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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 56 · 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 12 terms of the AP 3, 8, 13, …? (a) 732 (b) 396 (c) 58 (d) 366
  2. 2.What is the 27th term of the AP 4, 6, 8, 10, …? (a) 52 (b) 58 (c) 56 (d) 54
  3. 3.Which term of the AP 19, 27, 35, 43, … is 259? (a) 33rd (b) 30th (c) 32nd (d) 31st
  4. 4.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 105 (b) 210 (c) 27 (d) 119
  5. 5.What is the sum of all the whole numbers from 1 to 55? (a) 1540 (b) 3080 (c) 1541 (d) 1485
  6. 6.What is the sum of the first 11 terms of the AP 10, 14, 18, …? (a) 660 (b) 352 (c) 50 (d) 330
  7. 7.What is the missing term in the AP 16, ?, 20, 22, 24? (a) 17 (b) 19 (c) 20 (d) 18
  8. 8.Which term of the AP 3, 6, 9, 12, … is 69? (a) 22nd (b) 23rd (c) 24th (d) 25th
  9. 9.What is the 40th term of the AP 20, 25, 30, 35, …? (a) 200 (b) 215 (c) 220 (d) 195
  10. 10.Which term of the AP 17, 24, 31, 38, … is 290? (a) 42nd (b) 40th (c) 41st (d) 39th
  11. 11.What is the 17th term of the AP 19, 24, 29, 34, …? (a) 80 (b) 85 (c) 99 (d) 104
  12. 12.What is the 24th term of the AP 20, 24, 28, 32, …? (a) 92 (b) 116 (c) 96 (d) 112
  13. 13.What is the 33rd term of the AP 9, 13, 17, 21, …? (a) 128 (b) 137 (c) 132 (d) 141
  14. 14.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 930 (c) 59 (d) 465
  15. 15.What is the 16th term of the AP 10, 15, 20, 25, …? (a) 85 (b) 80 (c) 90 (d) 75
  16. 16.What is the sum of all the whole numbers from 1 to 51? (a) 1275 (b) 2652 (c) 1326 (d) 1327
  17. 17.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 39 (d) 400
  18. 18.Which term of the AP 1, 6, 11, 16, … is 181? (a) 37th (b) 36th (c) 38th (d) 39th
  19. 19.What is the 34th term of the AP 20, 22, 24, 26, …? (a) 68 (b) 88 (c) 66 (d) 86
  20. 20.What is the 24th term of the AP 4, 9, 14, 19, …? (a) 119 (b) 115 (c) 124 (d) 120
  21. 21.What is the missing term in the AP 15, 23, ?, 39, 47? (a) 32 (b) 39 (c) 31 (d) 30
  22. 22.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 82 (b) 162 (c) 13 (d) 81
  23. 23.What is the 20th term of the AP 14, 22, 30, 38, …? (a) 174 (b) 160 (c) 166 (d) 152
  24. 24.What is the missing term in the AP 5, ?, 11, 14, 17? (a) 11 (b) 9 (c) 7 (d) 8
  25. 25.What is the 40th term of the AP 3, 6, 9, 12, …? (a) 117 (b) 123 (c) 120 (d) 121
  26. 26.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 3486 (c) 7140 (d) 3570
  27. 27.Which term of the AP 19, 24, 29, 34, … is 164? (a) 30th (b) 32nd (c) 29th (d) 31st
  28. 28.What is the sum of all the whole numbers from 1 to 76? (a) 2888 (b) 2850 (c) 2926 (d) 5852
  29. 29.What is the 33rd term of the AP 6, 9, 12, 15, …? (a) 96 (b) 102 (c) 99 (d) 105
  30. 30.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 406 (d) 784
  31. 31.Which term of the AP 1, 3, 5, 7, … is 61? (a) 31st (b) 30th (c) 33rd (d) 32nd
  32. 32.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 57 (b) 330 (c) 600 (d) 300
  33. 33.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 120 (c) 105 (d) 121
  34. 34.What is the missing term in the AP 20, 28, ?, 44, 52? (a) 36 (b) 37 (c) 35 (d) 44
  35. 35.What is the 18th term of the AP 15, 17, 19, 21, …? (a) 36 (b) 49 (c) 34 (d) 51
  36. 36.Which term of the AP 9, 13, 17, 21, … is 65? (a) 14th (b) 16th (c) 15th (d) 17th
  37. 37.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 12 (b) 15 (c) 13 (d) 11
  38. 38.What is the 30th term of the AP 13, 21, 29, 37, …? (a) 232 (b) 240 (c) 253 (d) 245
  39. 39.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 11 (b) 40 (c) 70 (d) 35
  40. 40.What is the sum of the first 9 terms of the AP 10, 14, 18, …? (a) 42 (b) 468 (c) 252 (d) 234

Answer key

  1. 366
  2. 56
  3. 31st
  4. 105
  5. 1540
  6. 330
  7. 18
  8. 23rd
  9. 215
  10. 40th
  11. 99
  12. 112
  13. 137
  14. 900
  15. 85
  16. 1326
  17. 400
  18. 37th
  19. 86
  20. 119
  21. 31
  22. 81
  23. 166
  24. 8
  25. 120
  26. 3570
  27. 30th
  28. 2926
  29. 102
  30. 784
  31. 31st
  32. 300
  33. 120
  34. 36
  35. 49
  36. 15th
  37. 12
  38. 245
  39. 35
  40. 234

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