← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 397 · 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 25th term of the AP 16, 22, 28, 34, …? (a) 150 (b) 166 (c) 144 (d) 160
  2. 2.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 49 (b) 522 (c) 261 (d) 266
  3. 3.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 16 (b) 13 (c) 12 (d) 14
  4. 4.What is the sum of all the whole numbers from 1 to 17? (a) 136 (b) 153 (c) 154 (d) 306
  5. 5.Which term of the AP 4, 11, 18, 25, … is 270? (a) 40th (b) 41st (c) 38th (d) 39th
  6. 6.What is the sum of the first 9 terms of the AP 9, 13, 17, …? (a) 450 (b) 243 (c) 225 (d) 41
  7. 7.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 21 (c) 42 (d) 36
  8. 8.What is the sum of all the whole numbers from 1 to 77? (a) 2926 (b) 3004 (c) 6006 (d) 3003
  9. 9.What is the 13th term of the AP 16, 20, 24, 28, …? (a) 48 (b) 68 (c) 52 (d) 64
  10. 10.What is the 37th term of the AP 6, 14, 22, 30, …? (a) 288 (b) 294 (c) 296 (d) 302
  11. 11.What is the 11th term of the AP 10, 16, 22, 28, …? (a) 70 (b) 66 (c) 60 (d) 76
  12. 12.Which term of the AP 3, 7, 11, 15, … is 75? (a) 19th (b) 18th (c) 20th (d) 21st
  13. 13.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 435 (c) 841 (d) 870
  14. 14.What is the sum of all the whole numbers from 1 to 12? (a) 66 (b) 78 (c) 72 (d) 156
  15. 15.What is the 25th term of the AP 19, 26, 33, 40, …? (a) 194 (b) 175 (c) 168 (d) 187
  16. 16.What is the 16th term of the AP 5, 10, 15, 20, …? (a) 81 (b) 75 (c) 80 (d) 85
  17. 17.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 25 (d) 9
  18. 18.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 666 (c) 630 (d) 648
  19. 19.What is the missing term in the AP 1, 8, 15, ?, 29? (a) 22 (b) 21 (c) 29 (d) 23
  20. 20.What is the 37th term of the AP 3, 7, 11, 15, …? (a) 151 (b) 144 (c) 148 (d) 147
  21. 21.Which term of the AP 12, 16, 20, 24, … is 124? (a) 28th (b) 31st (c) 30th (d) 29th
  22. 22.What is the sum of all the whole numbers from 1 to 68? (a) 2312 (b) 4692 (c) 2346 (d) 2278
  23. 23.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 308 (b) 24 (c) 154 (d) 165
  24. 24.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 176 (b) 187 (c) 26 (d) 352
  25. 25.What is the 12th term of the AP 10, 16, 22, 28, …? (a) 82 (b) 66 (c) 76 (d) 72
  26. 26.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 378 (c) 392 (d) 406
  27. 27.What is the missing term in the AP 9, 12, ?, 18, 21? (a) 15 (b) 16 (c) 18 (d) 14
  28. 28.What is the sum of all the whole numbers from 1 to 35? (a) 631 (b) 630 (c) 595 (d) 1260
  29. 29.What is the 20th term of the AP 4, 8, 12, 16, …? (a) 80 (b) 81 (c) 76 (d) 84
  30. 30.What is the sum of the first 12 terms of the AP 7, 8, 9, …? (a) 156 (b) 300 (c) 18 (d) 150
  31. 31.What is the missing term in the AP 3, 8, 13, ?, 23? (a) 19 (b) 18 (c) 17 (d) 23
  32. 32.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 182 (d) 169
  33. 33.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 40 (b) 80 (c) 12 (d) 45
  34. 34.What is the 12th term of the AP 19, 21, 23, 25, …? (a) 24 (b) 41 (c) 43 (d) 22
  35. 35.What is the sum of all the whole numbers from 1 to 71? (a) 2556 (b) 5112 (c) 2485 (d) 2557
  36. 36.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 13 (c) 28 (d) 49
  37. 37.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 41 (c) 441 (d) 231
  38. 38.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 1035 (c) 1036 (d) 2070
  39. 39.Which term of the AP 5, 10, 15, 20, … is 110? (a) 24th (b) 22nd (c) 21st (d) 23rd
  40. 40.What is the missing term in the AP 15, 24, ?, 42, 51? (a) 32 (b) 42 (c) 34 (d) 33

Answer key

  1. 160
  2. 261
  3. 13
  4. 153
  5. 39th
  6. 225
  7. 36
  8. 3003
  9. 64
  10. 294
  11. 70
  12. 19th
  13. 841
  14. 78
  15. 187
  16. 80
  17. 25
  18. 666
  19. 22
  20. 147
  21. 29th
  22. 2346
  23. 154
  24. 176
  25. 76
  26. 406
  27. 15
  28. 630
  29. 80
  30. 150
  31. 18
  32. 169
  33. 40
  34. 41
  35. 2556
  36. 49
  37. 441
  38. 1035
  39. 22nd
  40. 33

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