91Ó°ÊÓ

Proving an Inequality In Exercises \(25-30\) , use mathematical induction to prove the inequality for the indicated integer values of \(n .\) $$ (1+a)^{n} \geq n a, \quad n \geq 1 \text { and } a>0 $$

Find the probability for the experiment of tossing a six-sided die twice. The sum is odd and no more than 7.

Posing for a Photograph In how many ways can five children posing for a photograph line up in a row?

Finding the \(n\) th Term In Exercises \(21 - 30\) , find a formula for \(a _ { n }\) for the arithmetic sequence. $$ a _ { 3 } = 94 , a _ { 6 } = 85 $$

Graphing the Terms of a Sequence In Exercises \(27-32,\) use a graphing utility to graph the first 10 terms of the sequence. (Assume that \(n\) begins with \(1 . )\) $$ a_{n}=16(-0.5)^{n-1} $$

Finding a Term of a Geometric Sequence, write an expression for the \(n\) th term of the geometric sequence. Then find the indicated term. $$ a_{1}=5, r=\frac{7}{2}, n=8 $$

Expanding an Expression In Exercises \(19-40,\) use the Binomial Theorem to expand and simplify the expression. $$(x+2 y)^{4}$$

Graphing the Terms of a Sequence In Exercises \(27-32,\) use a graphing utility to graph the first 10 terms of the sequence. (Assume that \(n\) begins with \(1 . )\) $$ a_{n}=8(0.75)^{n-1} $$

Riding in a Car In how many ways can six people sit in a six-passenger car?

Proving an Inequality In Exercises \(25-30\) , use mathematical induction to prove the inequality for the indicated integer values of \(n .\) $$ 2 n^{2}>(n+1)^{2}, \quad n \geq 3$$