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3205 page 6Challenge yourself

Higher Level Sequence• Definition: A power sequence is a

sequence where the common difference is beyond the first level difference.

• Definition: A quadratic function is a function that can be expressed as y = ax2 + bx + c, where a, b, c are real number coefficients and (otherwise it would be a linear function)

0a

• This is also classified as a second degree function because the highest exponent of x is 2.

• a is called the leading coefficient. It is the coefficient of the term with the highest power of x.

• Definition: A quadratic sequence is a sequence whose terms are generated by a ________________ (or rule).

2 ,nt an bn c n N

Examples

1. Generate the first 6 terms of the following. Find the sequences of difference until you find the common difference.

A) tn=n2

2. tn = 2n2 + n Calculator

3. tn = 3n2 + 5n - 6

• Compare the common difference D2 and the leading coefficient, a, of each sequence rule.– 1. a = 1 D2 = 2

– 2. a = 2 D2 = 4

– 3. a = 3 D2 = 6

2

12

a D2 2D aOR

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