91Ó°ÊÓ

Linear Model, Quadratic Model, or Neither? In Exercises \(61-68\) , write the first six terms of the sequence beginning with the given term. Then calculate the first and second differences of the sequence. State whether the sequence has a perfect linear model, a perfect quadratic model, or neither. $$a_{0}=2$$ $$a_{n}=\left(a_{n-1}\right)^{2}$$

Linear Model, Quadratic Model, or Neither? In Exercises \(61-68\) , write the first six terms of the sequence beginning with the given term. Then calculate the first and second differences of the sequence. State whether the sequence has a perfect linear model, a perfect quadratic model, or neither. $$a_{1}=0$$ $$a_{n}=a_{n-1}+2 n$$

Finding a Sum In Exercises \(67-74,\) find the sum. $$ \sum_{k=1}^{4} 10 $$

Graphing the Terms of a Sequence In Exercises \(69 - 72 ,\) use a graphing utility to graph the first 10 terms of the sequence. (Assume that \(n\) begins with \(1 . )\) $$ a _ { n } = - 5 + 2 n $$

Find a formula for the sum of the angles (in degrees) of a regular polygon. Then use mathematical induction to prove this formula for a general \(n\) -sided polygon. Equilateral triangle \(\left(180^{\circ}\right)\) Square \(\left(360^{\circ}\right)\) Regular pentagon \(\left(540^{\circ}\right)\)

Using Sigma Notation to Write a Sum In Exercises \(79-88\) , use sigma notation to write the sum. $$ 1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\dots-\frac{1}{128} $$

Depreciation A tool and die company buys a machine for \(\$ 175,000\) and it depreciates at a rate of 30\(\%\) per year. (In other words, at the end of each year the depreciated value is 70\(\%\) of what it was at the beginning of the year.) Find the depreciated value of the machine after 5 full years.

Writing In your own words, explain how to form the rows of Pascal's Triangle.

Proof In Exercises \(99-102,\) prove the property for all integers \(r\) and \(n\) where \(0 \leq r \leq n .\) $$_{n} C_{0}-_{n} C_{1}+_{n} C_{2}-\cdots \pm_{n} C_{n}=0$$