← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 307 · 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 40? (a) 800 (b) 820 (c) 780 (d) 1640
  2. 2.What is the sum of all the whole numbers from 1 to 32? (a) 512 (b) 496 (c) 1056 (d) 528
  3. 3.Which term of the AP 7, 9, 11, 13, … is 25? (a) 10th (b) 12th (c) 11th (d) 9th
  4. 4.What is the sum of the first 8 terms of the AP 6, 8, 10, …? (a) 208 (b) 112 (c) 20 (d) 104
  5. 5.Which term of the AP 3, 10, 17, 24, … is 164? (a) 25th (b) 23rd (c) 24th (d) 26th
  6. 6.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 28 (c) 56 (d) 13
  7. 7.What is the 20th term of the AP 19, 22, 25, 28, …? (a) 79 (b) 76 (c) 60 (d) 57
  8. 8.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 15 (c) 25 (d) 30
  9. 9.Which term of the AP 2, 4, 6, 8, … is 26? (a) 15th (b) 14th (c) 12th (d) 13th
  10. 10.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 7 (b) 9 (c) 10 (d) 8
  11. 11.What is the missing term in the AP 3, 11, ?, 27, 35? (a) 19 (b) 20 (c) 18 (d) 27
  12. 12.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 19 (d) 100
  13. 13.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 70 (b) 26 (c) 140 (d) 85
  14. 14.What is the sum of the first 5 terms of the AP 2, 3, 4, …? (a) 20 (b) 21 (c) 40 (d) 6
  15. 15.What is the missing term in the AP 7, ?, 11, 13, 15? (a) 11 (b) 8 (c) 10 (d) 9
  16. 16.What is the sum of the first 11 terms of the AP 2, 4, 6, …? (a) 143 (b) 132 (c) 264 (d) 22
  17. 17.What is the sum of the first 9 terms of the AP 1, 3, 5, …? (a) 162 (b) 90 (c) 17 (d) 81
  18. 18.What is the 25th term of the AP 12, 18, 24, 30, …? (a) 162 (b) 144 (c) 150 (d) 156
  19. 19.Which term of the AP 4, 6, 8, 10, … is 26? (a) 11th (b) 13th (c) 14th (d) 12th
  20. 20.What is the missing term in the AP 18, ?, 24, 27, 30? (a) 21 (b) 20 (c) 22 (d) 24
  21. 21.What is the sum of all the whole numbers from 1 to 43? (a) 946 (b) 1892 (c) 947 (d) 903
  22. 22.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 600 (d) 576
  23. 23.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 228 (b) 126 (c) 29 (d) 114
  24. 24.What is the 20th term of the AP 3, 8, 13, 18, …? (a) 100 (b) 98 (c) 103 (d) 95
  25. 25.What is the 34th term of the AP 3, 8, 13, 18, …? (a) 173 (b) 168 (c) 165 (d) 170
  26. 26.What is the 40th term of the AP 6, 15, 24, 33, …? (a) 357 (b) 351 (c) 360 (d) 366
  27. 27.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 67 (b) 816 (c) 444 (d) 408
  28. 28.What is the 40th term of the AP 8, 12, 16, 20, …? (a) 168 (b) 160 (c) 156 (d) 164
  29. 29.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 6162 (c) 3081 (d) 3003
  30. 30.What is the 23rd term of the AP 2, 5, 8, 11, …? (a) 71 (b) 68 (c) 66 (d) 69
  31. 31.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 240 (c) 29 (d) 120
  32. 32.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 588 (b) 294 (c) 41 (d) 312
  33. 33.What is the 35th term of the AP 2, 10, 18, 26, …? (a) 282 (b) 272 (c) 280 (d) 274
  34. 34.What is the sum of all the whole numbers from 1 to 28? (a) 406 (b) 378 (c) 392 (d) 812
  35. 35.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 32 (b) 204 (c) 102 (d) 120
  36. 36.What is the 32nd term of the AP 15, 18, 21, 24, …? (a) 111 (b) 96 (c) 93 (d) 108
  37. 37.What is the sum of all the whole numbers from 1 to 13? (a) 91 (b) 92 (c) 182 (d) 78
  38. 38.What is the sum of the first 5 terms of the AP 5, 6, 7, …? (a) 70 (b) 36 (c) 35 (d) 9
  39. 39.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 80 (b) 40 (c) 10 (d) 41
  40. 40.What is the missing term in the AP 5, ?, 17, 23, 29? (a) 17 (b) 11 (c) 12 (d) 10

Answer key

  1. 820
  2. 528
  3. 10th
  4. 104
  5. 24th
  6. 49
  7. 76
  8. 25
  9. 13th
  10. 8
  11. 19
  12. 100
  13. 70
  14. 20
  15. 9
  16. 132
  17. 81
  18. 156
  19. 12th
  20. 21
  21. 946
  22. 576
  23. 114
  24. 98
  25. 168
  26. 357
  27. 408
  28. 164
  29. 3081
  30. 68
  31. 225
  32. 294
  33. 274
  34. 406
  35. 102
  36. 108
  37. 91
  38. 35
  39. 40
  40. 11

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