← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 605 · 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 6, ?, 18, 24, 30? (a) 18 (b) 11 (c) 13 (d) 12
  2. 2.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 380 (c) 361 (d) 190
  3. 3.What is the missing term in the AP 8, 15, ?, 29, 36? (a) 21 (b) 23 (c) 22 (d) 29
  4. 4.What is the sum of all the whole numbers from 1 to 40? (a) 800 (b) 1640 (c) 820 (d) 780
  5. 5.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 32 (b) 374 (c) 187 (d) 190
  6. 6.What is the 20th term of the AP 10, 12, 14, 16, …? (a) 38 (b) 50 (c) 48 (d) 40
  7. 7.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 81 (c) 90 (d) 45
  8. 8.What is the sum of the first 8 terms of the AP 9, 15, 21, …? (a) 240 (b) 51 (c) 264 (d) 480
  9. 9.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 261 (b) 49 (c) 522 (d) 266
  10. 10.What is the 25th term of the AP 7, 16, 25, 34, …? (a) 225 (b) 216 (c) 232 (d) 223
  11. 11.What is the sum of all the whole numbers from 1 to 77? (a) 6006 (b) 3004 (c) 2926 (d) 3003
  12. 12.What is the sum of all the whole numbers from 1 to 43? (a) 947 (b) 1892 (c) 946 (d) 903
  13. 13.What is the 29th term of the AP 13, 17, 21, 25, …? (a) 129 (b) 125 (c) 116 (d) 112
  14. 14.What is the sum of the first 11 terms of the AP 7, 10, 13, …? (a) 484 (b) 37 (c) 242 (d) 245
  15. 15.Which term of the AP 3, 5, 7, 9, … is 17? (a) 9th (b) 8th (c) 7th (d) 10th
  16. 16.What is the 35th term of the AP 20, 23, 26, 29, …? (a) 122 (b) 102 (c) 125 (d) 105
  17. 17.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 435 (c) 841 (d) 57
  18. 18.Which term of the AP 5, 7, 9, 11, … is 19? (a) 8th (b) 10th (c) 9th (d) 7th
  19. 19.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 36 (b) 450 (c) 225 (d) 240
  20. 20.What is the missing term in the AP 16, ?, 32, 40, 48? (a) 25 (b) 24 (c) 32 (d) 23
  21. 21.What is the missing term in the AP 7, ?, 25, 34, 43? (a) 16 (b) 17 (c) 15 (d) 25
  22. 22.What is the missing term in the AP 15, 17, ?, 21, 23? (a) 18 (b) 20 (c) 19 (d) 21
  23. 23.What is the 14th term of the AP 13, 15, 17, 19, …? (a) 28 (b) 41 (c) 39 (d) 26
  24. 24.What is the 25th term of the AP 19, 21, 23, 25, …? (a) 69 (b) 48 (c) 67 (d) 50
  25. 25.What is the 40th term of the AP 14, 23, 32, 41, …? (a) 351 (b) 374 (c) 360 (d) 365
  26. 26.What is the 38th term of the AP 15, 21, 27, 33, …? (a) 237 (b) 228 (c) 222 (d) 243
  27. 27.What is the sum of the first 11 terms of the AP 6, 7, 8, …? (a) 122 (b) 242 (c) 16 (d) 121
  28. 28.Which term of the AP 17, 26, 35, 44, … is 215? (a) 23rd (b) 22nd (c) 24th (d) 25th
  29. 29.What is the missing term in the AP 11, 14, ?, 20, 23? (a) 20 (b) 16 (c) 17 (d) 18
  30. 30.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 600 (b) 300 (c) 57 (d) 330
  31. 31.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 11 (b) 13 (c) 15 (d) 12
  32. 32.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 80 (b) 40 (c) 43 (d) 14
  33. 33.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 115 (b) 100 (c) 200 (d) 32
  34. 34.What is the 21st term of the AP 5, 7, 9, 11, …? (a) 45 (b) 42 (c) 47 (d) 40
  35. 35.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 225 (d) 240
  36. 36.What is the missing term in the AP 13, 16, 19, ?, 25? (a) 23 (b) 25 (c) 21 (d) 22
  37. 37.What is the 17th term of the AP 11, 17, 23, 29, …? (a) 113 (b) 96 (c) 107 (d) 102
  38. 38.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 21 (b) 105 (c) 210 (d) 112
  39. 39.What is the 13th term of the AP 12, 16, 20, 24, …? (a) 64 (b) 60 (c) 52 (d) 48
  40. 40.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 504 (b) 1008 (c) 75 (d) 540

Answer key

  1. 12
  2. 361
  3. 22
  4. 820
  5. 187
  6. 48
  7. 81
  8. 240
  9. 261
  10. 223
  11. 3003
  12. 946
  13. 125
  14. 242
  15. 8th
  16. 122
  17. 841
  18. 8th
  19. 225
  20. 24
  21. 16
  22. 19
  23. 39
  24. 67
  25. 365
  26. 237
  27. 121
  28. 23rd
  29. 17
  30. 300
  31. 12
  32. 40
  33. 100
  34. 45
  35. 225
  36. 22
  37. 107
  38. 105
  39. 60
  40. 504

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