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Quadratic sequences

Now Playing:Quadratic sequences – Example 0a
Intros
  1. Quadratic Sequences Overview:
  2. Quadratic Sequences Overview:
    What are quadratic sequences?
  3. Quadratic Sequences Overview:
    nth term for quadratic sequences
Examples
  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

Arithmetic sequences
Jump to:Notes
Notes
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!