← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 103 · 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 5 terms of the AP 8, 10, 12, …? (a) 60 (b) 120 (c) 65 (d) 16
  2. 2.What is the 31st term of the AP 4, 8, 12, 16, …? (a) 125 (b) 128 (c) 124 (d) 120
  3. 3.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 31 (b) 8 (c) 30 (d) 60
  4. 4.What is the 40th term of the AP 17, 21, 25, 29, …? (a) 160 (b) 177 (c) 156 (d) 173
  5. 5.What is the 11th term of the AP 4, 11, 18, 25, …? (a) 77 (b) 81 (c) 74 (d) 70
  6. 6.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 456 (b) 68 (c) 420 (d) 840
  7. 7.What is the missing term in the AP 7, 10, 13, ?, 19? (a) 15 (b) 17 (c) 19 (d) 16
  8. 8.What is the sum of all the whole numbers from 1 to 81? (a) 6642 (b) 3321 (c) 3322 (d) 3240
  9. 9.What is the 27th term of the AP 4, 12, 20, 28, …? (a) 216 (b) 212 (c) 208 (d) 220
  10. 10.What is the 10th term of the AP 11, 15, 19, 23, …? (a) 51 (b) 36 (c) 47 (d) 40
  11. 11.What is the missing term in the AP 15, 18, 21, ?, 27? (a) 24 (b) 27 (c) 23 (d) 25
  12. 12.What is the missing term in the AP 13, ?, 23, 28, 33? (a) 17 (b) 19 (c) 18 (d) 23
  13. 13.What is the sum of the first 10 terms of the AP 6, 7, 8, …? (a) 15 (b) 105 (c) 210 (d) 110
  14. 14.What is the sum of the first 6 terms of the AP 1, 4, 7, …? (a) 102 (b) 60 (c) 16 (d) 51
  15. 15.What is the sum of all the whole numbers from 1 to 11? (a) 55 (b) 66 (c) 67 (d) 132
  16. 16.What is the 40th term of the AP 7, 13, 19, 25, …? (a) 247 (b) 240 (c) 234 (d) 241
  17. 17.What is the sum of all the whole numbers from 1 to 84? (a) 3528 (b) 3570 (c) 7140 (d) 3486
  18. 18.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 35 (c) 324 (d) 171
  19. 19.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 16 (b) 72 (c) 144 (d) 80
  20. 20.What is the sum of all the whole numbers from 1 to 94? (a) 4418 (b) 4371 (c) 8930 (d) 4465
  21. 21.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 98 (b) 196 (c) 20 (d) 105
  22. 22.What is the sum of all the whole numbers from 1 to 100? (a) 10100 (b) 4950 (c) 5050 (d) 5000
  23. 23.What is the sum of all the whole numbers from 1 to 16? (a) 128 (b) 272 (c) 120 (d) 136
  24. 24.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 114 (b) 228 (c) 132 (d) 34
  25. 25.What is the missing term in the AP 17, ?, 31, 38, 45? (a) 23 (b) 25 (c) 24 (d) 31
  26. 26.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 406 (c) 55 (d) 812
  27. 27.What is the 18th term of the AP 1, 3, 5, 7, …? (a) 35 (b) 36 (c) 34 (d) 37
  28. 28.What is the 24th term of the AP 19, 22, 25, 28, …? (a) 91 (b) 72 (c) 69 (d) 88
  29. 29.What is the 39th term of the AP 1, 7, 13, 19, …? (a) 234 (b) 228 (c) 235 (d) 229
  30. 30.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 291 (b) 51 (c) 572 (d) 286
  31. 31.Which term of the AP 16, 19, 22, 25, … is 82? (a) 22nd (b) 25th (c) 23rd (d) 24th
  32. 32.What is the sum of all the whole numbers from 1 to 61? (a) 1891 (b) 3782 (c) 1830 (d) 1892
  33. 33.What is the 20th term of the AP 19, 21, 23, 25, …? (a) 38 (b) 57 (c) 40 (d) 59
  34. 34.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 24 (b) 75 (c) 140 (d) 70
  35. 35.What is the sum of all the whole numbers from 1 to 68? (a) 2346 (b) 2278 (c) 4692 (d) 2312
  36. 36.What is the missing term in the AP 13, 16, 19, ?, 25? (a) 21 (b) 23 (c) 25 (d) 22
  37. 37.What is the sum of all the whole numbers from 1 to 95? (a) 4465 (b) 4561 (c) 4560 (d) 9120
  38. 38.What is the 29th term of the AP 4, 11, 18, 25, …? (a) 196 (b) 200 (c) 207 (d) 203
  39. 39.Which term of the AP 3, 5, 7, 9, … is 57? (a) 28th (b) 30th (c) 27th (d) 29th
  40. 40.Which term of the AP 18, 23, 28, 33, … is 213? (a) 42nd (b) 40th (c) 39th (d) 41st

Answer key

  1. 60
  2. 124
  3. 30
  4. 173
  5. 74
  6. 420
  7. 16
  8. 3321
  9. 212
  10. 47
  11. 24
  12. 18
  13. 105
  14. 51
  15. 66
  16. 241
  17. 3570
  18. 324
  19. 72
  20. 4465
  21. 98
  22. 5050
  23. 136
  24. 114
  25. 24
  26. 784
  27. 35
  28. 88
  29. 229
  30. 286
  31. 23rd
  32. 1891
  33. 57
  34. 70
  35. 2346
  36. 22
  37. 4560
  38. 200
  39. 28th
  40. 40th

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