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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 517 · 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 33rd term of the AP 6, 9, 12, 15, …? (a) 102 (b) 96 (c) 105 (d) 99
  2. 2.What is the 33rd term of the AP 20, 22, 24, 26, …? (a) 86 (b) 66 (c) 84 (d) 64
  3. 3.What is the missing term in the AP 14, ?, 26, 32, 38? (a) 21 (b) 26 (c) 20 (d) 19
  4. 4.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 324 (c) 342 (d) 35
  5. 5.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 600 (b) 300 (c) 47 (d) 576
  6. 6.What is the 17th term of the AP 2, 9, 16, 23, …? (a) 114 (b) 112 (c) 121 (d) 119
  7. 7.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 50 (b) 100 (c) 55 (d) 14
  8. 8.What is the missing term in the AP 5, 13, ?, 29, 37? (a) 20 (b) 29 (c) 22 (d) 21
  9. 9.What is the sum of the first 10 terms of the AP 5, 10, 15, …? (a) 50 (b) 550 (c) 300 (d) 275
  10. 10.Which term of the AP 12, 16, 20, 24, … is 96? (a) 21st (b) 23rd (c) 24th (d) 22nd
  11. 11.Which term of the AP 15, 24, 33, 42, … is 132? (a) 15th (b) 13th (c) 16th (d) 14th
  12. 12.What is the sum of all the whole numbers from 1 to 94? (a) 8930 (b) 4371 (c) 4465 (d) 4418
  13. 13.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 12 (b) 45 (c) 80 (d) 40
  14. 14.What is the 27th term of the AP 5, 11, 17, 23, …? (a) 167 (b) 162 (c) 156 (d) 161
  15. 15.Which term of the AP 12, 18, 24, 30, … is 72? (a) 13th (b) 11th (c) 12th (d) 10th
  16. 16.What is the sum of all the whole numbers from 1 to 59? (a) 3540 (b) 1771 (c) 1770 (d) 1711
  17. 17.Which term of the AP 14, 22, 30, 38, … is 318? (a) 38th (b) 41st (c) 39th (d) 40th
  18. 18.What is the missing term in the AP 18, ?, 22, 24, 26? (a) 22 (b) 20 (c) 21 (d) 19
  19. 19.What is the 19th term of the AP 18, 27, 36, 45, …? (a) 189 (b) 180 (c) 171 (d) 162
  20. 20.What is the 26th term of the AP 2, 10, 18, 26, …? (a) 208 (b) 202 (c) 200 (d) 210
  21. 21.What is the 31st term of the AP 5, 10, 15, 20, …? (a) 160 (b) 150 (c) 156 (d) 155
  22. 22.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 108 (b) 26 (c) 96 (d) 192
  23. 23.What is the 20th term of the AP 16, 23, 30, 37, …? (a) 133 (b) 149 (c) 140 (d) 156
  24. 24.What is the sum of all the whole numbers from 1 to 13? (a) 91 (b) 92 (c) 182 (d) 78
  25. 25.What is the sum of all the whole numbers from 1 to 37? (a) 666 (b) 703 (c) 1406 (d) 704
  26. 26.What is the missing term in the AP 17, 21, ?, 29, 33? (a) 29 (b) 24 (c) 26 (d) 25
  27. 27.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 59 (c) 900 (d) 465
  28. 28.Which term of the AP 14, 22, 30, 38, … is 70? (a) 8th (b) 10th (c) 9th (d) 7th
  29. 29.What is the missing term in the AP 4, 6, 8, ?, 12? (a) 9 (b) 12 (c) 11 (d) 10
  30. 30.What is the 27th term of the AP 13, 20, 27, 34, …? (a) 195 (b) 189 (c) 182 (d) 202
  31. 31.What is the sum of the first 11 terms of the AP 4, 6, 8, …? (a) 165 (b) 308 (c) 154 (d) 24
  32. 32.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 638 (b) 319 (c) 49 (d) 341
  33. 33.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 60 (b) 61 (c) 14 (d) 120
  34. 34.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 20 (b) 180 (c) 174 (d) 348
  35. 35.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 17 (c) 81 (d) 45
  36. 36.What is the sum of all the whole numbers from 1 to 69? (a) 2416 (b) 2346 (c) 2415 (d) 4830
  37. 37.What is the 28th term of the AP 19, 23, 27, 31, …? (a) 127 (b) 131 (c) 112 (d) 108
  38. 38.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 75 (b) 1008 (c) 504 (d) 540
  39. 39.What is the 19th term of the AP 1, 8, 15, 22, …? (a) 134 (b) 133 (c) 127 (d) 126
  40. 40.What is the 16th term of the AP 19, 22, 25, 28, …? (a) 64 (b) 45 (c) 67 (d) 48

Answer key

  1. 102
  2. 84
  3. 20
  4. 324
  5. 576
  6. 114
  7. 50
  8. 21
  9. 275
  10. 22nd
  11. 14th
  12. 4465
  13. 40
  14. 161
  15. 11th
  16. 1770
  17. 39th
  18. 20
  19. 180
  20. 202
  21. 155
  22. 96
  23. 149
  24. 91
  25. 703
  26. 25
  27. 900
  28. 8th
  29. 10
  30. 195
  31. 154
  32. 319
  33. 60
  34. 174
  35. 81
  36. 2415
  37. 127
  38. 504
  39. 127
  40. 64

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