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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 841 · 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 19th term of the AP 5, 7, 9, 11, …? (a) 38 (b) 41 (c) 43 (d) 36
  2. 2.What is the 29th term of the AP 15, 20, 25, 30, …? (a) 160 (b) 155 (c) 145 (d) 140
  3. 3.What is the sum of the first 8 terms of the AP 7, 9, 11, …? (a) 21 (b) 120 (c) 112 (d) 224
  4. 4.What is the sum of the first 10 terms of the AP 7, 12, 17, …? (a) 590 (b) 320 (c) 295 (d) 52
  5. 5.What is the missing term in the AP 19, ?, 27, 31, 35? (a) 27 (b) 23 (c) 22 (d) 24
  6. 6.What is the 32nd term of the AP 7, 10, 13, 16, …? (a) 103 (b) 100 (c) 93 (d) 96
  7. 7.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 330 (b) 20 (c) 165 (d) 166
  8. 8.What is the 19th term of the AP 1, 10, 19, 28, …? (a) 172 (b) 171 (c) 162 (d) 163
  9. 9.What is the missing term in the AP 20, ?, 34, 41, 48? (a) 27 (b) 34 (c) 26 (d) 28
  10. 10.What is the 32nd term of the AP 3, 9, 15, 21, …? (a) 192 (b) 186 (c) 189 (d) 195
  11. 11.Which term of the AP 4, 7, 10, 13, … is 109? (a) 36th (b) 35th (c) 38th (d) 37th
  12. 12.What is the sum of the first 7 terms of the AP 10, 15, 20, …? (a) 180 (b) 40 (c) 175 (d) 350
  13. 13.What is the sum of all the whole numbers from 1 to 50? (a) 2550 (b) 1250 (c) 1275 (d) 1225
  14. 14.Which term of the AP 4, 6, 8, 10, … is 76? (a) 36th (b) 39th (c) 38th (d) 37th
  15. 15.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 336 (b) 189 (c) 168 (d) 42
  16. 16.What is the 13th term of the AP 18, 25, 32, 39, …? (a) 102 (b) 84 (c) 109 (d) 91
  17. 17.What is the missing term in the AP 16, 18, 20, ?, 24? (a) 22 (b) 21 (c) 24 (d) 23
  18. 18.What is the 12th term of the AP 5, 13, 21, 29, …? (a) 88 (b) 101 (c) 93 (d) 96
  19. 19.Which term of the AP 12, 15, 18, 21, … is 66? (a) 18th (b) 22nd (c) 19th (d) 20th
  20. 20.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 2450 (c) 1225 (d) 1226
  21. 21.Which term of the AP 2, 9, 16, 23, … is 93? (a) 16th (b) 14th (c) 15th (d) 13th
  22. 22.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 16 (b) 30 (c) 5 (d) 15
  23. 23.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 120 (c) 121 (d) 105
  24. 24.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 37 (c) 190 (d) 380
  25. 25.Which term of the AP 6, 8, 10, 12, … is 66? (a) 33rd (b) 31st (c) 30th (d) 32nd
  26. 26.What is the missing term in the AP 16, 19, ?, 25, 28? (a) 25 (b) 22 (c) 21 (d) 23
  27. 27.What is the missing term in the AP 18, 27, ?, 45, 54? (a) 37 (b) 45 (c) 36 (d) 35
  28. 28.What is the 19th term of the AP 19, 26, 33, 40, …? (a) 145 (b) 126 (c) 152 (d) 133
  29. 29.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 500 (b) 43 (c) 270 (d) 250
  30. 30.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 120 (c) 240 (d) 225
  31. 31.What is the sum of all the whole numbers from 1 to 13? (a) 78 (b) 91 (c) 182 (d) 92
  32. 32.What is the missing term in the AP 13, ?, 25, 31, 37? (a) 20 (b) 25 (c) 19 (d) 18
  33. 33.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 22 (b) 264 (c) 143 (d) 132
  34. 34.What is the 12th term of the AP 4, 10, 16, 22, …? (a) 76 (b) 70 (c) 72 (d) 66
  35. 35.What is the 10th term of the AP 6, 8, 10, 12, …? (a) 20 (b) 24 (c) 26 (d) 18
  36. 36.What is the missing term in the AP 10, 14, 18, ?, 26? (a) 26 (b) 22 (c) 21 (d) 23
  37. 37.Which term of the AP 4, 8, 12, 16, … is 96? (a) 24th (b) 23rd (c) 26th (d) 25th
  38. 38.Which term of the AP 5, 13, 21, 29, … is 285? (a) 37th (b) 38th (c) 35th (d) 36th
  39. 39.What is the 10th term of the AP 15, 20, 25, 30, …? (a) 50 (b) 60 (c) 45 (d) 65
  40. 40.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 41 (c) 462 (d) 441

Answer key

  1. 41
  2. 155
  3. 112
  4. 295
  5. 23
  6. 100
  7. 165
  8. 163
  9. 27
  10. 189
  11. 36th
  12. 175
  13. 1275
  14. 37th
  15. 168
  16. 102
  17. 22
  18. 93
  19. 19th
  20. 1225
  21. 14th
  22. 15
  23. 120
  24. 361
  25. 31st
  26. 22
  27. 36
  28. 145
  29. 250
  30. 225
  31. 91
  32. 19
  33. 132
  34. 70
  35. 24
  36. 22
  37. 24th
  38. 36th
  39. 60
  40. 441

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