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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 390 · 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 28th term of the AP 17, 21, 25, 29, …? (a) 112 (b) 129 (c) 125 (d) 108
  2. 2.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 27 (b) 180 (c) 360 (d) 190
  3. 3.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 1122 (c) 562 (d) 528
  4. 4.What is the missing term in the AP 4, ?, 8, 10, 12? (a) 7 (b) 5 (c) 8 (d) 6
  5. 5.Which term of the AP 6, 8, 10, 12, … is 26? (a) 12th (b) 13th (c) 11th (d) 10th
  6. 6.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 21 (c) 132 (d) 66
  7. 7.What is the sum of the first 7 terms of the AP 6, 12, 18, …? (a) 189 (b) 42 (c) 336 (d) 168
  8. 8.What is the sum of the first 11 terms of the AP 4, 9, 14, …? (a) 324 (b) 319 (c) 54 (d) 638
  9. 9.What is the 32nd term of the AP 8, 10, 12, 14, …? (a) 62 (b) 72 (c) 70 (d) 64
  10. 10.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 496 (c) 528 (d) 1056
  11. 11.What is the 34th term of the AP 4, 9, 14, 19, …? (a) 170 (b) 165 (c) 174 (d) 169
  12. 12.What is the sum of all the whole numbers from 1 to 87? (a) 3829 (b) 7656 (c) 3828 (d) 3741
  13. 13.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 625 (c) 325 (d) 49
  14. 14.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 11 (b) 67 (c) 66 (d) 132
  15. 15.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 19 (b) 22 (c) 17 (d) 18
  16. 16.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 9 (b) 78 (c) 42 (d) 39
  17. 17.What is the 34th term of the AP 11, 15, 19, 23, …? (a) 147 (b) 132 (c) 136 (d) 143
  18. 18.What is the sum of the first 10 terms of the AP 6, 7, 8, …? (a) 210 (b) 110 (c) 105 (d) 15
  19. 19.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 56 (c) 49 (d) 13
  20. 20.What is the sum of all the whole numbers from 1 to 42? (a) 903 (b) 1806 (c) 882 (d) 861
  21. 21.Which term of the AP 19, 22, 25, 28, … is 94? (a) 27th (b) 25th (c) 28th (d) 26th
  22. 22.What is the 24th term of the AP 9, 12, 15, 18, …? (a) 78 (b) 81 (c) 69 (d) 72
  23. 23.What is the 23rd term of the AP 9, 16, 23, 30, …? (a) 163 (b) 161 (c) 154 (d) 170
  24. 24.What is the 15th term of the AP 17, 22, 27, 32, …? (a) 92 (b) 75 (c) 70 (d) 87
  25. 25.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 11 (b) 36 (c) 42 (d) 72
  26. 26.Which term of the AP 17, 25, 33, 41, … is 297? (a) 36th (b) 37th (c) 35th (d) 38th
  27. 27.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 120 (b) 138 (c) 240 (d) 35
  28. 28.Which term of the AP 15, 17, 19, 21, … is 79? (a) 32nd (b) 34th (c) 35th (d) 33rd
  29. 29.What is the sum of all the whole numbers from 1 to 39? (a) 1560 (b) 780 (c) 741 (d) 781
  30. 30.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 406 (c) 378 (d) 812
  31. 31.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 60 (b) 65 (c) 120 (d) 22
  32. 32.What is the 20th term of the AP 20, 25, 30, 35, …? (a) 95 (b) 115 (c) 120 (d) 100
  33. 33.What is the 23rd term of the AP 19, 21, 23, 25, …? (a) 65 (b) 44 (c) 46 (d) 63
  34. 34.What is the 18th term of the AP 3, 9, 15, 21, …? (a) 111 (b) 102 (c) 108 (d) 105
  35. 35.What is the missing term in the AP 3, ?, 21, 30, 39? (a) 12 (b) 11 (c) 21 (d) 13
  36. 36.What is the 12th term of the AP 19, 22, 25, 28, …? (a) 55 (b) 36 (c) 52 (d) 33
  37. 37.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 130 (b) 80 (c) 65 (d) 25
  38. 38.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 420 (c) 400 (d) 210
  39. 39.Which term of the AP 19, 25, 31, 37, … is 163? (a) 27th (b) 25th (c) 26th (d) 24th
  40. 40.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 306 (c) 289 (d) 33

Answer key

  1. 125
  2. 180
  3. 561
  4. 6
  5. 11th
  6. 121
  7. 168
  8. 319
  9. 70
  10. 528
  11. 169
  12. 3828
  13. 625
  14. 66
  15. 18
  16. 39
  17. 143
  18. 105
  19. 49
  20. 903
  21. 26th
  22. 78
  23. 163
  24. 87
  25. 36
  26. 36th
  27. 120
  28. 33rd
  29. 780
  30. 406
  31. 60
  32. 115
  33. 63
  34. 105
  35. 12
  36. 52
  37. 65
  38. 400
  39. 25th
  40. 289

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