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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 772 · 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 11, 17, 23, 29, … is 161? (a) 27th (b) 28th (c) 25th (d) 26th
  2. 2.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 176 (b) 13 (c) 88 (d) 89
  3. 3.What is the 14th term of the AP 18, 20, 22, 24, …? (a) 46 (b) 28 (c) 26 (d) 44
  4. 4.What is the 13th term of the AP 8, 12, 16, 20, …? (a) 52 (b) 60 (c) 56 (d) 48
  5. 5.Which term of the AP 4, 13, 22, 31, … is 103? (a) 11th (b) 13th (c) 14th (d) 12th
  6. 6.What is the missing term in the AP 3, 8, ?, 18, 23? (a) 18 (b) 13 (c) 14 (d) 12
  7. 7.What is the missing term in the AP 16, ?, 32, 40, 48? (a) 25 (b) 23 (c) 32 (d) 24
  8. 8.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 19 (c) 55 (d) 110
  9. 9.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 39 (c) 210 (d) 400
  10. 10.What is the 21st term of the AP 16, 21, 26, 31, …? (a) 105 (b) 100 (c) 116 (d) 121
  11. 11.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 30 (b) 10 (c) 35 (d) 60
  12. 12.What is the missing term in the AP 20, 28, 36, ?, 52? (a) 44 (b) 43 (c) 45 (d) 52
  13. 13.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 930 (c) 900 (d) 59
  14. 14.What is the 24th term of the AP 4, 6, 8, 10, …? (a) 48 (b) 52 (c) 46 (d) 50
  15. 15.Which term of the AP 2, 8, 14, 20, … is 86? (a) 15th (b) 14th (c) 17th (d) 16th
  16. 16.What is the 34th term of the AP 19, 21, 23, 25, …? (a) 68 (b) 66 (c) 85 (d) 87
  17. 17.What is the sum of all the whole numbers from 1 to 26? (a) 702 (b) 338 (c) 325 (d) 351
  18. 18.What is the 28th term of the AP 5, 13, 21, 29, …? (a) 221 (b) 216 (c) 224 (d) 229
  19. 19.What is the 28th term of the AP 16, 19, 22, 25, …? (a) 100 (b) 81 (c) 97 (d) 84
  20. 20.What is the sum of the first 5 terms of the AP 5, 7, 9, …? (a) 50 (b) 90 (c) 45 (d) 13
  21. 21.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 42 (d) 21
  22. 22.What is the 16th term of the AP 2, 4, 6, 8, …? (a) 33 (b) 34 (c) 32 (d) 30
  23. 23.What is the 18th term of the AP 19, 25, 31, 37, …? (a) 108 (b) 121 (c) 127 (d) 102
  24. 24.What is the missing term in the AP 19, 28, ?, 46, 55? (a) 38 (b) 46 (c) 36 (d) 37
  25. 25.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 3655 (c) 7482 (d) 3741
  26. 26.What is the sum of the first 5 terms of the AP 8, 14, 20, …? (a) 200 (b) 115 (c) 100 (d) 32
  27. 27.What is the sum of the first 11 terms of the AP 4, 7, 10, …? (a) 418 (b) 34 (c) 212 (d) 209
  28. 28.What is the missing term in the AP 6, ?, 10, 12, 14? (a) 9 (b) 10 (c) 8 (d) 7
  29. 29.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 465 (c) 930 (d) 435
  30. 30.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 99 (b) 29 (c) 114 (d) 198
  31. 31.What is the 17th term of the AP 13, 16, 19, 22, …? (a) 61 (b) 51 (c) 48 (d) 64
  32. 32.What is the sum of the first 6 terms of the AP 3, 9, 15, …? (a) 108 (b) 33 (c) 126 (d) 216
  33. 33.What is the 29th term of the AP 13, 18, 23, 28, …? (a) 158 (b) 153 (c) 145 (d) 140
  34. 34.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 31 (b) 114 (c) 192 (d) 96
  35. 35.What is the 10th term of the AP 6, 15, 24, 33, …? (a) 96 (b) 90 (c) 87 (d) 81
  36. 36.What is the sum of the first 11 terms of the AP 2, 7, 12, …? (a) 52 (b) 594 (c) 302 (d) 297
  37. 37.What is the sum of all the whole numbers from 1 to 48? (a) 1152 (b) 1128 (c) 1176 (d) 2352
  38. 38.What is the sum of the first 7 terms of the AP 5, 8, 11, …? (a) 23 (b) 196 (c) 98 (d) 101
  39. 39.What is the 34th term of the AP 17, 23, 29, 35, …? (a) 221 (b) 198 (c) 215 (d) 204
  40. 40.Which term of the AP 9, 13, 17, 21, … is 49? (a) 11th (b) 13th (c) 12th (d) 10th

Answer key

  1. 26th
  2. 88
  3. 44
  4. 56
  5. 12th
  6. 13
  7. 24
  8. 100
  9. 400
  10. 116
  11. 30
  12. 44
  13. 900
  14. 50
  15. 15th
  16. 85
  17. 351
  18. 221
  19. 97
  20. 45
  21. 36
  22. 32
  23. 121
  24. 37
  25. 3741
  26. 100
  27. 209
  28. 8
  29. 465
  30. 99
  31. 61
  32. 108
  33. 153
  34. 96
  35. 87
  36. 297
  37. 1176
  38. 98
  39. 215
  40. 11th

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