← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 918 · 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 all the whole numbers from 1 to 31? (a) 497 (b) 992 (c) 465 (d) 496
  2. 2.What is the sum of all the whole numbers from 1 to 64? (a) 2016 (b) 2048 (c) 2080 (d) 4160
  3. 3.What is the missing term in the AP 19, ?, 33, 40, 47? (a) 25 (b) 26 (c) 33 (d) 27
  4. 4.What is the sum of all the whole numbers from 1 to 49? (a) 1225 (b) 2450 (c) 1226 (d) 1176
  5. 5.What is the 10th term of the AP 15, 23, 31, 39, …? (a) 80 (b) 72 (c) 95 (d) 87
  6. 6.What is the 32nd term of the AP 17, 23, 29, 35, …? (a) 203 (b) 192 (c) 209 (d) 186
  7. 7.What is the 15th term of the AP 8, 17, 26, 35, …? (a) 134 (b) 135 (c) 143 (d) 126
  8. 8.What is the sum of all the whole numbers from 1 to 22? (a) 506 (b) 231 (c) 253 (d) 242
  9. 9.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 42 (b) 264 (c) 242 (d) 484
  10. 10.What is the sum of all the whole numbers from 1 to 63? (a) 2016 (b) 2017 (c) 4032 (d) 1953
  11. 11.What is the 27th term of the AP 15, 19, 23, 27, …? (a) 108 (b) 119 (c) 123 (d) 104
  12. 12.What is the missing term in the AP 20, 25, ?, 35, 40? (a) 35 (b) 31 (c) 29 (d) 30
  13. 13.What is the missing term in the AP 5, ?, 19, 26, 33? (a) 13 (b) 12 (c) 11 (d) 19
  14. 14.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 726 (b) 58 (c) 368 (d) 363
  15. 15.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 5 (b) 3 (c) 4 (d) 7
  16. 16.What is the missing term in the AP 17, 19, 21, ?, 25? (a) 25 (b) 24 (c) 22 (d) 23
  17. 17.Which term of the AP 13, 21, 29, 37, … is 165? (a) 22nd (b) 21st (c) 20th (d) 19th
  18. 18.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 119 (b) 32 (c) 238 (d) 124
  19. 19.What is the missing term in the AP 4, 7, ?, 13, 16? (a) 10 (b) 13 (c) 9 (d) 11
  20. 20.Which term of the AP 6, 10, 14, 18, … is 90? (a) 24th (b) 21st (c) 22nd (d) 23rd
  21. 21.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 43 (c) 484 (d) 506
  22. 22.What is the 21st term of the AP 18, 20, 22, 24, …? (a) 42 (b) 60 (c) 40 (d) 58
  23. 23.What is the missing term in the AP 7, ?, 13, 16, 19? (a) 13 (b) 11 (c) 10 (d) 9
  24. 24.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 59 (c) 465 (d) 900
  25. 25.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 729 (d) 378
  26. 26.What is the 14th term of the AP 3, 8, 13, 18, …? (a) 73 (b) 65 (c) 68 (d) 70
  27. 27.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 256 (c) 31 (d) 136
  28. 28.What is the missing term in the AP 11, ?, 23, 29, 35? (a) 18 (b) 17 (c) 16 (d) 23
  29. 29.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 33 (b) 198 (c) 201 (d) 396
  30. 30.Which term of the AP 20, 25, 30, 35, … is 75? (a) 11th (b) 13th (c) 15th (d) 12th
  31. 31.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 1122 (c) 562 (d) 528
  32. 32.What is the 37th term of the AP 12, 20, 28, 36, …? (a) 300 (b) 308 (c) 296 (d) 288
  33. 33.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 384 (b) 216 (c) 192 (d) 45
  34. 34.Which term of the AP 2, 9, 16, 23, … is 107? (a) 17th (b) 18th (c) 15th (d) 16th
  35. 35.What is the 29th term of the AP 3, 10, 17, 24, …? (a) 203 (b) 199 (c) 196 (d) 206
  36. 36.What is the 14th term of the AP 19, 23, 27, 31, …? (a) 52 (b) 75 (c) 56 (d) 71
  37. 37.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 380 (b) 190 (c) 361 (d) 37
  38. 38.What is the 24th term of the AP 20, 28, 36, 44, …? (a) 192 (b) 204 (c) 212 (d) 184
  39. 39.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 21 (c) 36 (d) 42
  40. 40.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 14 (b) 77 (c) 78 (d) 154

Answer key

  1. 496
  2. 2080
  3. 26
  4. 1225
  5. 87
  6. 203
  7. 134
  8. 253
  9. 242
  10. 2016
  11. 119
  12. 30
  13. 12
  14. 363
  15. 4
  16. 23
  17. 20th
  18. 119
  19. 10
  20. 22nd
  21. 484
  22. 58
  23. 10
  24. 900
  25. 729
  26. 68
  27. 256
  28. 17
  29. 198
  30. 12th
  31. 561
  32. 300
  33. 192
  34. 16th
  35. 199
  36. 71
  37. 361
  38. 204
  39. 36
  40. 77

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