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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 282 · 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 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 45 (d) 81
  2. 2.What is the sum of the first 10 terms of the AP 3, 6, 9, …? (a) 30 (b) 180 (c) 330 (d) 165
  3. 3.Which term of the AP 17, 26, 35, 44, … is 89? (a) 11th (b) 10th (c) 8th (d) 9th
  4. 4.Which term of the AP 3, 6, 9, 12, … is 39? (a) 15th (b) 14th (c) 13th (d) 12th
  5. 5.What is the missing term in the AP 16, 18, ?, 22, 24? (a) 19 (b) 21 (c) 22 (d) 20
  6. 6.What is the missing term in the AP 5, 10, ?, 20, 25? (a) 20 (b) 14 (c) 16 (d) 15
  7. 7.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 84 (b) 42 (c) 9 (d) 43
  8. 8.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 222 (b) 31 (c) 111 (d) 126
  9. 9.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 41 (c) 462 (d) 231
  10. 10.What is the sum of the first 10 terms of the AP 1, 6, 11, …? (a) 46 (b) 235 (c) 470 (d) 260
  11. 11.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 21 (b) 66 (c) 78 (d) 132
  12. 12.What is the 24th term of the AP 17, 25, 33, 41, …? (a) 184 (b) 192 (c) 209 (d) 201
  13. 13.What is the 11th term of the AP 15, 18, 21, 24, …? (a) 45 (b) 30 (c) 33 (d) 48
  14. 14.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 168 (b) 90 (c) 84 (d) 19
  15. 15.What is the sum of all the whole numbers from 1 to 85? (a) 7310 (b) 3570 (c) 3655 (d) 3656
  16. 16.What is the 10th term of the AP 19, 22, 25, 28, …? (a) 30 (b) 46 (c) 49 (d) 27
  17. 17.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 380 (c) 191 (d) 190
  18. 18.What is the sum of all the whole numbers from 1 to 51? (a) 1326 (b) 2652 (c) 1275 (d) 1327
  19. 19.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 132 (c) 121 (d) 66
  20. 20.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 105 (b) 180 (c) 90 (d) 30
  21. 21.What is the 29th term of the AP 13, 18, 23, 28, …? (a) 153 (b) 158 (c) 140 (d) 145
  22. 22.What is the 38th term of the AP 20, 23, 26, 29, …? (a) 114 (b) 111 (c) 134 (d) 131
  23. 23.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 56 (c) 28 (d) 49
  24. 24.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 171 (c) 35 (d) 342
  25. 25.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 55 (b) 15 (c) 60 (d) 110
  26. 26.What is the sum of all the whole numbers from 1 to 41? (a) 861 (b) 1722 (c) 862 (d) 820
  27. 27.What is the 37th term of the AP 20, 27, 34, 41, …? (a) 279 (b) 252 (c) 272 (d) 259
  28. 28.What is the 31st term of the AP 20, 25, 30, 35, …? (a) 155 (b) 150 (c) 175 (d) 170
  29. 29.Which term of the AP 20, 26, 32, 38, … is 212? (a) 35th (b) 34th (c) 32nd (d) 33rd
  30. 30.What is the sum of the first 5 terms of the AP 8, 12, 16, …? (a) 24 (b) 80 (c) 90 (d) 160
  31. 31.What is the 31st term of the AP 5, 14, 23, 32, …? (a) 275 (b) 284 (c) 270 (d) 279
  32. 32.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 23 (c) 78 (d) 156
  33. 33.Which term of the AP 11, 20, 29, 38, … is 245? (a) 28th (b) 26th (c) 29th (d) 27th
  34. 34.What is the 19th term of the AP 18, 24, 30, 36, …? (a) 108 (b) 126 (c) 114 (d) 132
  35. 35.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 930 (c) 59 (d) 900
  36. 36.Which term of the AP 11, 20, 29, 38, … is 101? (a) 10th (b) 11th (c) 13th (d) 12th
  37. 37.What is the sum of the first 12 terms of the AP 2, 4, 6, …? (a) 24 (b) 156 (c) 168 (d) 312
  38. 38.What is the 38th term of the AP 7, 16, 25, 34, …? (a) 349 (b) 342 (c) 340 (d) 333
  39. 39.What is the 18th term of the AP 2, 8, 14, 20, …? (a) 104 (b) 108 (c) 110 (d) 102
  40. 40.What is the missing term in the AP 13, 17, ?, 25, 29? (a) 25 (b) 20 (c) 21 (d) 22

Answer key

  1. 81
  2. 165
  3. 9th
  4. 13th
  5. 20
  6. 15
  7. 42
  8. 111
  9. 441
  10. 235
  11. 66
  12. 201
  13. 45
  14. 84
  15. 3655
  16. 46
  17. 190
  18. 1326
  19. 121
  20. 90
  21. 153
  22. 131
  23. 49
  24. 324
  25. 55
  26. 861
  27. 272
  28. 170
  29. 33rd
  30. 80
  31. 275
  32. 144
  33. 27th
  34. 126
  35. 900
  36. 11th
  37. 156
  38. 340
  39. 104
  40. 21

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