← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 634 · 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 82? (a) 3362 (b) 3321 (c) 3403 (d) 6806
  2. 2.What is the 10th term of the AP 7, 16, 25, 34, …? (a) 81 (b) 88 (c) 90 (d) 97
  3. 3.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 27 (c) 196 (d) 210
  4. 4.Which term of the AP 17, 21, 25, 29, … is 45? (a) 9th (b) 8th (c) 10th (d) 7th
  5. 5.What is the missing term in the AP 20, ?, 34, 41, 48? (a) 28 (b) 34 (c) 26 (d) 27
  6. 6.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 300 (c) 326 (d) 325
  7. 7.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 26 (b) 85 (c) 70 (d) 140
  8. 8.What is the missing term in the AP 16, ?, 26, 31, 36? (a) 20 (b) 26 (c) 22 (d) 21
  9. 9.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 186 (b) 108 (c) 93 (d) 28
  10. 10.What is the sum of all the whole numbers from 1 to 38? (a) 1482 (b) 703 (c) 741 (d) 722
  11. 11.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 40 (b) 6 (c) 21 (d) 20
  12. 12.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 930 (c) 435 (d) 465
  13. 13.What is the sum of all the whole numbers from 1 to 56? (a) 1596 (b) 3192 (c) 1568 (d) 1540
  14. 14.What is the sum of the first 10 terms of the AP 10, 13, 16, …? (a) 37 (b) 470 (c) 250 (d) 235
  15. 15.What is the 13th term of the AP 14, 22, 30, 38, …? (a) 96 (b) 110 (c) 118 (d) 104
  16. 16.What is the 14th term of the AP 9, 15, 21, 27, …? (a) 84 (b) 78 (c) 87 (d) 93
  17. 17.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 42 (b) 9 (c) 43 (d) 84
  18. 18.What is the 31st term of the AP 4, 9, 14, 19, …? (a) 159 (b) 155 (c) 150 (d) 154
  19. 19.What is the 27th term of the AP 19, 26, 33, 40, …? (a) 182 (b) 208 (c) 201 (d) 189
  20. 20.Which term of the AP 2, 5, 8, 11, … is 74? (a) 27th (b) 24th (c) 26th (d) 25th
  21. 21.What is the missing term in the AP 3, 6, 9, ?, 15? (a) 12 (b) 15 (c) 13 (d) 11
  22. 22.Which term of the AP 4, 9, 14, 19, … is 49? (a) 9th (b) 12th (c) 11th (d) 10th
  23. 23.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 11 (b) 10 (c) 12 (d) 13
  24. 24.What is the 10th term of the AP 9, 17, 25, 33, …? (a) 80 (b) 72 (c) 89 (d) 81
  25. 25.Which term of the AP 15, 20, 25, 30, … is 95? (a) 18th (b) 19th (c) 17th (d) 16th
  26. 26.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 2278 (c) 4556 (d) 2279
  27. 27.What is the 21st term of the AP 8, 12, 16, 20, …? (a) 88 (b) 84 (c) 92 (d) 80
  28. 28.What is the sum of all the whole numbers from 1 to 72? (a) 5256 (b) 2556 (c) 2628 (d) 2592
  29. 29.What is the missing term in the AP 11, ?, 15, 17, 19? (a) 14 (b) 12 (c) 13 (d) 15
  30. 30.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 18 (b) 180 (c) 90 (d) 99
  31. 31.What is the missing term in the AP 4, 9, ?, 19, 24? (a) 13 (b) 15 (c) 19 (d) 14
  32. 32.Which term of the AP 15, 19, 23, 27, … is 151? (a) 34th (b) 35th (c) 36th (d) 37th
  33. 33.What is the sum of all the whole numbers from 1 to 94? (a) 4418 (b) 4371 (c) 8930 (d) 4465
  34. 34.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 21 (c) 11 (d) 42
  35. 35.Which term of the AP 20, 22, 24, 26, … is 86? (a) 43rd (b) 34th (c) 35th (d) 33rd
  36. 36.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 497 (c) 992 (d) 496
  37. 37.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 325 (c) 650 (d) 625
  38. 38.What is the missing term in the AP 13, 22, 31, ?, 49? (a) 49 (b) 39 (c) 40 (d) 41
  39. 39.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 306 (d) 289
  40. 40.What is the missing term in the AP 15, ?, 31, 39, 47? (a) 23 (b) 22 (c) 31 (d) 24

Answer key

  1. 3403
  2. 88
  3. 196
  4. 8th
  5. 27
  6. 325
  7. 70
  8. 21
  9. 93
  10. 741
  11. 20
  12. 465
  13. 1596
  14. 235
  15. 110
  16. 87
  17. 42
  18. 154
  19. 201
  20. 25th
  21. 12
  22. 10th
  23. 11
  24. 81
  25. 17th
  26. 2278
  27. 88
  28. 2628
  29. 13
  30. 90
  31. 14
  32. 35th
  33. 4465
  34. 36
  35. 34th
  36. 496
  37. 625
  38. 40
  39. 289
  40. 23

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