. 225
  4. 5050
  5. 113
  6. 70
  7. 100
  8. 153
  9. 169
  10. 576
  11. 7
  12. 90
  13. 115
  14. 35th
  15. 13th
  16. 80
  17. 288
  18. 19
  19. 194
  20. 37th
  21. 58
  22. 55
  23. 13
  24. 35
  25. 36
  26. 26
  27. 4371
  28. 98
  29. 348
  30. 81
  31. 135
  32. 11th
  33. 243
  34. 17
  35. 31
  36. 166
  37. 39th
  38. 36th
  39. 93
  40. 35

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