← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 97 · 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.Which term of the AP 2, 10, 18, 26, … is 106? (a) 14th (b) 13th (c) 16th (d) 15th
  2. 2.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 385 (b) 62 (c) 704 (d) 352
  3. 3.Which term of the AP 12, 14, 16, 18, … is 38? (a) 19th (b) 14th (c) 15th (d) 13th
  4. 4.What is the missing term in the AP 15, 18, 21, ?, 27? (a) 24 (b) 25 (c) 27 (d) 23
  5. 5.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 552 (c) 276 (d) 45
  6. 6.What is the sum of all the whole numbers from 1 to 62? (a) 3906 (b) 1891 (c) 1922 (d) 1953
  7. 7.What is the 10th term of the AP 1, 6, 11, 16, …? (a) 45 (b) 46 (c) 50 (d) 51
  8. 8.What is the 30th term of the AP 6, 8, 10, 12, …? (a) 58 (b) 66 (c) 60 (d) 64
  9. 9.What is the 32nd term of the AP 13, 22, 31, 40, …? (a) 301 (b) 288 (c) 279 (d) 292
  10. 10.What is the missing term in the AP 8, 13, ?, 23, 28? (a) 17 (b) 19 (c) 23 (d) 18
  11. 11.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 465 (c) 59 (d) 900
  12. 12.What is the 19th term of the AP 17, 21, 25, 29, …? (a) 93 (b) 72 (c) 89 (d) 76
  13. 13.What is the sum of the first 12 terms of the AP 8, 13, 18, …? (a) 852 (b) 456 (c) 63 (d) 426
  14. 14.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 140 (b) 71 (c) 70 (d) 13
  15. 15.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 169 (c) 182 (d) 91
  16. 16.What is the missing term in the AP 18, 21, ?, 27, 30? (a) 24 (b) 23 (c) 27 (d) 25
  17. 17.What is the sum of the first 9 terms of the AP 6, 12, 18, …? (a) 270 (b) 54 (c) 297 (d) 540
  18. 18.What is the 30th term of the AP 17, 23, 29, 35, …? (a) 191 (b) 174 (c) 197 (d) 180
  19. 19.What is the sum of all the whole numbers from 1 to 82? (a) 3321 (b) 6806 (c) 3362 (d) 3403
  20. 20.What is the 38th term of the AP 8, 11, 14, 17, …? (a) 122 (b) 119 (c) 111 (d) 114
  21. 21.What is the 23rd term of the AP 20, 24, 28, 32, …? (a) 88 (b) 108 (c) 112 (d) 92
  22. 22.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 11 (d) 36
  23. 23.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 28 (b) 95 (c) 160 (d) 80
  24. 24.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 406 (c) 812 (d) 784
  25. 25.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 14 (b) 180 (c) 91 (d) 90
  26. 26.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 256 (b) 30 (c) 128 (d) 144
  27. 27.What is the 32nd term of the AP 20, 25, 30, 35, …? (a) 155 (b) 160 (c) 180 (d) 175
  28. 28.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 870 (c) 435 (d) 57
  29. 29.Which term of the AP 14, 17, 20, 23, … is 98? (a) 29th (b) 28th (c) 30th (d) 31st
  30. 30.What is the missing term in the AP 14, 18, 22, ?, 30? (a) 26 (b) 30 (c) 25 (d) 27
  31. 31.What is the 35th term of the AP 12, 20, 28, 36, …? (a) 272 (b) 280 (c) 292 (d) 284
  32. 32.What is the 21st term of the AP 1, 9, 17, 25, …? (a) 160 (b) 161 (c) 168 (d) 169
  33. 33.What is the 32nd term of the AP 7, 13, 19, 25, …? (a) 199 (b) 186 (c) 192 (d) 193
  34. 34.What is the 13th term of the AP 2, 7, 12, 17, …? (a) 62 (b) 67 (c) 60 (d) 65
  35. 35.What is the sum of the first 7 terms of the AP 6, 11, 16, …? (a) 147 (b) 36 (c) 152 (d) 294
  36. 36.What is the 14th term of the AP 20, 23, 26, 29, …? (a) 39 (b) 62 (c) 42 (d) 59
  37. 37.What is the 26th term of the AP 16, 25, 34, 43, …? (a) 234 (b) 250 (c) 241 (d) 225
  38. 38.What is the sum of the first 10 terms of the AP 3, 5, 7, …? (a) 120 (b) 21 (c) 240 (d) 130
  39. 39.Which term of the AP 20, 25, 30, 35, … is 200? (a) 36th (b) 37th (c) 40th (d) 38th
  40. 40.What is the 20th term of the AP 10, 15, 20, 25, …? (a) 95 (b) 110 (c) 105 (d) 100

Answer key

  1. 14th
  2. 352
  3. 14th
  4. 24
  5. 529
  6. 1953
  7. 46
  8. 64
  9. 292
  10. 18
  11. 900
  12. 89
  13. 426
  14. 70
  15. 169
  16. 24
  17. 270
  18. 191
  19. 3403
  20. 119
  21. 108
  22. 36
  23. 80
  24. 784
  25. 90
  26. 128
  27. 175
  28. 841
  29. 29th
  30. 26
  31. 284
  32. 161
  33. 193
  34. 62
  35. 147
  36. 59
  37. 241
  38. 120
  39. 37th
  40. 105

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