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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 985 · 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 9 terms of the AP 3, 5, 7, …? (a) 108 (b) 19 (c) 99 (d) 198
  2. 2.Which term of the AP 17, 19, 21, 23, … is 53? (a) 21st (b) 19th (c) 20th (d) 18th
  3. 3.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 182 (b) 16 (c) 92 (d) 91
  4. 4.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 240 (c) 120 (d) 29
  5. 5.Which term of the AP 18, 26, 34, 42, … is 250? (a) 29th (b) 31st (c) 30th (d) 32nd
  6. 6.What is the 11th term of the AP 4, 8, 12, 16, …? (a) 45 (b) 48 (c) 40 (d) 44
  7. 7.What is the missing term in the AP 6, ?, 14, 18, 22? (a) 14 (b) 11 (c) 9 (d) 10
  8. 8.What is the 27th term of the AP 16, 18, 20, 22, …? (a) 54 (b) 52 (c) 70 (d) 68
  9. 9.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 702 (c) 676 (d) 51
  10. 10.What is the 33rd term of the AP 16, 24, 32, 40, …? (a) 256 (b) 264 (c) 280 (d) 272
  11. 11.What is the 40th term of the AP 14, 19, 24, 29, …? (a) 214 (b) 209 (c) 200 (d) 195
  12. 12.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 100 (d) 55
  13. 13.What is the 26th term of the AP 11, 14, 17, 20, …? (a) 86 (b) 75 (c) 78 (d) 89
  14. 14.What is the missing term in the AP 18, 20, 22, ?, 26? (a) 26 (b) 23 (c) 24 (d) 25
  15. 15.Which term of the AP 16, 23, 30, 37, … is 240? (a) 34th (b) 33rd (c) 35th (d) 32nd
  16. 16.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 500 (b) 270 (c) 250 (d) 43
  17. 17.What is the sum of the first 7 terms of the AP 3, 4, 5, …? (a) 43 (b) 42 (c) 84 (d) 9
  18. 18.Which term of the AP 10, 16, 22, 28, … is 136? (a) 21st (b) 22nd (c) 23rd (d) 24th
  19. 19.What is the 14th term of the AP 18, 21, 24, 27, …? (a) 57 (b) 60 (c) 42 (d) 39
  20. 20.What is the 28th term of the AP 10, 13, 16, 19, …? (a) 91 (b) 94 (c) 81 (d) 84
  21. 21.What is the 25th term of the AP 16, 24, 32, 40, …? (a) 216 (b) 192 (c) 200 (d) 208
  22. 22.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 828 (b) 414 (c) 444 (d) 62
  23. 23.What is the sum of all the whole numbers from 1 to 51? (a) 2652 (b) 1327 (c) 1326 (d) 1275
  24. 24.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 26 (b) 352 (c) 176 (d) 187
  25. 25.What is the sum of the first 6 terms of the AP 7, 11, 15, …? (a) 204 (b) 102 (c) 114 (d) 27
  26. 26.What is the 12th term of the AP 17, 19, 21, 23, …? (a) 39 (b) 22 (c) 41 (d) 24
  27. 27.What is the 12th term of the AP 7, 16, 25, 34, …? (a) 108 (b) 115 (c) 99 (d) 106
  28. 28.What is the sum of all the whole numbers from 1 to 75? (a) 2775 (b) 2850 (c) 2851 (d) 5700
  29. 29.What is the sum of all the whole numbers from 1 to 49? (a) 2450 (b) 1226 (c) 1176 (d) 1225
  30. 30.What is the 33rd term of the AP 10, 12, 14, 16, …? (a) 74 (b) 64 (c) 66 (d) 76
  31. 31.What is the 10th term of the AP 1, 5, 9, 13, …? (a) 36 (b) 40 (c) 41 (d) 37
  32. 32.Which term of the AP 10, 12, 14, 16, … is 64? (a) 27th (b) 29th (c) 32nd (d) 28th
  33. 33.What is the 16th term of the AP 8, 16, 24, 32, …? (a) 136 (b) 129 (c) 120 (d) 128
  34. 34.What is the sum of the first 8 terms of the AP 3, 9, 15, …? (a) 216 (b) 45 (c) 192 (d) 384
  35. 35.What is the 37th term of the AP 4, 7, 10, 13, …? (a) 108 (b) 112 (c) 115 (d) 111
  36. 36.What is the 31st term of the AP 18, 24, 30, 36, …? (a) 204 (b) 198 (c) 186 (d) 180
  37. 37.Which term of the AP 13, 21, 29, 37, … is 85? (a) 12th (b) 9th (c) 11th (d) 10th
  38. 38.Which term of the AP 12, 19, 26, 33, … is 236? (a) 35th (b) 32nd (c) 33rd (d) 34th
  39. 39.What is the 33rd term of the AP 2, 6, 10, 14, …? (a) 134 (b) 130 (c) 128 (d) 132
  40. 40.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 102 (b) 54 (c) 51 (d) 11

Answer key

  1. 99
  2. 19th
  3. 91
  4. 225
  5. 30th
  6. 44
  7. 10
  8. 68
  9. 676
  10. 272
  11. 209
  12. 100
  13. 86
  14. 24
  15. 33rd
  16. 250
  17. 42
  18. 22nd
  19. 57
  20. 91
  21. 208
  22. 414
  23. 1326
  24. 176
  25. 102
  26. 39
  27. 106
  28. 2850
  29. 1225
  30. 74
  31. 37
  32. 28th
  33. 128
  34. 192
  35. 112
  36. 198
  37. 10th
  38. 33rd
  39. 130
  40. 51

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