2) Consider the quadratic sequence 72, 100, 120, 132 2.1.1) Determine Tn the nth term of the quadratic.​​

9514 1404 393

  Tn = -4n² +40n +36

Step-by-step explanation:

A graphing calculator readily performs the quadratic regression, yielding the formula ...

  Tn = -4n² +40n +36

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The first and second differences of the given sequence terms are ...

  28, 20, 12 and -8, -8

The coefficient of the squared term is half the second difference, so is -4. Then the sequence of squared terms is -4n²:

  -4, -16, -36, -64

Subtracting these values from the original sequence gives the linear sequence ...

  76, 116, 156, 196

which has first term 76 and common difference 40. The equation for the n-th term of this is ...

  an = 76 +40(n -1) = 36 +40n

Adding this linear sequence to the sequence of squared terms, we get ...

  Tn = -4n² +40n +36

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