← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 1 · 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.Which term of the AP 12, 14, 16, 18, … is 38? (a) 14th (b) 15th (c) 19th (d) 13th
  2. 2.What is the 35th term of the AP 15, 22, 29, 36, …? (a) 238 (b) 260 (c) 245 (d) 253
  3. 3.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1682 (c) 1653 (d) 1711
  4. 4.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 379 (c) 378 (d) 756
  5. 5.What is the 19th term of the AP 13, 17, 21, 25, …? (a) 76 (b) 89 (c) 85 (d) 72
  6. 6.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 29 (c) 240 (d) 120
  7. 7.What is the 16th term of the AP 16, 20, 24, 28, …? (a) 60 (b) 76 (c) 64 (d) 80
  8. 8.What is the sum of the first 7 terms of the AP 5, 9, 13, …? (a) 133 (b) 29 (c) 238 (d) 119
  9. 9.What is the 21st term of the AP 9, 17, 25, 33, …? (a) 168 (b) 177 (c) 169 (d) 160
  10. 10.What is the 13th term of the AP 19, 27, 35, 43, …? (a) 123 (b) 115 (c) 104 (d) 96
  11. 11.What is the missing term in the AP 2, 4, ?, 8, 10? (a) 7 (b) 8 (c) 5 (d) 6
  12. 12.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 406 (c) 784 (d) 812
  13. 13.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 435 (c) 841 (d) 57
  14. 14.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 23 (b) 85 (c) 75 (d) 150
  15. 15.What is the missing term in the AP 4, ?, 20, 28, 36? (a) 13 (b) 11 (c) 20 (d) 12
  16. 16.What is the 36th term of the AP 12, 20, 28, 36, …? (a) 280 (b) 292 (c) 300 (d) 288
  17. 17.Which term of the AP 14, 19, 24, 29, … is 144? (a) 27th (b) 29th (c) 26th (d) 28th
  18. 18.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 441 (c) 231 (d) 41
  19. 19.What is the sum of all the whole numbers from 1 to 18? (a) 153 (b) 162 (c) 171 (d) 342
  20. 20.What is the sum of the first 5 terms of the AP 9, 13, 17, …? (a) 170 (b) 95 (c) 85 (d) 25
  21. 21.What is the missing term in the AP 15, 23, 31, ?, 47? (a) 47 (b) 38 (c) 40 (d) 39
  22. 22.Which term of the AP 6, 12, 18, 24, … is 180? (a) 31st (b) 30th (c) 32nd (d) 29th
  23. 23.What is the missing term in the AP 18, 20, ?, 24, 26? (a) 21 (b) 23 (c) 24 (d) 22
  24. 24.Which term of the AP 20, 24, 28, 32, … is 104? (a) 21st (b) 22nd (c) 26th (d) 23rd
  25. 25.What is the sum of all the whole numbers from 1 to 37? (a) 704 (b) 666 (c) 703 (d) 1406
  26. 26.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 42 (b) 6 (c) 21 (d) 24
  27. 27.Which term of the AP 11, 13, 15, 17, … is 35? (a) 15th (b) 12th (c) 14th (d) 13th
  28. 28.Which term of the AP 4, 9, 14, 19, … is 164? (a) 35th (b) 32nd (c) 33rd (d) 34th
  29. 29.What is the sum of all the whole numbers from 1 to 36? (a) 1332 (b) 630 (c) 666 (d) 648
  30. 30.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 119 (b) 27 (c) 210 (d) 105
  31. 31.Which term of the AP 16, 20, 24, 28, … is 140? (a) 33rd (b) 35th (c) 32nd (d) 31st
  32. 32.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 17 (b) 88 (c) 80 (d) 160
  33. 33.What is the 36th term of the AP 9, 14, 19, 24, …? (a) 175 (b) 184 (c) 180 (d) 189
  34. 34.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 52 (b) 297 (c) 594 (d) 302
  35. 35.What is the 29th term of the AP 3, 6, 9, 12, …? (a) 84 (b) 88 (c) 90 (d) 87
  36. 36.What is the sum of the first 12 terms of the AP 6, 12, 18, …? (a) 504 (b) 936 (c) 468 (d) 72
  37. 37.What is the missing term in the AP 17, 23, ?, 35, 41? (a) 35 (b) 30 (c) 28 (d) 29
  38. 38.What is the sum of all the whole numbers from 1 to 42? (a) 861 (b) 1806 (c) 882 (d) 903
  39. 39.What is the 16th term of the AP 6, 14, 22, 30, …? (a) 128 (b) 134 (c) 126 (d) 120
  40. 40.What is the sum of the first 7 terms of the AP 2, 8, 14, …? (a) 140 (b) 38 (c) 280 (d) 161

Answer key

  1. 14th
  2. 253
  3. 1711
  4. 378
  5. 85
  6. 225
  7. 76
  8. 119
  9. 169
  10. 115
  11. 6
  12. 784
  13. 841
  14. 75
  15. 12
  16. 292
  17. 27th
  18. 441
  19. 171
  20. 85
  21. 39
  22. 30th
  23. 22
  24. 22nd
  25. 703
  26. 21
  27. 13th
  28. 33rd
  29. 666
  30. 105
  31. 32nd
  32. 80
  33. 184
  34. 297
  35. 87
  36. 468
  37. 29
  38. 903
  39. 126
  40. 140

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