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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 970 · 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 the first 8 terms of the AP 2, 7, 12, …? (a) 312 (b) 176 (c) 37 (d) 156
  2. 2.What is the missing term in the AP 10, 17, 24, ?, 38? (a) 31 (b) 38 (c) 30 (d) 32
  3. 3.What is the 35th term of the AP 7, 9, 11, 13, …? (a) 70 (b) 75 (c) 68 (d) 77
  4. 4.Which term of the AP 10, 16, 22, 28, … is 112? (a) 17th (b) 20th (c) 18th (d) 19th
  5. 5.Which term of the AP 17, 24, 31, 38, … is 73? (a) 8th (b) 10th (c) 9th (d) 11th
  6. 6.What is the 39th term of the AP 6, 9, 12, 15, …? (a) 120 (b) 114 (c) 123 (d) 117
  7. 7.What is the sum of all the whole numbers from 1 to 91? (a) 4095 (b) 8372 (c) 4187 (d) 4186
  8. 8.What is the 16th term of the AP 18, 25, 32, 39, …? (a) 123 (b) 112 (c) 130 (d) 105
  9. 9.What is the 35th term of the AP 11, 18, 25, 32, …? (a) 238 (b) 249 (c) 256 (d) 245
  10. 10.What is the 16th term of the AP 20, 28, 36, 44, …? (a) 140 (b) 128 (c) 120 (d) 148
  11. 11.Which term of the AP 17, 21, 25, 29, … is 133? (a) 30th (b) 31st (c) 32nd (d) 29th
  12. 12.What is the 40th term of the AP 9, 15, 21, 27, …? (a) 243 (b) 240 (c) 234 (d) 249
  13. 13.What is the sum of all the whole numbers from 1 to 63? (a) 4032 (b) 1953 (c) 2016 (d) 2017
  14. 14.Which term of the AP 5, 8, 11, 14, … is 47? (a) 14th (b) 17th (c) 15th (d) 16th
  15. 15.What is the missing term in the AP 5, ?, 13, 17, 21? (a) 9 (b) 8 (c) 10 (d) 13
  16. 16.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 140 (b) 18 (c) 135 (d) 270
  17. 17.What is the 28th term of the AP 1, 8, 15, 22, …? (a) 189 (b) 197 (c) 190 (d) 196
  18. 18.What is the 18th term of the AP 17, 23, 29, 35, …? (a) 125 (b) 108 (c) 119 (d) 102
  19. 19.What is the 36th term of the AP 2, 9, 16, 23, …? (a) 254 (b) 247 (c) 252 (d) 245
  20. 20.What is the 40th term of the AP 9, 16, 23, 30, …? (a) 282 (b) 273 (c) 289 (d) 280
  21. 21.What is the missing term in the AP 8, 14, 20, ?, 32? (a) 25 (b) 32 (c) 26 (d) 27
  22. 22.What is the 21st term of the AP 4, 11, 18, 25, …? (a) 140 (b) 147 (c) 151 (d) 144
  23. 23.What is the 20th term of the AP 4, 9, 14, 19, …? (a) 100 (b) 104 (c) 95 (d) 99
  24. 24.What is the sum of the first 11 terms of the AP 6, 9, 12, …? (a) 462 (b) 36 (c) 234 (d) 231
  25. 25.What is the 12th term of the AP 8, 12, 16, 20, …? (a) 56 (b) 48 (c) 52 (d) 44
  26. 26.What is the sum of the first 10 terms of the AP 1, 3, 5, …? (a) 19 (b) 100 (c) 110 (d) 200
  27. 27.What is the 34th term of the AP 13, 19, 25, 31, …? (a) 217 (b) 198 (c) 211 (d) 204
  28. 28.What is the 12th term of the AP 13, 15, 17, 19, …? (a) 35 (b) 37 (c) 22 (d) 24
  29. 29.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 363 (b) 58 (c) 368 (d) 726
  30. 30.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 2485 (c) 2415 (d) 4970
  31. 31.What is the 20th term of the AP 17, 22, 27, 32, …? (a) 112 (b) 117 (c) 100 (d) 95
  32. 32.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 126 (b) 63 (c) 64 (d) 12
  33. 33.What is the sum of the first 12 terms of the AP 5, 9, 13, …? (a) 348 (b) 49 (c) 324 (d) 648
  34. 34.What is the 39th term of the AP 9, 16, 23, 30, …? (a) 282 (b) 273 (c) 266 (d) 275
  35. 35.Which term of the AP 1, 4, 7, 10, … is 46? (a) 15th (b) 18th (c) 16th (d) 17th
  36. 36.What is the 20th term of the AP 18, 20, 22, 24, …? (a) 56 (b) 38 (c) 40 (d) 58
  37. 37.Which term of the AP 20, 28, 36, 44, … is 188? (a) 22nd (b) 23rd (c) 24th (d) 21st
  38. 38.What is the 34th term of the AP 11, 19, 27, 35, …? (a) 275 (b) 272 (c) 283 (d) 264
  39. 39.What is the 21st term of the AP 9, 13, 17, 21, …? (a) 89 (b) 80 (c) 93 (d) 84
  40. 40.What is the sum of all the whole numbers from 1 to 56? (a) 1540 (b) 3192 (c) 1596 (d) 1568

Answer key

  1. 156
  2. 31
  3. 75
  4. 18th
  5. 9th
  6. 120
  7. 4186
  8. 123
  9. 249
  10. 140
  11. 30th
  12. 243
  13. 2016
  14. 15th
  15. 9
  16. 135
  17. 190
  18. 119
  19. 247
  20. 282
  21. 26
  22. 144
  23. 99
  24. 231
  25. 52
  26. 100
  27. 211
  28. 35
  29. 363
  30. 2485
  31. 112
  32. 63
  33. 324
  34. 275
  35. 16th
  36. 56
  37. 22nd
  38. 275
  39. 89
  40. 1596

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