← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 40 · 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, 17, 19, ?, 23? (a) 23 (b) 20 (c) 22 (d) 21
  2. 2.What is the missing term in the AP 17, 20, ?, 26, 29? (a) 23 (b) 24 (c) 26 (d) 22
  3. 3.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 300 (b) 600 (c) 330 (d) 57
  4. 4.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 91 (c) 105 (d) 210
  5. 5.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 4422 (c) 2145 (d) 2211
  6. 6.What is the 20th term of the AP 3, 10, 17, 24, …? (a) 136 (b) 140 (c) 143 (d) 133
  7. 7.What is the sum of all the whole numbers from 1 to 35? (a) 630 (b) 631 (c) 595 (d) 1260
  8. 8.What is the 20th term of the AP 11, 18, 25, 32, …? (a) 151 (b) 133 (c) 144 (d) 140
  9. 9.What is the 27th term of the AP 12, 17, 22, 27, …? (a) 135 (b) 147 (c) 130 (d) 142
  10. 10.What is the missing term in the AP 10, 19, 28, ?, 46? (a) 38 (b) 46 (c) 37 (d) 36
  11. 11.What is the sum of all the whole numbers from 1 to 39? (a) 780 (b) 781 (c) 1560 (d) 741
  12. 12.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 648 (c) 666 (d) 630
  13. 13.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 170 (b) 95 (c) 25 (d) 85
  14. 14.What is the 11th term of the AP 20, 27, 34, 41, …? (a) 70 (b) 77 (c) 97 (d) 90
  15. 15.What is the missing term in the AP 12, 14, 16, ?, 20? (a) 19 (b) 17 (c) 20 (d) 18
  16. 16.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 729 (b) 378 (c) 756 (d) 53
  17. 17.What is the sum of the first 6 terms of the AP 10, 16, 22, …? (a) 150 (b) 300 (c) 40 (d) 168
  18. 18.What is the missing term in the AP 6, 13, 20, ?, 34? (a) 34 (b) 27 (c) 28 (d) 26
  19. 19.What is the sum of the first 9 terms of the AP 6, 10, 14, …? (a) 38 (b) 198 (c) 216 (d) 396
  20. 20.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 168 (b) 19 (c) 90 (d) 84
  21. 21.What is the sum of all the whole numbers from 1 to 84? (a) 7140 (b) 3486 (c) 3570 (d) 3528
  22. 22.What is the missing term in the AP 1, 3, 5, ?, 9? (a) 9 (b) 8 (c) 7 (d) 6
  23. 23.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 210 (b) 105 (c) 24 (d) 108
  24. 24.What is the missing term in the AP 13, ?, 19, 22, 25? (a) 16 (b) 15 (c) 19 (d) 17
  25. 25.What is the sum of all the whole numbers from 1 to 47? (a) 1081 (b) 1129 (c) 2256 (d) 1128
  26. 26.What is the missing term in the AP 4, 11, 18, ?, 32? (a) 25 (b) 26 (c) 24 (d) 32
  27. 27.What is the 13th term of the AP 5, 8, 11, 14, …? (a) 44 (b) 39 (c) 36 (d) 41
  28. 28.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 380 (c) 361 (d) 190
  29. 29.Which term of the AP 2, 4, 6, 8, … is 16? (a) 9th (b) 8th (c) 10th (d) 7th
  30. 30.What is the missing term in the AP 17, 21, 25, ?, 33? (a) 29 (b) 33 (c) 28 (d) 30
  31. 31.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 342 (c) 171 (d) 324
  32. 32.What is the 35th term of the AP 4, 11, 18, 25, …? (a) 242 (b) 249 (c) 238 (d) 245
  33. 33.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 304 (b) 33 (c) 152 (d) 168
  34. 34.What is the sum of all the whole numbers from 1 to 28? (a) 378 (b) 392 (c) 406 (d) 812
  35. 35.What is the missing term in the AP 10, 18, ?, 34, 42? (a) 34 (b) 27 (c) 25 (d) 26
  36. 36.What is the 21st term of the AP 17, 22, 27, 32, …? (a) 122 (b) 100 (c) 105 (d) 117
  37. 37.What is the 34th term of the AP 17, 20, 23, 26, …? (a) 102 (b) 99 (c) 116 (d) 119
  38. 38.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 96 (b) 192 (c) 19 (d) 104
  39. 39.What is the missing term in the AP 4, 10, 16, ?, 28? (a) 23 (b) 21 (c) 28 (d) 22
  40. 40.What is the missing term in the AP 3, ?, 11, 15, 19? (a) 11 (b) 8 (c) 6 (d) 7

Answer key

  1. 21
  2. 23
  3. 300
  4. 105
  5. 2211
  6. 136
  7. 630
  8. 144
  9. 142
  10. 37
  11. 780
  12. 666
  13. 85
  14. 90
  15. 18
  16. 729
  17. 150
  18. 27
  19. 198
  20. 84
  21. 3570
  22. 7
  23. 105
  24. 16
  25. 1128
  26. 25
  27. 41
  28. 361
  29. 8th
  30. 29
  31. 324
  32. 242
  33. 152
  34. 406
  35. 26
  36. 117
  37. 116
  38. 96
  39. 22
  40. 7

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