Quadratic sequences

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Intros
Lessons
  1. Quadratic Sequences Overview:
  2. What are quadratic sequences?
  3. nth term for quadratic sequences
  4. How to find the nth term
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Examples
Lessons
  1. Identifying the a,b,c's
    The nth term of a quadratic sequence is always in the form:
    an2+bn+can^{2}+bn+c

    For each following quadratic expressions, find the values of a, b, c. Then list the first three terms of the sequence:
    1. 3n2+2n+73n^{2}+2n+7
    2. −2n2+4n−2-2n^{2}+4n-2
    3. n23−n\frac{n^{2}}{3}-n
  2. Finding the second common difference
    Find the second common difference of the following sequence:
    3, 13, 27, 45, 67, ...
    1. Find the second common difference of the following sequence:
      1, 5, 15, 31, 53, ...
      1. Finding the nth term
        Find the nth term of the following quadratic sequence:
        8, 11, 16, 23, ...
        1. Find the nth term of the following quadratic sequence:
          7, 16, 27, 40, ...
          Topic Notes
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          The nth term of a quadratic sequence is always in the form
          an2+bn+can^{2}+bn+c

          Second common difference (2nd difference): the common difference of the common difference.
          To find the nth term of the quadratic sequence, we need to find the values of a,b, and c. We find them using the three following formulas:
          a=(2nddifference)2a = \frac{(2^{nd} difference)}{2}

          3a+b=2ndterm−1stterm3a+b=2^{nd} term-1^{st} term

          a+b+c=1stterma+b+c=1^{st} term

          Isolate to solve for a,b and c and plug those values into the quadratic sequence. Then you will have the nth term!