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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 303 · 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 4, 5, 6, …? (a) 85 (b) 13 (c) 170 (d) 90
  2. 2.What is the 28th term of the AP 14, 23, 32, 41, …? (a) 266 (b) 252 (c) 243 (d) 257
  3. 3.What is the sum of the first 9 terms of the AP 10, 14, 18, …? (a) 234 (b) 252 (c) 468 (d) 42
  4. 4.What is the sum of all the whole numbers from 1 to 71? (a) 2485 (b) 5112 (c) 2556 (d) 2557
  5. 5.What is the sum of the first 7 terms of the AP 4, 8, 12, …? (a) 112 (b) 126 (c) 28 (d) 224
  6. 6.Which term of the AP 20, 23, 26, 29, … is 83? (a) 22nd (b) 23rd (c) 24th (d) 21st
  7. 7.What is the missing term in the AP 18, ?, 22, 24, 26? (a) 20 (b) 19 (c) 21 (d) 22
  8. 8.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 110 (b) 200 (c) 100 (d) 19
  9. 9.What is the missing term in the AP 12, ?, 22, 27, 32? (a) 17 (b) 16 (c) 18 (d) 22
  10. 10.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 625 (c) 650 (d) 49
  11. 11.What is the 19th term of the AP 20, 27, 34, 41, …? (a) 153 (b) 146 (c) 133 (d) 126
  12. 12.Which term of the AP 7, 12, 17, 22, … is 107? (a) 22nd (b) 23rd (c) 20th (d) 21st
  13. 13.What is the 35th term of the AP 14, 22, 30, 38, …? (a) 294 (b) 286 (c) 272 (d) 280
  14. 14.What is the 21st term of the AP 15, 22, 29, 36, …? (a) 162 (b) 155 (c) 147 (d) 140
  15. 15.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 105 (c) 210 (d) 27
  16. 16.What is the 32nd term of the AP 5, 9, 13, 17, …? (a) 129 (b) 128 (c) 124 (d) 133
  17. 17.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 25 (c) 91 (d) 169
  18. 18.What is the 25th term of the AP 20, 22, 24, 26, …? (a) 48 (b) 70 (c) 68 (d) 50
  19. 19.What is the sum of the first 12 terms of the AP 5, 9, 13, …? (a) 324 (b) 348 (c) 49 (d) 648
  20. 20.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 19 (b) 154 (c) 308 (d) 155
  21. 21.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 42 (c) 36 (d) 21
  22. 22.What is the 33rd term of the AP 15, 17, 19, 21, …? (a) 81 (b) 66 (c) 64 (d) 79
  23. 23.What is the sum of all the whole numbers from 1 to 50? (a) 1250 (b) 1275 (c) 2550 (d) 1225
  24. 24.Which term of the AP 17, 26, 35, 44, … is 278? (a) 30th (b) 32nd (c) 29th (d) 31st
  25. 25.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 136 (c) 256 (d) 31
  26. 26.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 23 (c) 156 (d) 144
  27. 27.Which term of the AP 7, 12, 17, 22, … is 82? (a) 16th (b) 15th (c) 18th (d) 17th
  28. 28.Which term of the AP 10, 14, 18, 22, … is 38? (a) 7th (b) 9th (c) 8th (d) 10th
  29. 29.What is the sum of the first 6 terms of the AP 5, 10, 15, …? (a) 30 (b) 210 (c) 105 (d) 120
  30. 30.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 24 (b) 150 (c) 300 (d) 160
  31. 31.What is the 25th term of the AP 12, 20, 28, 36, …? (a) 200 (b) 212 (c) 204 (d) 192
  32. 32.What is the missing term in the AP 15, ?, 31, 39, 47? (a) 24 (b) 22 (c) 31 (d) 23
  33. 33.What is the 18th term of the AP 20, 24, 28, 32, …? (a) 92 (b) 72 (c) 68 (d) 88
  34. 34.What is the sum of the first 8 terms of the AP 8, 9, 10, …? (a) 15 (b) 96 (c) 184 (d) 92
  35. 35.What is the 28th term of the AP 1, 3, 5, 7, …? (a) 54 (b) 57 (c) 55 (d) 56
  36. 36.What is the 20th term of the AP 16, 19, 22, 25, …? (a) 57 (b) 73 (c) 76 (d) 60
  37. 37.What is the 15th term of the AP 5, 9, 13, 17, …? (a) 65 (b) 56 (c) 61 (d) 60
  38. 38.What is the missing term in the AP 15, 23, ?, 39, 47? (a) 32 (b) 30 (c) 31 (d) 39
  39. 39.What is the sum of the first 8 terms of the AP 4, 7, 10, …? (a) 25 (b) 116 (c) 128 (d) 232
  40. 40.What is the sum of the first 7 terms of the AP 2, 4, 6, …? (a) 56 (b) 14 (c) 63 (d) 112

Answer key

  1. 85
  2. 257
  3. 234
  4. 2556
  5. 112
  6. 22nd
  7. 20
  8. 100
  9. 17
  10. 625
  11. 146
  12. 21st
  13. 286
  14. 155
  15. 196
  16. 129
  17. 169
  18. 68
  19. 324
  20. 154
  21. 36
  22. 79
  23. 1275
  24. 30th
  25. 256
  26. 144
  27. 16th
  28. 8th
  29. 105
  30. 150
  31. 204
  32. 23
  33. 88
  34. 92
  35. 55
  36. 73
  37. 61
  38. 31
  39. 116
  40. 56

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