← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 356 · 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 17, ?, 25, 29, 33? (a) 22 (b) 21 (c) 20 (d) 25
  2. 2.What is the 33rd term of the AP 19, 24, 29, 34, …? (a) 184 (b) 165 (c) 160 (d) 179
  3. 3.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 19 (b) 90 (c) 84 (d) 168
  4. 4.What is the sum of the first 11 terms of the AP 7, 11, 15, …? (a) 297 (b) 594 (c) 319 (d) 47
  5. 5.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 130 (b) 21 (c) 75 (d) 65
  6. 6.What is the 16th term of the AP 3, 12, 21, 30, …? (a) 135 (b) 138 (c) 147 (d) 144
  7. 7.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 61 (b) 14 (c) 60 (d) 120
  8. 8.What is the sum of the first 8 terms of the AP 6, 9, 12, …? (a) 264 (b) 144 (c) 132 (d) 27
  9. 9.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 133 (b) 119 (c) 238 (d) 29
  10. 10.What is the 40th term of the AP 9, 13, 17, 21, …? (a) 156 (b) 160 (c) 169 (d) 165
  11. 11.Which term of the AP 19, 28, 37, 46, … is 100? (a) 12th (b) 9th (c) 10th (d) 11th
  12. 12.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 124 (b) 32 (c) 119 (d) 238
  13. 13.What is the 15th term of the AP 18, 25, 32, 39, …? (a) 116 (b) 105 (c) 123 (d) 98
  14. 14.What is the 10th term of the AP 1, 8, 15, 22, …? (a) 64 (b) 63 (c) 70 (d) 71
  15. 15.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 25 (b) 105 (c) 182 (d) 91
  16. 16.What is the sum of all the whole numbers from 1 to 94? (a) 4371 (b) 8930 (c) 4418 (d) 4465
  17. 17.What is the 26th term of the AP 2, 7, 12, 17, …? (a) 130 (b) 127 (c) 132 (d) 125
  18. 18.What is the 15th term of the AP 20, 26, 32, 38, …? (a) 90 (b) 84 (c) 104 (d) 110
  19. 19.What is the 28th term of the AP 16, 21, 26, 31, …? (a) 156 (b) 140 (c) 151 (d) 135
  20. 20.What is the sum of the first 8 terms of the AP 4, 9, 14, …? (a) 39 (b) 192 (c) 344 (d) 172
  21. 21.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 121 (c) 21 (d) 66
  22. 22.What is the 26th term of the AP 6, 9, 12, 15, …? (a) 78 (b) 81 (c) 75 (d) 84
  23. 23.What is the sum of the first 11 terms of the AP 7, 10, 13, …? (a) 245 (b) 242 (c) 484 (d) 37
  24. 24.What is the sum of the first 9 terms of the AP 10, 15, 20, …? (a) 50 (b) 275 (c) 540 (d) 270
  25. 25.What is the 33rd term of the AP 13, 18, 23, 28, …? (a) 165 (b) 160 (c) 178 (d) 173
  26. 26.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 210 (c) 196 (d) 27
  27. 27.What is the sum of the first 5 terms of the AP 6, 9, 12, …? (a) 60 (b) 120 (c) 18 (d) 63
  28. 28.What is the missing term in the AP 4, 9, ?, 19, 24? (a) 14 (b) 15 (c) 13 (d) 19
  29. 29.What is the 13th term of the AP 2, 6, 10, 14, …? (a) 54 (b) 50 (c) 52 (d) 48
  30. 30.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 190 (c) 37 (d) 380
  31. 31.What is the 24th term of the AP 6, 8, 10, 12, …? (a) 48 (b) 46 (c) 52 (d) 54
  32. 32.What is the sum of all the whole numbers from 1 to 28? (a) 406 (b) 392 (c) 812 (d) 378
  33. 33.What is the 12th term of the AP 11, 20, 29, 38, …? (a) 110 (b) 119 (c) 108 (d) 99
  34. 34.What is the sum of all the whole numbers from 1 to 83? (a) 3403 (b) 6972 (c) 3486 (d) 3487
  35. 35.Which term of the AP 10, 16, 22, 28, … is 172? (a) 28th (b) 27th (c) 29th (d) 30th
  36. 36.What is the missing term in the AP 15, 20, 25, ?, 35? (a) 29 (b) 35 (c) 30 (d) 31
  37. 37.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 130 (b) 23 (c) 65 (d) 70
  38. 38.What is the sum of all the whole numbers from 1 to 76? (a) 5852 (b) 2888 (c) 2926 (d) 2850
  39. 39.What is the 34th term of the AP 17, 25, 33, 41, …? (a) 289 (b) 281 (c) 264 (d) 272
  40. 40.What is the 25th term of the AP 16, 21, 26, 31, …? (a) 136 (b) 125 (c) 141 (d) 120

Answer key

  1. 21
  2. 179
  3. 84
  4. 297
  5. 65
  6. 138
  7. 60
  8. 132
  9. 119
  10. 165
  11. 10th
  12. 119
  13. 116
  14. 64
  15. 91
  16. 4465
  17. 127
  18. 104
  19. 151
  20. 172
  21. 121
  22. 81
  23. 242
  24. 270
  25. 173
  26. 196
  27. 60
  28. 14
  29. 50
  30. 361
  31. 52
  32. 406
  33. 110
  34. 3486
  35. 28th
  36. 30
  37. 65
  38. 2926
  39. 281
  40. 136

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