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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 687 · 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 40th term of the AP 9, 11, 13, 15, …? (a) 80 (b) 87 (c) 78 (d) 89
  2. 2.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 6162 (c) 3081 (d) 3003
  3. 3.What is the 20th term of the AP 13, 20, 27, 34, …? (a) 133 (b) 153 (c) 140 (d) 146
  4. 4.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 70 (b) 9 (c) 35 (d) 36
  5. 5.What is the missing term in the AP 1, 9, 17, ?, 33? (a) 33 (b) 25 (c) 26 (d) 24
  6. 6.Which term of the AP 6, 9, 12, 15, … is 114? (a) 39th (b) 36th (c) 38th (d) 37th
  7. 7.Which term of the AP 15, 23, 31, 39, … is 287? (a) 34th (b) 36th (c) 37th (d) 35th
  8. 8.Which term of the AP 6, 12, 18, 24, … is 168? (a) 27th (b) 30th (c) 29th (d) 28th
  9. 9.What is the 13th term of the AP 3, 9, 15, 21, …? (a) 75 (b) 72 (c) 81 (d) 78
  10. 10.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 290 (b) 145 (c) 28 (d) 160
  11. 11.What is the 16th term of the AP 20, 22, 24, 26, …? (a) 52 (b) 32 (c) 30 (d) 50
  12. 12.What is the missing term in the AP 4, 9, ?, 19, 24? (a) 15 (b) 13 (c) 14 (d) 19
  13. 13.What is the 34th term of the AP 10, 12, 14, 16, …? (a) 68 (b) 76 (c) 78 (d) 66
  14. 14.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 253 (c) 277 (d) 276
  15. 15.What is the 40th term of the AP 2, 9, 16, 23, …? (a) 273 (b) 282 (c) 275 (d) 280
  16. 16.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 462 (d) 441
  17. 17.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 60 (b) 15 (c) 66 (d) 120
  18. 18.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 21 (d) 42
  19. 19.What is the 24th term of the AP 9, 16, 23, 30, …? (a) 170 (b) 168 (c) 161 (d) 177
  20. 20.What is the missing term in the AP 4, 8, 12, ?, 20? (a) 16 (b) 17 (c) 20 (d) 15
  21. 21.Which term of the AP 16, 19, 22, 25, … is 46? (a) 13th (b) 11th (c) 10th (d) 12th
  22. 22.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 37 (c) 190 (d) 380
  23. 23.What is the 10th term of the AP 6, 11, 16, 21, …? (a) 50 (b) 45 (c) 51 (d) 56
  24. 24.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 43 (b) 200 (c) 352 (d) 176
  25. 25.What is the 33rd term of the AP 10, 17, 24, 31, …? (a) 231 (b) 234 (c) 241 (d) 224
  26. 26.What is the sum of the first 10 terms of the AP 9, 13, 17, …? (a) 45 (b) 290 (c) 540 (d) 270
  27. 27.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 16 (b) 109 (c) 108 (d) 216
  28. 28.What is the 34th term of the AP 3, 11, 19, 27, …? (a) 267 (b) 272 (c) 275 (d) 264
  29. 29.What is the sum of the first 12 terms of the AP 4, 7, 10, …? (a) 246 (b) 264 (c) 492 (d) 37
  30. 30.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 13 (b) 170 (c) 85 (d) 90
  31. 31.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 70 (b) 75 (c) 18 (d) 140
  32. 32.Which term of the AP 15, 21, 27, 33, … is 249? (a) 40th (b) 39th (c) 42nd (d) 41st
  33. 33.What is the sum of the first 5 terms of the AP 10, 14, 18, …? (a) 26 (b) 180 (c) 90 (d) 100
  34. 34.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 378 (c) 53 (d) 729
  35. 35.What is the 13th term of the AP 9, 17, 25, 33, …? (a) 113 (b) 96 (c) 105 (d) 104
  36. 36.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 19 (c) 100 (d) 110
  37. 37.What is the missing term in the AP 5, 12, ?, 26, 33? (a) 19 (b) 26 (c) 18 (d) 20
  38. 38.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 39 (d) 400
  39. 39.Which term of the AP 2, 11, 20, 29, … is 326? (a) 36th (b) 38th (c) 39th (d) 37th
  40. 40.What is the 34th term of the AP 9, 13, 17, 21, …? (a) 136 (b) 145 (c) 141 (d) 132

Answer key

  1. 87
  2. 3081
  3. 146
  4. 35
  5. 25
  6. 37th
  7. 35th
  8. 28th
  9. 75
  10. 145
  11. 50
  12. 14
  13. 76
  14. 276
  15. 275
  16. 441
  17. 60
  18. 36
  19. 170
  20. 16
  21. 11th
  22. 361
  23. 51
  24. 176
  25. 234
  26. 270
  27. 108
  28. 267
  29. 246
  30. 85
  31. 70
  32. 40th
  33. 90
  34. 729
  35. 105
  36. 100
  37. 19
  38. 400
  39. 37th
  40. 141

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