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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 432 · 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 all the whole numbers from 1 to 66? (a) 4422 (b) 2145 (c) 2211 (d) 2178
  2. 2.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 196 (c) 105 (d) 210
  3. 3.What is the 24th term of the AP 6, 12, 18, 24, …? (a) 138 (b) 144 (c) 150 (d) 145
  4. 4.Which term of the AP 11, 13, 15, 17, … is 71? (a) 33rd (b) 32nd (c) 31st (d) 30th
  5. 5.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 276 (c) 45 (d) 529
  6. 6.What is the sum of all the whole numbers from 1 to 41? (a) 820 (b) 862 (c) 1722 (d) 861
  7. 7.What is the 38th term of the AP 7, 10, 13, 16, …? (a) 121 (b) 114 (c) 111 (d) 118
  8. 8.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 286 (b) 143 (c) 154 (d) 23
  9. 9.What is the 26th term of the AP 12, 17, 22, 27, …? (a) 142 (b) 137 (c) 125 (d) 130
  10. 10.What is the 18th term of the AP 20, 24, 28, 32, …? (a) 68 (b) 72 (c) 92 (d) 88
  11. 11.What is the missing term in the AP 9, 18, ?, 36, 45? (a) 28 (b) 26 (c) 27 (d) 36
  12. 12.What is the sum of the first 10 terms of the AP 1, 7, 13, …? (a) 310 (b) 560 (c) 55 (d) 280
  13. 13.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 65 (b) 11 (c) 70 (d) 130
  14. 14.What is the sum of the first 6 terms of the AP 1, 2, 3, …? (a) 21 (b) 6 (c) 24 (d) 42
  15. 15.What is the missing term in the AP 14, 22, ?, 38, 46? (a) 38 (b) 29 (c) 30 (d) 31
  16. 16.Which term of the AP 18, 25, 32, 39, … is 123? (a) 17th (b) 18th (c) 16th (d) 15th
  17. 17.Which term of the AP 2, 6, 10, 14, … is 50? (a) 12th (b) 15th (c) 13th (d) 14th
  18. 18.Which term of the AP 3, 11, 19, 27, … is 299? (a) 39th (b) 40th (c) 37th (d) 38th
  19. 19.What is the 15th term of the AP 19, 26, 33, 40, …? (a) 124 (b) 98 (c) 117 (d) 105
  20. 20.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 406 (c) 812 (d) 55
  21. 21.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 136 (c) 256 (d) 31
  22. 22.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 25 (b) 130 (c) 80 (d) 65
  23. 23.What is the 12th term of the AP 11, 15, 19, 23, …? (a) 55 (b) 48 (c) 44 (d) 59
  24. 24.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 252 (b) 127 (c) 18 (d) 126
  25. 25.What is the 27th term of the AP 3, 10, 17, 24, …? (a) 192 (b) 185 (c) 189 (d) 182
  26. 26.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 11 (b) 46 (c) 90 (d) 45
  27. 27.What is the missing term in the AP 4, ?, 8, 10, 12? (a) 5 (b) 7 (c) 8 (d) 6
  28. 28.What is the missing term in the AP 5, 13, ?, 29, 37? (a) 22 (b) 20 (c) 29 (d) 21
  29. 29.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 171 (c) 35 (d) 324
  30. 30.What is the 12th term of the AP 9, 18, 27, 36, …? (a) 99 (b) 109 (c) 108 (d) 117
  31. 31.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 121 (c) 132 (d) 66
  32. 32.What is the 16th term of the AP 2, 8, 14, 20, …? (a) 90 (b) 98 (c) 96 (d) 92
  33. 33.What is the 25th term of the AP 5, 9, 13, 17, …? (a) 105 (b) 96 (c) 101 (d) 100
  34. 34.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 182 (c) 91 (d) 169
  35. 35.What is the missing term in the AP 2, ?, 14, 20, 26? (a) 14 (b) 9 (c) 8 (d) 7
  36. 36.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1653 (c) 1682 (d) 1711
  37. 37.What is the sum of the first 12 terms of the AP 8, 13, 18, …? (a) 426 (b) 456 (c) 63 (d) 852
  38. 38.What is the sum of the first 6 terms of the AP 10, 15, 20, …? (a) 35 (b) 270 (c) 150 (d) 135
  39. 39.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 72 (b) 64 (c) 128 (d) 15
  40. 40.What is the 17th term of the AP 6, 13, 20, 27, …? (a) 119 (b) 112 (c) 118 (d) 125

Answer key

  1. 2211
  2. 196
  3. 144
  4. 31st
  5. 529
  6. 861
  7. 118
  8. 143
  9. 137
  10. 88
  11. 27
  12. 280
  13. 65
  14. 21
  15. 30
  16. 16th
  17. 13th
  18. 38th
  19. 117
  20. 784
  21. 256
  22. 65
  23. 55
  24. 126
  25. 185
  26. 45
  27. 6
  28. 21
  29. 324
  30. 108
  31. 121
  32. 92
  33. 101
  34. 169
  35. 8
  36. 1711
  37. 426
  38. 135
  39. 64
  40. 118

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