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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 111 · 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 10 terms of the AP 5, 6, 7, …? (a) 100 (b) 95 (c) 190 (d) 14
  2. 2.What is the 33rd term of the AP 6, 12, 18, 24, …? (a) 199 (b) 198 (c) 204 (d) 192
  3. 3.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 10 (b) 35 (c) 60 (d) 30
  4. 4.What is the missing term in the AP 18, 21, 24, ?, 30? (a) 27 (b) 30 (c) 28 (d) 26
  5. 5.What is the missing term in the AP 11, 18, ?, 32, 39? (a) 24 (b) 25 (c) 26 (d) 32
  6. 6.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 60 (b) 100 (c) 50 (d) 18
  7. 7.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 91 (b) 16 (c) 182 (d) 92
  8. 8.What is the missing term in the AP 16, ?, 32, 40, 48? (a) 32 (b) 25 (c) 24 (d) 23
  9. 9.What is the sum of the first 10 terms of the AP 5, 7, 9, …? (a) 23 (b) 150 (c) 140 (d) 280
  10. 10.What is the sum of the first 8 terms of the AP 2, 3, 4, …? (a) 88 (b) 48 (c) 44 (d) 9
  11. 11.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 57 (b) 435 (c) 870 (d) 841
  12. 12.What is the 29th term of the AP 17, 21, 25, 29, …? (a) 133 (b) 112 (c) 129 (d) 116
  13. 13.What is the missing term in the AP 3, ?, 11, 15, 19? (a) 11 (b) 8 (c) 7 (d) 6
  14. 14.What is the sum of all the whole numbers from 1 to 48? (a) 1176 (b) 1128 (c) 1152 (d) 2352
  15. 15.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 15 (b) 16 (c) 5 (d) 30
  16. 16.What is the sum of the first 11 terms of the AP 7, 8, 9, …? (a) 264 (b) 132 (c) 17 (d) 133
  17. 17.What is the 15th term of the AP 17, 24, 31, 38, …? (a) 122 (b) 115 (c) 105 (d) 98
  18. 18.What is the 20th term of the AP 16, 20, 24, 28, …? (a) 76 (b) 96 (c) 80 (d) 92
  19. 19.What is the sum of the first 6 terms of the AP 5, 11, 17, …? (a) 240 (b) 35 (c) 138 (d) 120
  20. 20.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 300 (c) 600 (d) 47
  21. 21.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 12 (b) 144 (c) 73 (d) 72
  22. 22.What is the 19th term of the AP 10, 19, 28, 37, …? (a) 162 (b) 172 (c) 171 (d) 181
  23. 23.What is the 17th term of the AP 4, 12, 20, 28, …? (a) 128 (b) 132 (c) 136 (d) 140
  24. 24.What is the sum of all the whole numbers from 1 to 78? (a) 3081 (b) 6162 (c) 3042 (d) 3003
  25. 25.What is the 37th term of the AP 14, 21, 28, 35, …? (a) 273 (b) 266 (c) 252 (d) 259
  26. 26.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 130 (b) 21 (c) 65 (d) 75
  27. 27.What is the missing term in the AP 14, 21, 28, ?, 42? (a) 36 (b) 42 (c) 35 (d) 34
  28. 28.What is the 24th term of the AP 1, 9, 17, 25, …? (a) 193 (b) 184 (c) 185 (d) 192
  29. 29.What is the sum of the first 6 terms of the AP 4, 6, 8, …? (a) 108 (b) 54 (c) 14 (d) 60
  30. 30.What is the sum of all the whole numbers from 1 to 52? (a) 1378 (b) 2756 (c) 1326 (d) 1352
  31. 31.What is the sum of the first 5 terms of the AP 3, 4, 5, …? (a) 25 (b) 26 (c) 7 (d) 50
  32. 32.What is the 16th term of the AP 10, 15, 20, 25, …? (a) 80 (b) 85 (c) 75 (d) 90
  33. 33.What is the 26th term of the AP 7, 10, 13, 16, …? (a) 75 (b) 82 (c) 85 (d) 78
  34. 34.What is the 22nd term of the AP 17, 21, 25, 29, …? (a) 105 (b) 84 (c) 88 (d) 101
  35. 35.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 81 (c) 17 (d) 45
  36. 36.What is the sum of the first 10 terms of the AP 4, 5, 6, …? (a) 170 (b) 85 (c) 13 (d) 90
  37. 37.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 49 (c) 625 (d) 325
  38. 38.Which term of the AP 19, 23, 27, 31, … is 47? (a) 10th (b) 9th (c) 8th (d) 7th
  39. 39.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 90 (b) 30 (c) 105 (d) 180
  40. 40.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 325 (c) 650 (d) 300

Answer key

  1. 95
  2. 198
  3. 30
  4. 27
  5. 25
  6. 50
  7. 91
  8. 24
  9. 140
  10. 44
  11. 841
  12. 129
  13. 7
  14. 1176
  15. 15
  16. 132
  17. 115
  18. 92
  19. 120
  20. 576
  21. 72
  22. 172
  23. 132
  24. 3081
  25. 266
  26. 65
  27. 35
  28. 185
  29. 54
  30. 1378
  31. 25
  32. 85
  33. 82
  34. 101
  35. 81
  36. 85
  37. 625
  38. 8th
  39. 90
  40. 325

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