← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 929 · 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 missing term in the AP 15, ?, 27, 33, 39? (a) 21 (b) 20 (c) 27 (d) 22
  2. 2.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 152 (b) 168 (c) 304 (d) 33
  3. 3.What is the 33rd term of the AP 6, 10, 14, 18, …? (a) 138 (b) 128 (c) 132 (d) 134
  4. 4.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 400 (d) 420
  5. 5.What is the sum of all the whole numbers from 1 to 57? (a) 1653 (b) 3306 (c) 1596 (d) 1654
  6. 6.What is the 12th term of the AP 1, 6, 11, 16, …? (a) 61 (b) 56 (c) 60 (d) 55
  7. 7.Which term of the AP 4, 12, 20, 28, … is 292? (a) 39th (b) 36th (c) 37th (d) 38th
  8. 8.What is the 10th term of the AP 16, 25, 34, 43, …? (a) 97 (b) 81 (c) 90 (d) 106
  9. 9.What is the 35th term of the AP 19, 22, 25, 28, …? (a) 105 (b) 124 (c) 102 (d) 121
  10. 10.What is the sum of all the whole numbers from 1 to 98? (a) 4851 (b) 9702 (c) 4802 (d) 4753
  11. 11.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 36 (c) 11 (d) 42
  12. 12.What is the 28th term of the AP 1, 5, 9, 13, …? (a) 108 (b) 113 (c) 112 (d) 109
  13. 13.What is the sum of the first 12 terms of the AP 5, 6, 7, …? (a) 132 (b) 126 (c) 16 (d) 252
  14. 14.Which term of the AP 19, 24, 29, 34, … is 84? (a) 16th (b) 14th (c) 13th (d) 15th
  15. 15.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 56 (d) 28
  16. 16.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 44 (b) 88 (c) 48 (d) 9
  17. 17.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 27 (b) 270 (c) 138 (d) 135
  18. 18.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 78 (c) 91 (d) 92
  19. 19.Which term of the AP 4, 11, 18, 25, … is 214? (a) 32nd (b) 33rd (c) 30th (d) 31st
  20. 20.What is the 30th term of the AP 8, 12, 16, 20, …? (a) 116 (b) 120 (c) 124 (d) 128
  21. 21.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 23 (c) 78 (d) 156
  22. 22.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 192 (b) 96 (c) 114 (d) 31
  23. 23.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 277 (c) 276 (d) 253
  24. 24.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 280 (b) 520 (c) 260 (d) 44
  25. 25.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 44 (b) 182 (c) 203 (d) 364
  26. 26.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 160 (b) 170 (c) 320 (d) 25
  27. 27.What is the 16th term of the AP 17, 21, 25, 29, …? (a) 81 (b) 64 (c) 77 (d) 60
  28. 28.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 160 (b) 150 (c) 24 (d) 300
  29. 29.What is the missing term in the AP 12, 21, 30, ?, 48? (a) 40 (b) 48 (c) 39 (d) 38
  30. 30.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 176 (b) 179 (c) 352 (d) 31
  31. 31.Which term of the AP 12, 17, 22, 27, … is 132? (a) 25th (b) 26th (c) 27th (d) 24th
  32. 32.What is the 11th term of the AP 9, 12, 15, 18, …? (a) 33 (b) 30 (c) 42 (d) 39
  33. 33.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 100 (d) 55
  34. 34.What is the sum of the first 6 terms of the AP 6, 12, 18, …? (a) 36 (b) 252 (c) 144 (d) 126
  35. 35.What is the 35th term of the AP 3, 6, 9, 12, …? (a) 102 (b) 108 (c) 106 (d) 105
  36. 36.What is the 10th term of the AP 16, 23, 30, 37, …? (a) 79 (b) 70 (c) 63 (d) 86
  37. 37.Which term of the AP 16, 20, 24, 28, … is 64? (a) 12th (b) 13th (c) 14th (d) 16th
  38. 38.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 42 (b) 84 (c) 12 (d) 48
  39. 39.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 300 (c) 600 (d) 47
  40. 40.What is the sum of all the whole numbers from 1 to 56? (a) 3192 (b) 1540 (c) 1596 (d) 1568

Answer key

  1. 21
  2. 152
  3. 134
  4. 400
  5. 1653
  6. 56
  7. 37th
  8. 97
  9. 121
  10. 4851
  11. 36
  12. 109
  13. 126
  14. 14th
  15. 49
  16. 44
  17. 135
  18. 91
  19. 31st
  20. 124
  21. 144
  22. 96
  23. 276
  24. 260
  25. 182
  26. 160
  27. 77
  28. 150
  29. 39
  30. 176
  31. 25th
  32. 39
  33. 100
  34. 126
  35. 105
  36. 79
  37. 13th
  38. 42
  39. 576
  40. 1596

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