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    patterns and sequences Hills

    how do u find the 'n' term in a quadratic pattern please help!

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      RyanS

      Tn= an^2 + bn + c

      a = double second difference (so half this second difference and put in instead of a)

      for n you sub in the term no. i.e. term 1, 2, 3... and let it be equal to that term

      then simultaneous equations

      Example:

      Find term n (general term) of:

      1, 5, 10, 16

      Okay so second difference is +1

      Thus, 2a = 1

      a = 0.5

      => 0.5n^2 + bn + c

      First term is 1

      => 0.5(1)^2 + b(1) + c = 1

      0.5 + b + c =1

      b + c = 0.5

      Second Term is 5

      => 0.5(2)^2 + b(2) + c = 5

      2 + 2b + 2c = 1

      2b + 2c = -1

      Now Simultaneous equations.. Note that any term can be used, but 1st and 2nd Term is generally much easier :)

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      hamzamughees

      https://www.youtube.com/watch?v=dFTRZONntq8

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      Me

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