← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 550 · 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 12th term of the AP 15, 17, 19, 21, …? (a) 37 (b) 39 (c) 24 (d) 22
  2. 2.Which term of the AP 6, 9, 12, 15, … is 96? (a) 32nd (b) 33rd (c) 30th (d) 31st
  3. 3.What is the 15th term of the AP 14, 20, 26, 32, …? (a) 90 (b) 98 (c) 84 (d) 104
  4. 4.What is the 33rd term of the AP 2, 4, 6, 8, …? (a) 66 (b) 68 (c) 67 (d) 64
  5. 5.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 441 (d) 462
  6. 6.What is the sum of all the whole numbers from 1 to 54? (a) 1458 (b) 1485 (c) 2970 (d) 1431
  7. 7.What is the 30th term of the AP 8, 12, 16, 20, …? (a) 124 (b) 120 (c) 128 (d) 116
  8. 8.What is the 26th term of the AP 3, 6, 9, 12, …? (a) 78 (b) 81 (c) 75 (d) 79
  9. 9.What is the sum of all the whole numbers from 1 to 39? (a) 781 (b) 780 (c) 741 (d) 1560
  10. 10.What is the 29th term of the AP 17, 21, 25, 29, …? (a) 116 (b) 133 (c) 112 (d) 129
  11. 11.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 14 (b) 108 (c) 102 (d) 204
  12. 12.What is the 27th term of the AP 4, 7, 10, 13, …? (a) 78 (b) 81 (c) 82 (d) 85
  13. 13.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 100 (b) 99 (c) 14 (d) 198
  14. 14.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 102 (b) 11 (c) 54 (d) 51
  15. 15.Which term of the AP 9, 16, 23, 30, … is 282? (a) 39th (b) 40th (c) 41st (d) 42nd
  16. 16.Which term of the AP 15, 18, 21, 24, … is 87? (a) 29th (b) 25th (c) 24th (d) 26th
  17. 17.What is the 20th term of the AP 7, 10, 13, 16, …? (a) 67 (b) 64 (c) 57 (d) 60
  18. 18.Which term of the AP 11, 18, 25, 32, … is 270? (a) 40th (b) 37th (c) 38th (d) 39th
  19. 19.What is the 30th term of the AP 20, 28, 36, 44, …? (a) 260 (b) 232 (c) 240 (d) 252
  20. 20.What is the 32nd term of the AP 10, 17, 24, 31, …? (a) 227 (b) 217 (c) 234 (d) 224
  21. 21.What is the sum of all the whole numbers from 1 to 91? (a) 8372 (b) 4187 (c) 4095 (d) 4186
  22. 22.What is the 40th term of the AP 1, 10, 19, 28, …? (a) 351 (b) 361 (c) 360 (d) 352
  23. 23.What is the 13th term of the AP 18, 21, 24, 27, …? (a) 57 (b) 54 (c) 36 (d) 39
  24. 24.What is the missing term in the AP 20, 22, ?, 26, 28? (a) 25 (b) 26 (c) 23 (d) 24
  25. 25.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 594 (b) 297 (c) 52 (d) 302
  26. 26.What is the missing term in the AP 20, 25, ?, 35, 40? (a) 35 (b) 31 (c) 29 (d) 30
  27. 27.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 6 (b) 7 (c) 5 (d) 10
  28. 28.What is the sum of all the whole numbers from 1 to 37? (a) 1406 (b) 666 (c) 704 (d) 703
  29. 29.Which term of the AP 15, 22, 29, 36, … is 134? (a) 19th (b) 18th (c) 20th (d) 17th
  30. 30.What is the sum of all the whole numbers from 1 to 72? (a) 5256 (b) 2556 (c) 2592 (d) 2628
  31. 31.What is the sum of the first 9 terms of the AP 5, 10, 15, …? (a) 450 (b) 230 (c) 225 (d) 45
  32. 32.What is the 23rd term of the AP 1, 3, 5, 7, …? (a) 47 (b) 44 (c) 46 (d) 45
  33. 33.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 66 (c) 78 (d) 156
  34. 34.What is the 17th term of the AP 20, 29, 38, 47, …? (a) 153 (b) 173 (c) 144 (d) 164
  35. 35.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 150 (b) 132 (c) 37 (d) 264
  36. 36.Which term of the AP 10, 12, 14, 16, … is 76? (a) 33rd (b) 38th (c) 35th (d) 34th
  37. 37.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 440 (b) 40 (c) 220 (d) 240
  38. 38.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 165 (b) 330 (c) 166 (d) 20
  39. 39.What is the missing term in the AP 19, ?, 29, 34, 39? (a) 25 (b) 29 (c) 24 (d) 23
  40. 40.What is the missing term in the AP 20, 26, 32, ?, 44? (a) 39 (b) 44 (c) 38 (d) 37

Answer key

  1. 37
  2. 31st
  3. 98
  4. 66
  5. 441
  6. 1485
  7. 124
  8. 78
  9. 780
  10. 129
  11. 102
  12. 82
  13. 99
  14. 51
  15. 40th
  16. 25th
  17. 64
  18. 38th
  19. 252
  20. 227
  21. 4186
  22. 352
  23. 54
  24. 24
  25. 297
  26. 30
  27. 6
  28. 703
  29. 18th
  30. 2628
  31. 225
  32. 45
  33. 78
  34. 164
  35. 132
  36. 34th
  37. 220
  38. 165
  39. 24
  40. 38

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad