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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 949 · 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 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 729 (d) 378
  2. 2.What is the 11th term of the AP 1, 6, 11, 16, …? (a) 55 (b) 50 (c) 56 (d) 51
  3. 3.What is the sum of the first 11 terms of the AP 1, 7, 13, …? (a) 374 (b) 341 (c) 682 (d) 61
  4. 4.What is the sum of all the whole numbers from 1 to 17? (a) 154 (b) 153 (c) 136 (d) 306
  5. 5.Which term of the AP 18, 20, 22, 24, … is 52? (a) 17th (b) 26th (c) 19th (d) 18th
  6. 6.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 441 (c) 462 (d) 41
  7. 7.What is the sum of the first 5 terms of the AP 10, 14, 18, …? (a) 100 (b) 26 (c) 180 (d) 90
  8. 8.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 21 (c) 121 (d) 66
  9. 9.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 484 (c) 506 (d) 43
  10. 10.What is the 24th term of the AP 1, 10, 19, 28, …? (a) 208 (b) 217 (c) 216 (d) 207
  11. 11.What is the sum of all the whole numbers from 1 to 14? (a) 91 (b) 98 (c) 210 (d) 105
  12. 12.What is the 24th term of the AP 19, 25, 31, 37, …? (a) 157 (b) 163 (c) 144 (d) 138
  13. 13.What is the sum of all the whole numbers from 1 to 49? (a) 1226 (b) 2450 (c) 1225 (d) 1176
  14. 14.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 200 (b) 115 (c) 100 (d) 32
  15. 15.What is the missing term in the AP 19, 27, ?, 43, 51? (a) 34 (b) 43 (c) 35 (d) 36
  16. 16.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 210 (c) 196 (d) 27
  17. 17.What is the 34th term of the AP 14, 18, 22, 26, …? (a) 136 (b) 146 (c) 132 (d) 150
  18. 18.What is the missing term in the AP 15, ?, 27, 33, 39? (a) 22 (b) 20 (c) 21 (d) 27
  19. 19.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 36 (c) 64 (d) 15
  20. 20.What is the 23rd term of the AP 19, 27, 35, 43, …? (a) 203 (b) 176 (c) 184 (d) 195
  21. 21.What is the 38th term of the AP 3, 7, 11, 15, …? (a) 155 (b) 148 (c) 152 (d) 151
  22. 22.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 105 (b) 27 (c) 119 (d) 210
  23. 23.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 55 (c) 100 (d) 110
  24. 24.What is the sum of the first 8 terms of the AP 7, 10, 13, …? (a) 140 (b) 280 (c) 152 (d) 28
  25. 25.What is the 26th term of the AP 5, 8, 11, 14, …? (a) 83 (b) 75 (c) 78 (d) 80
  26. 26.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 529 (c) 45 (d) 276
  27. 27.Which term of the AP 12, 16, 20, 24, … is 52? (a) 12th (b) 13th (c) 11th (d) 10th
  28. 28.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 870 (c) 841 (d) 435
  29. 29.What is the 24th term of the AP 13, 22, 31, 40, …? (a) 229 (b) 207 (c) 216 (d) 220
  30. 30.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 144 (c) 23 (d) 156
  31. 31.What is the missing term in the AP 13, ?, 29, 37, 45? (a) 29 (b) 22 (c) 21 (d) 20
  32. 32.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 406 (d) 784
  33. 33.Which term of the AP 1, 4, 7, 10, … is 31? (a) 10th (b) 11th (c) 12th (d) 13th
  34. 34.What is the sum of the first 10 terms of the AP 5, 10, 15, …? (a) 50 (b) 550 (c) 275 (d) 300
  35. 35.What is the sum of all the whole numbers from 1 to 92? (a) 4232 (b) 4278 (c) 4186 (d) 8556
  36. 36.Which term of the AP 1, 6, 11, 16, … is 171? (a) 36th (b) 35th (c) 37th (d) 34th
  37. 37.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 170 (b) 27 (c) 90 (d) 85
  38. 38.What is the 16th term of the AP 8, 12, 16, 20, …? (a) 60 (b) 72 (c) 64 (d) 68
  39. 39.Which term of the AP 4, 8, 12, 16, … is 108? (a) 26th (b) 27th (c) 29th (d) 28th
  40. 40.What is the 27th term of the AP 14, 22, 30, 38, …? (a) 216 (b) 222 (c) 208 (d) 230

Answer key

  1. 729
  2. 51
  3. 341
  4. 153
  5. 18th
  6. 441
  7. 90
  8. 121
  9. 484
  10. 208
  11. 105
  12. 157
  13. 1225
  14. 100
  15. 35
  16. 196
  17. 146
  18. 21
  19. 64
  20. 195
  21. 151
  22. 105
  23. 100
  24. 140
  25. 80
  26. 529
  27. 11th
  28. 841
  29. 220
  30. 144
  31. 21
  32. 784
  33. 11th
  34. 275
  35. 4278
  36. 35th
  37. 85
  38. 68
  39. 27th
  40. 222

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