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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 951 · 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 the first 6 terms of the AP 9, 14, 19, …? (a) 34 (b) 129 (c) 258 (d) 144
  2. 2.What is the 10th term of the AP 13, 18, 23, 28, …? (a) 58 (b) 45 (c) 50 (d) 63
  3. 3.What is the 10th term of the AP 6, 9, 12, 15, …? (a) 36 (b) 27 (c) 33 (d) 30
  4. 4.What is the missing term in the AP 11, 19, 27, ?, 43? (a) 34 (b) 36 (c) 43 (d) 35
  5. 5.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 126 (b) 12 (c) 63 (d) 64
  6. 6.What is the 16th term of the AP 12, 20, 28, 36, …? (a) 128 (b) 120 (c) 132 (d) 140
  7. 7.What is the missing term in the AP 15, 22, 29, ?, 43? (a) 37 (b) 43 (c) 35 (d) 36
  8. 8.What is the sum of all the whole numbers from 1 to 98? (a) 4851 (b) 9702 (c) 4802 (d) 4753
  9. 9.What is the missing term in the AP 4, 13, ?, 31, 40? (a) 23 (b) 21 (c) 22 (d) 31
  10. 10.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 240 (b) 222 (c) 35 (d) 444
  11. 11.What is the sum of all the whole numbers from 1 to 57? (a) 1596 (b) 1653 (c) 1654 (d) 3306
  12. 12.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 308 (b) 24 (c) 154 (d) 165
  13. 13.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 14 (b) 78 (c) 77 (d) 154
  14. 14.What is the 33rd term of the AP 4, 8, 12, 16, …? (a) 132 (b) 128 (c) 133 (d) 136
  15. 15.Which term of the AP 3, 6, 9, 12, … is 66? (a) 24th (b) 22nd (c) 23rd (d) 21st
  16. 16.What is the missing term in the AP 1, 9, 17, ?, 33? (a) 24 (b) 33 (c) 26 (d) 25
  17. 17.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 19 (d) 55
  18. 18.What is the 22nd term of the AP 4, 11, 18, 25, …? (a) 154 (b) 147 (c) 158 (d) 151
  19. 19.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 324 (c) 342 (d) 171
  20. 20.Which term of the AP 14, 17, 20, 23, … is 101? (a) 32nd (b) 29th (c) 31st (d) 30th
  21. 21.What is the 21st term of the AP 3, 11, 19, 27, …? (a) 171 (b) 160 (c) 163 (d) 168
  22. 22.What is the 18th term of the AP 16, 21, 26, 31, …? (a) 85 (b) 101 (c) 106 (d) 90
  23. 23.What is the 26th term of the AP 9, 14, 19, 24, …? (a) 130 (b) 125 (c) 139 (d) 134
  24. 24.What is the 28th term of the AP 20, 22, 24, 26, …? (a) 54 (b) 74 (c) 76 (d) 56
  25. 25.What is the missing term in the AP 19, 21, 23, ?, 27? (a) 25 (b) 26 (c) 24 (d) 27
  26. 26.What is the 35th term of the AP 13, 19, 25, 31, …? (a) 210 (b) 223 (c) 204 (d) 217
  27. 27.What is the 34th term of the AP 9, 16, 23, 30, …? (a) 240 (b) 247 (c) 231 (d) 238
  28. 28.What is the 13th term of the AP 5, 12, 19, 26, …? (a) 84 (b) 91 (c) 89 (d) 96
  29. 29.What is the missing term in the AP 14, 18, ?, 26, 30? (a) 26 (b) 23 (c) 21 (d) 22
  30. 30.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 49 (c) 325 (d) 650
  31. 31.What is the sum of all the whole numbers from 1 to 38? (a) 741 (b) 1482 (c) 722 (d) 703
  32. 32.What is the 24th term of the AP 5, 11, 17, 23, …? (a) 149 (b) 144 (c) 138 (d) 143
  33. 33.What is the 13th term of the AP 20, 24, 28, 32, …? (a) 68 (b) 48 (c) 52 (d) 72
  34. 34.Which term of the AP 13, 16, 19, 22, … is 46? (a) 12th (b) 14th (c) 13th (d) 11th
  35. 35.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 47 (b) 245 (c) 490 (d) 270
  36. 36.What is the 12th term of the AP 5, 8, 11, 14, …? (a) 33 (b) 38 (c) 36 (d) 41
  37. 37.What is the 32nd term of the AP 2, 9, 16, 23, …? (a) 224 (b) 217 (c) 219 (d) 226
  38. 38.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 57 (b) 330 (c) 600 (d) 300
  39. 39.What is the 14th term of the AP 19, 23, 27, 31, …? (a) 75 (b) 52 (c) 71 (d) 56
  40. 40.What is the missing term in the AP 20, ?, 32, 38, 44? (a) 26 (b) 25 (c) 27 (d) 32

Answer key

  1. 129
  2. 58
  3. 33
  4. 35
  5. 63
  6. 132
  7. 36
  8. 4851
  9. 22
  10. 222
  11. 1653
  12. 154
  13. 77
  14. 132
  15. 22nd
  16. 25
  17. 100
  18. 151
  19. 324
  20. 30th
  21. 163
  22. 101
  23. 134
  24. 74
  25. 25
  26. 217
  27. 240
  28. 89
  29. 22
  30. 625
  31. 741
  32. 143
  33. 68
  34. 12th
  35. 245
  36. 38
  37. 219
  38. 300
  39. 71
  40. 26

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