← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 133 · 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 all the whole numbers from 1 to 11? (a) 66 (b) 132 (c) 67 (d) 55
  2. 2.What is the 36th term of the AP 18, 23, 28, 33, …? (a) 180 (b) 198 (c) 175 (d) 193
  3. 3.What is the missing term in the AP 17, 19, ?, 23, 25? (a) 22 (b) 20 (c) 23 (d) 21
  4. 4.What is the 27th term of the AP 12, 14, 16, 18, …? (a) 52 (b) 54 (c) 66 (d) 64
  5. 5.What is the sum of the first 7 terms of the AP 6, 8, 10, …? (a) 18 (b) 84 (c) 168 (d) 91
  6. 6.What is the 10th term of the AP 2, 9, 16, 23, …? (a) 70 (b) 65 (c) 72 (d) 63
  7. 7.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 53 (c) 756 (d) 378
  8. 8.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 41 (b) 10 (c) 80 (d) 40
  9. 9.What is the 23rd term of the AP 2, 8, 14, 20, …? (a) 134 (b) 140 (c) 132 (d) 138
  10. 10.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 520 (b) 44 (c) 280 (d) 260
  11. 11.Which term of the AP 2, 4, 6, 8, … is 28? (a) 15th (b) 14th (c) 13th (d) 16th
  12. 12.What is the 22nd term of the AP 6, 10, 14, 18, …? (a) 90 (b) 84 (c) 88 (d) 94
  13. 13.What is the sum of the first 10 terms of the AP 5, 6, 7, …? (a) 100 (b) 190 (c) 95 (d) 14
  14. 14.What is the missing term in the AP 18, 24, ?, 36, 42? (a) 29 (b) 30 (c) 36 (d) 31
  15. 15.What is the 23rd term of the AP 13, 19, 25, 31, …? (a) 138 (b) 151 (c) 132 (d) 145
  16. 16.What is the sum of the first 8 terms of the AP 4, 8, 12, …? (a) 32 (b) 160 (c) 288 (d) 144
  17. 17.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 240 (c) 120 (d) 225
  18. 18.What is the 36th term of the AP 4, 12, 20, 28, …? (a) 280 (b) 288 (c) 284 (d) 292
  19. 19.What is the 10th term of the AP 8, 11, 14, 17, …? (a) 35 (b) 38 (c) 30 (d) 27
  20. 20.Which term of the AP 12, 21, 30, 39, … is 318? (a) 34th (b) 37th (c) 35th (d) 36th
  21. 21.What is the 25th term of the AP 2, 11, 20, 29, …? (a) 218 (b) 225 (c) 216 (d) 227
  22. 22.What is the missing term in the AP 11, ?, 27, 35, 43? (a) 20 (b) 18 (c) 27 (d) 19
  23. 23.What is the missing term in the AP 9, 14, ?, 24, 29? (a) 19 (b) 24 (c) 18 (d) 20
  24. 24.What is the 26th term of the AP 3, 7, 11, 15, …? (a) 107 (b) 103 (c) 100 (d) 104
  25. 25.What is the 22nd term of the AP 14, 23, 32, 41, …? (a) 189 (b) 198 (c) 212 (d) 203
  26. 26.What is the 13th term of the AP 16, 20, 24, 28, …? (a) 48 (b) 52 (c) 68 (d) 64
  27. 27.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 14 (b) 61 (c) 60 (d) 120
  28. 28.What is the sum of the first 7 terms of the AP 1, 3, 5, …? (a) 56 (b) 13 (c) 49 (d) 98
  29. 29.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 272 (d) 256
  30. 30.Which term of the AP 10, 14, 18, 22, … is 134? (a) 32nd (b) 33rd (c) 31st (d) 34th
  31. 31.What is the 15th term of the AP 4, 10, 16, 22, …? (a) 94 (b) 88 (c) 90 (d) 84
  32. 32.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 702 (d) 676
  33. 33.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 37 (c) 361 (d) 190
  34. 34.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 90 (b) 180 (c) 96 (d) 13
  35. 35.What is the 12th term of the AP 18, 27, 36, 45, …? (a) 108 (b) 117 (c) 126 (d) 99
  36. 36.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 99 (b) 114 (c) 29 (d) 198
  37. 37.Which term of the AP 9, 14, 19, 24, … is 154? (a) 30th (b) 29th (c) 31st (d) 32nd
  38. 38.What is the 11th term of the AP 3, 6, 9, 12, …? (a) 30 (b) 36 (c) 34 (d) 33
  39. 39.What is the sum of all the whole numbers from 1 to 12? (a) 72 (b) 66 (c) 78 (d) 156
  40. 40.What is the 14th term of the AP 6, 12, 18, 24, …? (a) 84 (b) 78 (c) 90 (d) 85

Answer key

  1. 66
  2. 193
  3. 21
  4. 64
  5. 84
  6. 65
  7. 729
  8. 40
  9. 134
  10. 260
  11. 14th
  12. 90
  13. 95
  14. 30
  15. 145
  16. 144
  17. 225
  18. 284
  19. 35
  20. 35th
  21. 218
  22. 19
  23. 19
  24. 103
  25. 203
  26. 64
  27. 60
  28. 49
  29. 256
  30. 32nd
  31. 88
  32. 676
  33. 361
  34. 90
  35. 117
  36. 99
  37. 30th
  38. 33
  39. 78
  40. 84

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