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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 837 · 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 27th term of the AP 10, 16, 22, 28, …? (a) 156 (b) 166 (c) 172 (d) 162
  2. 2.What is the 21st term of the AP 8, 12, 16, 20, …? (a) 92 (b) 80 (c) 88 (d) 84
  3. 3.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 650 (c) 49 (d) 625
  4. 4.What is the 39th term of the AP 4, 12, 20, 28, …? (a) 308 (b) 304 (c) 312 (d) 316
  5. 5.What is the 24th term of the AP 6, 11, 16, 21, …? (a) 126 (b) 120 (c) 115 (d) 121
  6. 6.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 99 (b) 24 (c) 108 (d) 198
  7. 7.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 480 (b) 240 (c) 42 (d) 260
  8. 8.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 45 (c) 81 (d) 17
  9. 9.What is the 37th term of the AP 1, 9, 17, 25, …? (a) 296 (b) 289 (c) 297 (d) 288
  10. 10.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 144 (c) 78 (d) 156
  11. 11.What is the sum of the first 11 terms of the AP 7, 8, 9, …? (a) 133 (b) 264 (c) 132 (d) 17
  12. 12.What is the 25th term of the AP 18, 20, 22, 24, …? (a) 66 (b) 50 (c) 48 (d) 68
  13. 13.What is the missing term in the AP 7, 12, 17, ?, 27? (a) 21 (b) 22 (c) 27 (d) 23
  14. 14.What is the 35th term of the AP 4, 6, 8, 10, …? (a) 70 (b) 72 (c) 68 (d) 74
  15. 15.What is the 36th term of the AP 16, 23, 30, 37, …? (a) 268 (b) 245 (c) 252 (d) 261
  16. 16.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 174 (b) 102 (c) 27 (d) 87
  17. 17.What is the sum of the first 9 terms of the AP 8, 14, 20, …? (a) 576 (b) 315 (c) 288 (d) 56
  18. 18.What is the 39th term of the AP 9, 14, 19, 24, …? (a) 199 (b) 190 (c) 204 (d) 195
  19. 19.What is the sum of the first 6 terms of the AP 1, 4, 7, …? (a) 16 (b) 60 (c) 51 (d) 102
  20. 20.What is the sum of all the whole numbers from 1 to 34? (a) 578 (b) 561 (c) 595 (d) 1190
  21. 21.Which term of the AP 15, 18, 21, 24, … is 66? (a) 17th (b) 18th (c) 22nd (d) 19th
  22. 22.What is the 11th term of the AP 9, 15, 21, 27, …? (a) 66 (b) 75 (c) 69 (d) 60
  23. 23.What is the missing term in the AP 8, 13, ?, 23, 28? (a) 23 (b) 18 (c) 17 (d) 19
  24. 24.What is the sum of all the whole numbers from 1 to 92? (a) 4278 (b) 8556 (c) 4186 (d) 4232
  25. 25.Which term of the AP 12, 20, 28, 36, … is 292? (a) 36th (b) 35th (c) 37th (d) 38th
  26. 26.What is the 36th term of the AP 4, 11, 18, 25, …? (a) 252 (b) 245 (c) 249 (d) 256
  27. 27.What is the sum of all the whole numbers from 1 to 41? (a) 820 (b) 1722 (c) 861 (d) 862
  28. 28.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 171 (c) 35 (d) 342
  29. 29.What is the 22nd term of the AP 16, 20, 24, 28, …? (a) 88 (b) 100 (c) 104 (d) 84
  30. 30.What is the 32nd term of the AP 16, 20, 24, 28, …? (a) 144 (b) 140 (c) 128 (d) 124
  31. 31.What is the sum of the first 12 terms of the AP 1, 5, 9, …? (a) 552 (b) 300 (c) 276 (d) 45
  32. 32.What is the sum of the first 7 terms of the AP 6, 10, 14, …? (a) 252 (b) 30 (c) 140 (d) 126
  33. 33.What is the missing term in the AP 16, 24, ?, 40, 48? (a) 33 (b) 31 (c) 40 (d) 32
  34. 34.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 55 (d) 100
  35. 35.What is the sum of the first 8 terms of the AP 8, 14, 20, …? (a) 50 (b) 256 (c) 232 (d) 464
  36. 36.What is the 17th term of the AP 2, 8, 14, 20, …? (a) 102 (b) 96 (c) 104 (d) 98
  37. 37.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 28 (b) 216 (c) 108 (d) 120
  38. 38.What is the 21st term of the AP 12, 14, 16, 18, …? (a) 52 (b) 54 (c) 40 (d) 42
  39. 39.What is the sum of the first 10 terms of the AP 7, 8, 9, …? (a) 120 (b) 16 (c) 230 (d) 115
  40. 40.What is the missing term in the AP 18, 24, ?, 36, 42? (a) 29 (b) 31 (c) 36 (d) 30

Answer key

  1. 166
  2. 88
  3. 625
  4. 308
  5. 121
  6. 99
  7. 240
  8. 81
  9. 289
  10. 144
  11. 132
  12. 66
  13. 22
  14. 72
  15. 261
  16. 87
  17. 288
  18. 199
  19. 51
  20. 595
  21. 18th
  22. 69
  23. 18
  24. 4278
  25. 36th
  26. 249
  27. 861
  28. 324
  29. 100
  30. 140
  31. 276
  32. 126
  33. 32
  34. 100
  35. 232
  36. 98
  37. 108
  38. 52
  39. 115
  40. 30

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