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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 380 · 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 missing term in the AP 5, 12, ?, 26, 33? (a) 18 (b) 26 (c) 19 (d) 20
  2. 2.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 144 (c) 23 (d) 78
  3. 3.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 66 (b) 132 (c) 78 (d) 21
  4. 4.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 132 (c) 21 (d) 121
  5. 5.Which term of the AP 12, 16, 20, 24, … is 160? (a) 38th (b) 39th (c) 40th (d) 37th
  6. 6.What is the sum of all the whole numbers from 1 to 99? (a) 9900 (b) 4851 (c) 4951 (d) 4950
  7. 7.What is the 15th term of the AP 18, 24, 30, 36, …? (a) 108 (b) 102 (c) 84 (d) 90
  8. 8.What is the 21st term of the AP 4, 6, 8, 10, …? (a) 44 (b) 42 (c) 40 (d) 46
  9. 9.What is the sum of the first 5 terms of the AP 2, 8, 14, …? (a) 85 (b) 140 (c) 70 (d) 26
  10. 10.What is the 10th term of the AP 14, 18, 22, 26, …? (a) 40 (b) 50 (c) 54 (d) 36
  11. 11.What is the 15th term of the AP 17, 19, 21, 23, …? (a) 28 (b) 47 (c) 45 (d) 30
  12. 12.Which term of the AP 12, 18, 24, 30, … is 60? (a) 11th (b) 10th (c) 9th (d) 8th
  13. 13.What is the 25th term of the AP 11, 16, 21, 26, …? (a) 125 (b) 120 (c) 136 (d) 131
  14. 14.What is the 32nd term of the AP 20, 22, 24, 26, …? (a) 64 (b) 62 (c) 84 (d) 82
  15. 15.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 3906 (c) 1953 (d) 1891
  16. 16.What is the missing term in the AP 15, 21, ?, 33, 39? (a) 33 (b) 26 (c) 27 (d) 28
  17. 17.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 42 (b) 36 (c) 72 (d) 11
  18. 18.What is the 25th term of the AP 14, 23, 32, 41, …? (a) 239 (b) 230 (c) 216 (d) 225
  19. 19.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 841 (b) 435 (c) 870 (d) 57
  20. 20.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 34 (b) 320 (c) 176 (d) 160
  21. 21.Which term of the AP 15, 24, 33, 42, … is 159? (a) 18th (b) 16th (c) 17th (d) 19th
  22. 22.What is the sum of the first 12 terms of the AP 1, 5, 9, …? (a) 276 (b) 300 (c) 552 (d) 45
  23. 23.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 240 (c) 120 (d) 225
  24. 24.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 4 (b) 7 (c) 6 (d) 5
  25. 25.Which term of the AP 8, 17, 26, 35, … is 143? (a) 15th (b) 17th (c) 16th (d) 18th
  26. 26.What is the 15th term of the AP 11, 17, 23, 29, …? (a) 95 (b) 101 (c) 90 (d) 84
  27. 27.What is the 32nd term of the AP 16, 22, 28, 34, …? (a) 186 (b) 192 (c) 202 (d) 208
  28. 28.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 64 (b) 15 (c) 36 (d) 72
  29. 29.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 324 (c) 171 (d) 342
  30. 30.What is the 39th term of the AP 18, 24, 30, 36, …? (a) 246 (b) 252 (c) 228 (d) 234
  31. 31.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 55 (c) 110 (d) 19
  32. 32.What is the missing term in the AP 18, ?, 34, 42, 50? (a) 25 (b) 27 (c) 26 (d) 34
  33. 33.What is the 18th term of the AP 6, 13, 20, 27, …? (a) 126 (b) 119 (c) 125 (d) 132
  34. 34.What is the 33rd term of the AP 10, 15, 20, 25, …? (a) 160 (b) 165 (c) 175 (d) 170
  35. 35.What is the 23rd term of the AP 3, 5, 7, 9, …? (a) 49 (b) 47 (c) 46 (d) 44
  36. 36.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 33 (b) 198 (c) 201 (d) 396
  37. 37.What is the sum of all the whole numbers from 1 to 15? (a) 120 (b) 240 (c) 105 (d) 121
  38. 38.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 729 (c) 53 (d) 378
  39. 39.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 306 (c) 153 (d) 289
  40. 40.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 120 (b) 22 (c) 128 (d) 240

Answer key

  1. 19
  2. 144
  3. 66
  4. 121
  5. 38th
  6. 4950
  7. 102
  8. 44
  9. 70
  10. 50
  11. 45
  12. 9th
  13. 131
  14. 82
  15. 1953
  16. 27
  17. 36
  18. 230
  19. 841
  20. 160
  21. 17th
  22. 276
  23. 225
  24. 5
  25. 16th
  26. 95
  27. 202
  28. 64
  29. 324
  30. 246
  31. 100
  32. 26
  33. 125
  34. 170
  35. 47
  36. 198
  37. 120
  38. 729
  39. 289
  40. 120

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