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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 248 · 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 19th term of the AP 3, 10, 17, 24, …? (a) 133 (b) 126 (c) 129 (d) 136
  2. 2.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 64 (b) 11 (c) 63 (d) 126
  3. 3.What is the sum of the first 6 terms of the AP 9, 15, 21, …? (a) 162 (b) 144 (c) 39 (d) 288
  4. 4.What is the 10th term of the AP 14, 16, 18, 20, …? (a) 18 (b) 20 (c) 34 (d) 32
  5. 5.What is the sum of the first 9 terms of the AP 8, 11, 14, …? (a) 180 (b) 360 (c) 32 (d) 183
  6. 6.Which term of the AP 8, 10, 12, 14, … is 86? (a) 40th (b) 41st (c) 39th (d) 43rd
  7. 7.Which term of the AP 9, 12, 15, 18, … is 51? (a) 15th (b) 16th (c) 17th (d) 14th
  8. 8.What is the sum of all the whole numbers from 1 to 45? (a) 2070 (b) 990 (c) 1036 (d) 1035
  9. 9.What is the 28th term of the AP 20, 28, 36, 44, …? (a) 244 (b) 236 (c) 216 (d) 224
  10. 10.Which term of the AP 4, 6, 8, 10, … is 80? (a) 38th (b) 40th (c) 39th (d) 41st
  11. 11.Which term of the AP 18, 24, 30, 36, … is 204? (a) 33rd (b) 31st (c) 34th (d) 32nd
  12. 12.What is the 20th term of the AP 6, 9, 12, 15, …? (a) 60 (b) 66 (c) 63 (d) 57
  13. 13.Which term of the AP 3, 9, 15, 21, … is 189? (a) 34th (b) 31st (c) 32nd (d) 33rd
  14. 14.What is the sum of the first 10 terms of the AP 4, 9, 14, …? (a) 265 (b) 290 (c) 530 (d) 49
  15. 15.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 43 (b) 500 (c) 250 (d) 270
  16. 16.What is the sum of the first 7 terms of the AP 9, 15, 21, …? (a) 210 (b) 45 (c) 189 (d) 378
  17. 17.Which term of the AP 17, 20, 23, 26, … is 98? (a) 29th (b) 28th (c) 27th (d) 30th
  18. 18.What is the 14th term of the AP 17, 22, 27, 32, …? (a) 87 (b) 65 (c) 82 (d) 70
  19. 19.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 45 (c) 17 (d) 90
  20. 20.What is the 23rd term of the AP 2, 7, 12, 17, …? (a) 117 (b) 115 (c) 112 (d) 110
  21. 21.What is the 33rd term of the AP 16, 20, 24, 28, …? (a) 128 (b) 144 (c) 132 (d) 148
  22. 22.What is the sum of the first 6 terms of the AP 5, 7, 9, …? (a) 60 (b) 15 (c) 120 (d) 66
  23. 23.What is the 37th term of the AP 13, 19, 25, 31, …? (a) 222 (b) 235 (c) 229 (d) 216
  24. 24.What is the 20th term of the AP 19, 27, 35, 43, …? (a) 160 (b) 152 (c) 179 (d) 171
  25. 25.What is the sum of all the whole numbers from 1 to 37? (a) 703 (b) 704 (c) 1406 (d) 666
  26. 26.What is the 34th term of the AP 20, 27, 34, 41, …? (a) 238 (b) 231 (c) 251 (d) 258
  27. 27.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 192 (b) 96 (c) 19 (d) 104
  28. 28.Which term of the AP 20, 26, 32, 38, … is 116? (a) 18th (b) 16th (c) 19th (d) 17th
  29. 29.What is the 36th term of the AP 6, 14, 22, 30, …? (a) 294 (b) 286 (c) 288 (d) 280
  30. 30.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 276 (c) 552 (d) 529
  31. 31.What is the 23rd term of the AP 12, 19, 26, 33, …? (a) 154 (b) 161 (c) 173 (d) 166
  32. 32.What is the missing term in the AP 9, ?, 13, 15, 17? (a) 12 (b) 10 (c) 13 (d) 11
  33. 33.What is the 28th term of the AP 6, 9, 12, 15, …? (a) 90 (b) 87 (c) 84 (d) 81
  34. 34.What is the 13th term of the AP 17, 21, 25, 29, …? (a) 65 (b) 52 (c) 48 (d) 69
  35. 35.What is the sum of the first 5 terms of the AP 2, 5, 8, …? (a) 80 (b) 43 (c) 40 (d) 14
  36. 36.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 576 (b) 47 (c) 600 (d) 300
  37. 37.What is the missing term in the AP 6, 14, ?, 30, 38? (a) 21 (b) 22 (c) 30 (d) 23
  38. 38.What is the sum of all the whole numbers from 1 to 12? (a) 78 (b) 72 (c) 66 (d) 156
  39. 39.What is the sum of all the whole numbers from 1 to 25? (a) 650 (b) 326 (c) 325 (d) 300
  40. 40.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 144 (b) 73 (c) 12 (d) 72

Answer key

  1. 129
  2. 63
  3. 144
  4. 32
  5. 180
  6. 40th
  7. 15th
  8. 1035
  9. 236
  10. 39th
  11. 32nd
  12. 63
  13. 32nd
  14. 265
  15. 250
  16. 189
  17. 28th
  18. 82
  19. 81
  20. 112
  21. 144
  22. 60
  23. 229
  24. 171
  25. 703
  26. 251
  27. 96
  28. 17th
  29. 286
  30. 529
  31. 166
  32. 11
  33. 87
  34. 65
  35. 40
  36. 576
  37. 22
  38. 78
  39. 325
  40. 72

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