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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 91 · 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 17th term of the AP 12, 14, 16, 18, …? (a) 34 (b) 46 (c) 44 (d) 32
  2. 2.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 63 (b) 12 (c) 126 (d) 64
  3. 3.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 36 (c) 42 (d) 21
  4. 4.What is the sum of the first 12 terms of the AP 3, 7, 11, …? (a) 324 (b) 600 (c) 300 (d) 47
  5. 5.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 552 (d) 529
  6. 6.What is the missing term in the AP 1, ?, 15, 22, 29? (a) 8 (b) 15 (c) 9 (d) 7
  7. 7.What is the sum of the first 7 terms of the AP 1, 4, 7, …? (a) 140 (b) 73 (c) 70 (d) 19
  8. 8.Which term of the AP 7, 10, 13, 16, … is 94? (a) 31st (b) 29th (c) 32nd (d) 30th
  9. 9.What is the missing term in the AP 1, 6, 11, ?, 21? (a) 17 (b) 16 (c) 15 (d) 21
  10. 10.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 180 (b) 13 (c) 96 (d) 90
  11. 11.What is the 28th term of the AP 9, 12, 15, 18, …? (a) 90 (b) 81 (c) 84 (d) 93
  12. 12.What is the sum of the first 6 terms of the AP 9, 14, 19, …? (a) 34 (b) 144 (c) 129 (d) 258
  13. 13.What is the sum of the first 12 terms of the AP 3, 9, 15, …? (a) 432 (b) 468 (c) 864 (d) 69
  14. 14.What is the 36th term of the AP 19, 22, 25, 28, …? (a) 105 (b) 127 (c) 108 (d) 124
  15. 15.What is the missing term in the AP 7, ?, 11, 13, 15? (a) 10 (b) 8 (c) 11 (d) 9
  16. 16.What is the 18th term of the AP 3, 11, 19, 27, …? (a) 147 (b) 136 (c) 144 (d) 139
  17. 17.What is the 24th term of the AP 2, 11, 20, 29, …? (a) 218 (b) 209 (c) 216 (d) 207
  18. 18.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 270 (b) 490 (c) 47 (d) 245
  19. 19.What is the 22nd term of the AP 17, 21, 25, 29, …? (a) 88 (b) 101 (c) 105 (d) 84
  20. 20.What is the missing term in the AP 5, 10, 15, ?, 25? (a) 21 (b) 20 (c) 19 (d) 25
  21. 21.What is the 27th term of the AP 8, 11, 14, 17, …? (a) 78 (b) 81 (c) 89 (d) 86
  22. 22.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 784 (c) 406 (d) 55
  23. 23.What is the 21st term of the AP 17, 24, 31, 38, …? (a) 164 (b) 157 (c) 147 (d) 140
  24. 24.What is the sum of all the whole numbers from 1 to 97? (a) 4753 (b) 9506 (c) 4656 (d) 4754
  25. 25.What is the 31st term of the AP 20, 23, 26, 29, …? (a) 93 (b) 110 (c) 90 (d) 113
  26. 26.What is the missing term in the AP 14, 16, 18, ?, 22? (a) 22 (b) 20 (c) 21 (d) 19
  27. 27.What is the missing term in the AP 19, 26, ?, 40, 47? (a) 34 (b) 33 (c) 40 (d) 32
  28. 28.What is the 30th term of the AP 15, 21, 27, 33, …? (a) 195 (b) 174 (c) 180 (d) 189
  29. 29.What is the missing term in the AP 14, ?, 30, 38, 46? (a) 30 (b) 23 (c) 21 (d) 22
  30. 30.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 28 (c) 56 (d) 49
  31. 31.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 3200 (c) 3240 (d) 6480
  32. 32.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 9 (b) 45 (c) 90 (d) 46
  33. 33.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 289 (c) 33 (d) 306
  34. 34.What is the sum of the first 9 terms of the AP 2, 7, 12, …? (a) 42 (b) 203 (c) 396 (d) 198
  35. 35.What is the sum of all the whole numbers from 1 to 31? (a) 496 (b) 497 (c) 992 (d) 465
  36. 36.What is the sum of the first 7 terms of the AP 6, 8, 10, …? (a) 84 (b) 168 (c) 18 (d) 91
  37. 37.What is the 27th term of the AP 1, 4, 7, 10, …? (a) 79 (b) 78 (c) 81 (d) 82
  38. 38.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 91 (c) 169 (d) 182
  39. 39.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 1226 (c) 2450 (d) 1225
  40. 40.What is the 13th term of the AP 20, 24, 28, 32, …? (a) 48 (b) 72 (c) 52 (d) 68

Answer key

  1. 44
  2. 63
  3. 36
  4. 300
  5. 529
  6. 8
  7. 70
  8. 30th
  9. 16
  10. 90
  11. 90
  12. 129
  13. 432
  14. 124
  15. 9
  16. 139
  17. 209
  18. 245
  19. 101
  20. 20
  21. 86
  22. 784
  23. 157
  24. 4753
  25. 110
  26. 20
  27. 33
  28. 189
  29. 22
  30. 49
  31. 3240
  32. 45
  33. 289
  34. 198
  35. 496
  36. 84
  37. 79
  38. 169
  39. 1225
  40. 68

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