← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 443 · 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 the first 6 terms of the AP 2, 4, 6, …? (a) 12 (b) 48 (c) 42 (d) 84
  2. 2.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 625 (c) 650 (d) 325
  3. 3.What is the 22nd term of the AP 20, 26, 32, 38, …? (a) 132 (b) 126 (c) 146 (d) 152
  4. 4.Which term of the AP 10, 13, 16, 19, … is 55? (a) 15th (b) 16th (c) 17th (d) 18th
  5. 5.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 21 (d) 121
  6. 6.What is the missing term in the AP 20, 26, 32, ?, 44? (a) 38 (b) 37 (c) 39 (d) 44
  7. 7.What is the missing term in the AP 3, ?, 17, 24, 31? (a) 9 (b) 17 (c) 11 (d) 10
  8. 8.What is the 12th term of the AP 11, 15, 19, 23, …? (a) 55 (b) 44 (c) 48 (d) 59
  9. 9.Which term of the AP 1, 5, 9, 13, … is 113? (a) 28th (b) 29th (c) 30th (d) 31st
  10. 10.Which term of the AP 10, 19, 28, 37, … is 316? (a) 35th (b) 34th (c) 36th (d) 37th
  11. 11.What is the 37th term of the AP 20, 29, 38, 47, …? (a) 353 (b) 324 (c) 344 (d) 333
  12. 12.What is the missing term in the AP 15, 18, ?, 24, 27? (a) 22 (b) 20 (c) 24 (d) 21
  13. 13.What is the 22nd term of the AP 4, 10, 16, 22, …? (a) 126 (b) 130 (c) 132 (d) 136
  14. 14.What is the 13th term of the AP 1, 9, 17, 25, …? (a) 96 (b) 104 (c) 105 (d) 97
  15. 15.What is the sum of the first 5 terms of the AP 4, 8, 12, …? (a) 60 (b) 120 (c) 70 (d) 20
  16. 16.What is the missing term in the AP 8, 17, 26, ?, 44? (a) 34 (b) 36 (c) 44 (d) 35
  17. 17.What is the 14th term of the AP 6, 11, 16, 21, …? (a) 76 (b) 71 (c) 70 (d) 65
  18. 18.Which term of the AP 2, 11, 20, 29, … is 335? (a) 38th (b) 37th (c) 39th (d) 40th
  19. 19.What is the sum of the first 11 terms of the AP 3, 9, 15, …? (a) 63 (b) 363 (c) 396 (d) 726
  20. 20.What is the sum of the first 6 terms of the AP 10, 15, 20, …? (a) 35 (b) 270 (c) 150 (d) 135
  21. 21.What is the missing term in the AP 18, 27, 36, ?, 54? (a) 54 (b) 46 (c) 44 (d) 45
  22. 22.What is the 24th term of the AP 9, 15, 21, 27, …? (a) 147 (b) 138 (c) 153 (d) 144
  23. 23.What is the sum of the first 8 terms of the AP 7, 8, 9, …? (a) 84 (b) 168 (c) 14 (d) 88
  24. 24.What is the missing term in the AP 16, 24, ?, 40, 48? (a) 33 (b) 32 (c) 31 (d) 40
  25. 25.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 21 (d) 42
  26. 26.Which term of the AP 14, 21, 28, 35, … is 287? (a) 41st (b) 39th (c) 42nd (d) 40th
  27. 27.What is the 29th term of the AP 17, 25, 33, 41, …? (a) 232 (b) 249 (c) 224 (d) 241
  28. 28.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 30 (d) 15
  29. 29.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 105 (b) 210 (c) 119 (d) 27
  30. 30.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 324 (c) 171 (d) 35
  31. 31.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 138 (b) 246 (c) 33 (d) 123
  32. 32.Which term of the AP 14, 20, 26, 32, … is 146? (a) 23rd (b) 25th (c) 22nd (d) 24th
  33. 33.What is the sum of all the whole numbers from 1 to 43? (a) 946 (b) 903 (c) 947 (d) 1892
  34. 34.What is the sum of the first 10 terms of the AP 8, 13, 18, …? (a) 330 (b) 610 (c) 305 (d) 53
  35. 35.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 48 (b) 44 (c) 9 (d) 88
  36. 36.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 4 (b) 5 (c) 3 (d) 6
  37. 37.Which term of the AP 15, 20, 25, 30, … is 90? (a) 15th (b) 16th (c) 17th (d) 18th
  38. 38.What is the sum of the first 7 terms of the AP 4, 8, 12, …? (a) 126 (b) 112 (c) 224 (d) 28
  39. 39.What is the missing term in the AP 1, 4, 7, ?, 13? (a) 10 (b) 9 (c) 13 (d) 11
  40. 40.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 36 (c) 64 (d) 15

Answer key

  1. 42
  2. 625
  3. 146
  4. 16th
  5. 121
  6. 38
  7. 10
  8. 55
  9. 29th
  10. 35th
  11. 344
  12. 21
  13. 130
  14. 97
  15. 60
  16. 35
  17. 71
  18. 38th
  19. 363
  20. 135
  21. 45
  22. 147
  23. 84
  24. 32
  25. 36
  26. 40th
  27. 241
  28. 25
  29. 105
  30. 324
  31. 123
  32. 23rd
  33. 946
  34. 305
  35. 44
  36. 4
  37. 16th
  38. 112
  39. 10
  40. 64

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