← Sequences and AP lesson New set →

Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 44 · 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 18th term of the AP 2, 9, 16, 23, …? (a) 119 (b) 126 (c) 128 (d) 121
  2. 2.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 144 (b) 12 (c) 73 (d) 72
  3. 3.Which term of the AP 5, 8, 11, 14, … is 113? (a) 37th (b) 38th (c) 36th (d) 39th
  4. 4.What is the missing term in the AP 6, 9, ?, 15, 18? (a) 11 (b) 12 (c) 13 (d) 15
  5. 5.What is the missing term in the AP 14, ?, 20, 23, 26? (a) 20 (b) 16 (c) 17 (d) 18
  6. 6.What is the sum of all the whole numbers from 1 to 61? (a) 1891 (b) 1892 (c) 3782 (d) 1830
  7. 7.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 7 (b) 10 (c) 6 (d) 5
  8. 8.What is the 11th term of the AP 14, 16, 18, 20, …? (a) 36 (b) 20 (c) 22 (d) 34
  9. 9.Which term of the AP 4, 8, 12, 16, … is 36? (a) 11th (b) 10th (c) 8th (d) 9th
  10. 10.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 90 (c) 45 (d) 81
  11. 11.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 210 (c) 27 (d) 196
  12. 12.What is the 10th term of the AP 15, 20, 25, 30, …? (a) 50 (b) 45 (c) 65 (d) 60
  13. 13.What is the sum of all the whole numbers from 1 to 16? (a) 120 (b) 136 (c) 272 (d) 128
  14. 14.What is the 14th term of the AP 12, 20, 28, 36, …? (a) 116 (b) 112 (c) 124 (d) 104
  15. 15.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 17 (b) 78 (c) 144 (d) 72
  16. 16.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 480 (b) 240 (c) 42 (d) 260
  17. 17.What is the 22nd term of the AP 4, 7, 10, 13, …? (a) 63 (b) 70 (c) 67 (d) 66
  18. 18.What is the 12th term of the AP 8, 15, 22, 29, …? (a) 84 (b) 77 (c) 85 (d) 92
  19. 19.What is the missing term in the AP 20, ?, 34, 41, 48? (a) 28 (b) 27 (c) 26 (d) 34
  20. 20.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 729 (c) 53 (d) 756
  21. 21.Which term of the AP 5, 13, 21, 29, … is 221? (a) 29th (b) 27th (c) 30th (d) 28th
  22. 22.What is the 16th term of the AP 1, 3, 5, 7, …? (a) 33 (b) 32 (c) 30 (d) 31
  23. 23.What is the sum of all the whole numbers from 1 to 41? (a) 1722 (b) 862 (c) 820 (d) 861
  24. 24.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 2926 (c) 5852 (d) 2888
  25. 25.What is the sum of the first 11 terms of the AP 9, 12, 15, …? (a) 39 (b) 264 (c) 267 (d) 528
  26. 26.What is the 12th term of the AP 1, 10, 19, 28, …? (a) 108 (b) 109 (c) 99 (d) 100
  27. 27.What is the missing term in the AP 10, 15, ?, 25, 30? (a) 25 (b) 21 (c) 20 (d) 19
  28. 28.What is the sum of the first 6 terms of the AP 1, 6, 11, …? (a) 26 (b) 81 (c) 96 (d) 162
  29. 29.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 88 (b) 18 (c) 176 (d) 96
  30. 30.What is the sum of the first 10 terms of the AP 6, 11, 16, …? (a) 285 (b) 310 (c) 570 (d) 51
  31. 31.What is the 36th term of the AP 12, 19, 26, 33, …? (a) 245 (b) 252 (c) 264 (d) 257
  32. 32.What is the sum of all the whole numbers from 1 to 24? (a) 600 (b) 300 (c) 276 (d) 288
  33. 33.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 220 (b) 110 (c) 20 (d) 120
  34. 34.What is the missing term in the AP 18, 21, 24, ?, 30? (a) 28 (b) 30 (c) 26 (d) 27
  35. 35.What is the sum of all the whole numbers from 1 to 10? (a) 110 (b) 45 (c) 55 (d) 50
  36. 36.What is the 30th term of the AP 14, 17, 20, 23, …? (a) 101 (b) 104 (c) 87 (d) 90
  37. 37.What is the missing term in the AP 11, ?, 27, 35, 43? (a) 27 (b) 20 (c) 18 (d) 19
  38. 38.What is the 20th term of the AP 10, 13, 16, 19, …? (a) 57 (b) 60 (c) 70 (d) 67
  39. 39.What is the missing term in the AP 10, 14, ?, 22, 26? (a) 19 (b) 18 (c) 22 (d) 17
  40. 40.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 55 (c) 19 (d) 100

Answer key

  1. 121
  2. 72
  3. 37th
  4. 12
  5. 17
  6. 1891
  7. 6
  8. 34
  9. 9th
  10. 81
  11. 196
  12. 60
  13. 136
  14. 116
  15. 72
  16. 240
  17. 67
  18. 85
  19. 27
  20. 729
  21. 28th
  22. 31
  23. 861
  24. 2926
  25. 264
  26. 100
  27. 20
  28. 81
  29. 88
  30. 285
  31. 257
  32. 300
  33. 110
  34. 27
  35. 55
  36. 101
  37. 19
  38. 67
  39. 18
  40. 100

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