91Ó°ÊÓ

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 \(n .\) $$ 2 n^{2}>(n+1)^{2}, \quad n \geq 3$$

Writing the Terms of an Arithmetic Sequence In Exercises \(31 - 38 ,\) write the first five terms of the arithmetic sequence. $$ a _ { 1 } = 5 , d = 6 $$

Find the probability for the experiment of drawing two marbles at random (without replacement) from a bag containing one green, two yellow, and three red marbles. Both marbles are red.

Expanding an Expression In Exercises \(19-40,\) use the Binomial Theorem to expand and simplify the expression. $$(3 a-4 b)^{5}$$

Finding a Term of a Geometric Sequence, write an expression for the \(n\) th term of the geometric sequence. Then find the indicated term. $$ a_{1}=6, r=-\frac{1}{3}, n=12 $$

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 \(1 . )\) $$ a_{n}=\frac{2 n}{n+1} $$

In Exercises \(31-34,\) evaluate \(_{n} P_{r}\) $$_{4} P_{4}$$

Writing the Terms of an Arithmetic Sequence In Exercises \(31 - 38 ,\) write the first five terms of the arithmetic sequence. $$ a _ { 1 } = 5 , d = - \frac { 3 } { 4 } $$

Finding a Term of a Geometric Sequence, write an expression for the \(n\) th term of the geometric sequence. Then find the indicated term. $$ a_{1}=64, r=-\frac{1}{4}, n=10 $$