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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 597 · 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 12 terms of the AP 8, 11, 14, …? (a) 588 (b) 294 (c) 41 (d) 312
  2. 2.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 625 (b) 650 (c) 325 (d) 49
  3. 3.What is the 24th term of the AP 8, 10, 12, 14, …? (a) 56 (b) 48 (c) 46 (d) 54
  4. 4.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 441 (d) 231
  5. 5.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 42 (b) 36 (c) 11 (d) 72
  6. 6.Which term of the AP 11, 16, 21, 26, … is 196? (a) 40th (b) 39th (c) 37th (d) 38th
  7. 7.Which term of the AP 6, 8, 10, 12, … is 44? (a) 20th (b) 21st (c) 22nd (d) 19th
  8. 8.What is the sum of the first 10 terms of the AP 1, 4, 7, …? (a) 290 (b) 28 (c) 160 (d) 145
  9. 9.What is the missing term in the AP 8, ?, 12, 14, 16? (a) 9 (b) 12 (c) 11 (d) 10
  10. 10.What is the 11th term of the AP 10, 14, 18, 22, …? (a) 40 (b) 44 (c) 54 (d) 50
  11. 11.What is the 32nd term of the AP 9, 13, 17, 21, …? (a) 137 (b) 133 (c) 124 (d) 128
  12. 12.What is the 22nd term of the AP 6, 13, 20, 27, …? (a) 147 (b) 160 (c) 153 (d) 154
  13. 13.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 176 (b) 187 (c) 352 (d) 26
  14. 14.What is the 15th term of the AP 4, 8, 12, 16, …? (a) 56 (b) 64 (c) 60 (d) 61
  15. 15.What is the 30th term of the AP 12, 20, 28, 36, …? (a) 232 (b) 240 (c) 252 (d) 244
  16. 16.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 380 (c) 361 (d) 37
  17. 17.What is the missing term in the AP 8, 15, 22, ?, 36? (a) 36 (b) 30 (c) 28 (d) 29
  18. 18.What is the 31st term of the AP 12, 19, 26, 33, …? (a) 217 (b) 229 (c) 210 (d) 222
  19. 19.What is the sum of all the whole numbers from 1 to 63? (a) 1953 (b) 2017 (c) 4032 (d) 2016
  20. 20.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 90 (d) 81
  21. 21.What is the missing term in the AP 20, ?, 38, 47, 56? (a) 29 (b) 30 (c) 38 (d) 28
  22. 22.What is the missing term in the AP 14, 21, 28, ?, 42? (a) 35 (b) 36 (c) 42 (d) 34
  23. 23.Which term of the AP 5, 14, 23, 32, … is 221? (a) 25th (b) 27th (c) 26th (d) 24th
  24. 24.What is the 18th term of the AP 11, 15, 19, 23, …? (a) 79 (b) 68 (c) 83 (d) 72
  25. 25.What is the 23rd term of the AP 16, 22, 28, 34, …? (a) 132 (b) 138 (c) 148 (d) 154
  26. 26.What is the 13th term of the AP 7, 14, 21, 28, …? (a) 98 (b) 92 (c) 84 (d) 91
  27. 27.What is the 14th term of the AP 5, 9, 13, 17, …? (a) 56 (b) 52 (c) 57 (d) 61
  28. 28.What is the sum of the first 11 terms of the AP 5, 8, 11, …? (a) 220 (b) 440 (c) 35 (d) 223
  29. 29.Which term of the AP 17, 21, 25, 29, … is 89? (a) 18th (b) 21st (c) 20th (d) 19th
  30. 30.What is the sum of the first 12 terms of the AP 1, 2, 3, …? (a) 78 (b) 84 (c) 156 (d) 12
  31. 31.What is the sum of the first 9 terms of the AP 9, 12, 15, …? (a) 189 (b) 192 (c) 33 (d) 378
  32. 32.What is the sum of all the whole numbers from 1 to 87? (a) 3741 (b) 3828 (c) 3829 (d) 7656
  33. 33.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 78 (b) 90 (c) 156 (d) 23
  34. 34.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 96 (b) 26 (c) 192 (d) 108
  35. 35.What is the 15th term of the AP 12, 19, 26, 33, …? (a) 105 (b) 110 (c) 98 (d) 117
  36. 36.Which term of the AP 17, 20, 23, 26, … is 56? (a) 15th (b) 13th (c) 16th (d) 14th
  37. 37.What is the 15th term of the AP 20, 26, 32, 38, …? (a) 110 (b) 84 (c) 90 (d) 104
  38. 38.What is the missing term in the AP 15, 23, 31, ?, 47? (a) 38 (b) 39 (c) 47 (d) 40
  39. 39.What is the 34th term of the AP 6, 8, 10, 12, …? (a) 66 (b) 74 (c) 72 (d) 68
  40. 40.What is the 17th term of the AP 14, 22, 30, 38, …? (a) 150 (b) 136 (c) 128 (d) 142

Answer key

  1. 294
  2. 625
  3. 54
  4. 441
  5. 36
  6. 38th
  7. 20th
  8. 145
  9. 10
  10. 50
  11. 133
  12. 153
  13. 176
  14. 60
  15. 244
  16. 361
  17. 29
  18. 222
  19. 2016
  20. 81
  21. 29
  22. 35
  23. 25th
  24. 79
  25. 148
  26. 91
  27. 57
  28. 220
  29. 19th
  30. 78
  31. 189
  32. 3828
  33. 78
  34. 96
  35. 110
  36. 14th
  37. 104
  38. 39
  39. 72
  40. 142

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