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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 882 · 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.Which term of the AP 2, 10, 18, 26, … is 266? (a) 36th (b) 33rd (c) 35th (d) 34th
  2. 2.What is the missing term in the AP 10, ?, 14, 16, 18? (a) 11 (b) 12 (c) 14 (d) 13
  3. 3.Which term of the AP 4, 12, 20, 28, … is 140? (a) 18th (b) 17th (c) 19th (d) 20th
  4. 4.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 10 (b) 40 (c) 41 (d) 80
  5. 5.What is the sum of all the whole numbers from 1 to 98? (a) 4802 (b) 4753 (c) 9702 (d) 4851
  6. 6.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 256 (b) 253 (c) 38 (d) 506
  7. 7.What is the sum of all the whole numbers from 1 to 91? (a) 4095 (b) 8372 (c) 4186 (d) 4187
  8. 8.What is the sum of all the whole numbers from 1 to 13? (a) 182 (b) 92 (c) 78 (d) 91
  9. 9.What is the sum of the first 6 terms of the AP 6, 10, 14, …? (a) 192 (b) 108 (c) 96 (d) 26
  10. 10.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 45 (c) 552 (d) 529
  11. 11.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 108 (b) 24 (c) 105 (d) 210
  12. 12.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 110 (b) 111 (c) 220 (d) 15
  13. 13.What is the sum of the first 8 terms of the AP 2, 7, 12, …? (a) 176 (b) 37 (c) 156 (d) 312
  14. 14.What is the sum of all the whole numbers from 1 to 40? (a) 820 (b) 1640 (c) 780 (d) 800
  15. 15.What is the sum of the first 7 terms of the AP 6, 10, 14, …? (a) 252 (b) 126 (c) 140 (d) 30
  16. 16.Which term of the AP 3, 6, 9, 12, … is 27? (a) 9th (b) 8th (c) 10th (d) 11th
  17. 17.Which term of the AP 3, 11, 19, 27, … is 59? (a) 8th (b) 9th (c) 7th (d) 10th
  18. 18.What is the sum of all the whole numbers from 1 to 79? (a) 3081 (b) 6320 (c) 3160 (d) 3161
  19. 19.Which term of the AP 13, 15, 17, 19, … is 75? (a) 31st (b) 33rd (c) 34th (d) 32nd
  20. 20.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 153 (c) 289 (d) 33
  21. 21.What is the sum of the first 11 terms of the AP 3, 5, 7, …? (a) 23 (b) 286 (c) 143 (d) 154
  22. 22.Which term of the AP 17, 19, 21, 23, … is 73? (a) 30th (b) 29th (c) 28th (d) 31st
  23. 23.What is the 37th term of the AP 4, 9, 14, 19, …? (a) 185 (b) 184 (c) 180 (d) 189
  24. 24.What is the 20th term of the AP 15, 19, 23, 27, …? (a) 91 (b) 76 (c) 95 (d) 80
  25. 25.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 55 (c) 67 (d) 66
  26. 26.What is the 26th term of the AP 18, 27, 36, 45, …? (a) 225 (b) 234 (c) 252 (d) 243
  27. 27.Which term of the AP 2, 10, 18, 26, … is 226? (a) 31st (b) 28th (c) 29th (d) 30th
  28. 28.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 78 (b) 14 (c) 77 (d) 154
  29. 29.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 13 (b) 180 (c) 96 (d) 90
  30. 30.What is the 15th term of the AP 9, 13, 17, 21, …? (a) 69 (b) 60 (c) 56 (d) 65
  31. 31.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 840 (b) 420 (c) 456 (d) 68
  32. 32.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 436 (c) 435 (d) 406
  33. 33.What is the sum of all the whole numbers from 1 to 27? (a) 351 (b) 756 (c) 379 (d) 378
  34. 34.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 324 (c) 171 (d) 342
  35. 35.What is the 30th term of the AP 10, 12, 14, 16, …? (a) 58 (b) 70 (c) 68 (d) 60
  36. 36.What is the 33rd term of the AP 18, 20, 22, 24, …? (a) 66 (b) 82 (c) 84 (d) 64
  37. 37.Which term of the AP 4, 8, 12, 16, … is 48? (a) 11th (b) 13th (c) 12th (d) 14th
  38. 38.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 47 (b) 270 (c) 245 (d) 490
  39. 39.What is the 27th term of the AP 17, 22, 27, 32, …? (a) 152 (b) 135 (c) 130 (d) 147
  40. 40.Which term of the AP 15, 24, 33, 42, … is 357? (a) 41st (b) 40th (c) 38th (d) 39th

Answer key

  1. 34th
  2. 12
  3. 18th
  4. 40
  5. 4851
  6. 253
  7. 4186
  8. 91
  9. 96
  10. 529
  11. 105
  12. 110
  13. 156
  14. 820
  15. 126
  16. 9th
  17. 8th
  18. 3160
  19. 32nd
  20. 289
  21. 143
  22. 29th
  23. 184
  24. 91
  25. 66
  26. 243
  27. 29th
  28. 77
  29. 90
  30. 65
  31. 420
  32. 435
  33. 378
  34. 324
  35. 68
  36. 82
  37. 12th
  38. 245
  39. 147
  40. 39th

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