Chapter 11

Write the explicit formula for each geometric sequence. Then generate the first three terms. $$ a_{1}=20, r=-0.5 $$

The graph of each equation is translated 2 units left and 3 units down. Write each new equation. $$ (x+2)^{2}+(y-1)^{2}=5 $$

Find the common ratio in the geometric sequence \(4,10,25,62.5, \ldots\) $$ \begin{array}{lllll}{\text { A. } 0.4} & {\text { B. } 2.5} & {\text { C. } 15} & {\text { D. } 25}\end{array} $$

Add or subtract. Simplify where possible. $$ \frac{5}{y+3}+\frac{15}{y-3} $$

Graph each equation. Describe each graph and its lines of symmetry. Give the domain and range for each graph. $$ x^{2}+3 y^{2}=36 $$

What is the geometric mean of 8 and 18\(?\) $$ \begin{array}{lllll}{\text { F. } 12} & {\text { G. } 13} & {\text { H. } 26} & {\text { J. } 36}\end{array} $$

Find the missing terms of each arithmetic sequence. (Hint: The arithmetic mean of the first and fifth terms is the third term.)

Add or subtract. Simplify where possible. $$ \frac{4}{x^{2}-36}+\frac{x}{x-6} $$

Graph each equation. Describe each graph and its lines of symmetry. Give the domain and range for each graph. $$ x^{2}-y^{2}=25 $$

Find the missing term in the geometric sequence \(8, \square, 0.5,-0.125, \dots\) $$ \begin{array}{lllll}{\text { A. } 2} & {\text { B. }-2} & {\text { C. } 4} & {\text { D. }-4}\end{array} $$

Add or subtract. Simplify where possible. $$ \frac{15}{3-d}-\frac{-3}{9-d^{2}} $$

Graph each equation. Describe each graph and its lines of symmetry. Give the domain and range for each graph. $$ x^{2}+y^{2}=4 $$

The first term of a geometric sequence is 1 and its common ratio is \(6 .\) What is the sixth term? $$ \begin{array}{lllll}{\text { F. } 31} & {\text { G. } 3176} & {\text { H. } 7776} & {\text { J. } 46,656}\end{array} $$

Find the missing terms of each arithmetic sequence. (Hint: The arithmetic mean of the first and fifth terms is the third term.)

Simplify each rational expression. $$ \frac{x^{2}+4 x+3}{x^{2}-3 x-4} $$

The first term of a geometric sequence is \(-1 .\) The common ratio is \(-5 .\) Find the eighth term in the sequence.

Simplify each rational expression. $$ \frac{c^{2}-8 c+12}{c^{2}-11 c+30} $$

The sixth term in a geometric sequence is \(120 .\) The seventh term is \(40 .\) What is the first term in the sequence?

Find the missing terms of each arithmetic sequence. (Hint: The arithmetic mean of the first and fifth terms is the third term.)

Simplify each rational expression. $$ \frac{3 z^{4}+36 z^{3}+60 z^{2}}{3 z^{3}-3 z^{2}} $$

Which is greater, the geometric mean of 4 and 16 or the arithmetic mean of 4 and 16\(?\) Show your work.

In a geometric sequence, \(a_{1}=3\) and \(a_{4}=192 .\) Explain how to find \(a_{2}\) and \(a_{3} .\)

Find the missing terms of each arithmetic sequence. (Hint: The arithmetic mean of the first and fifth terms is the third term.)

Write an explicit and a recursive formula for each arithmetic sequence. $$ -3,0,3,6, \dots $$

Write an explicit and a recursive formula for each arithmetic sequence. $$ 17,8,-1, \ldots $$

Graph the arithmetic sequence generated by each formula over the domain \(1 \leq n \leq 10 .\) \(a_{1}=-60, a_{n}=a_{n-1}+9\)

Write an explicit and a recursive formula for each arithmetic sequence. $$ -2,-13,-24, \ldots $$

Write an equation of the circle with the given center and radius. Graph the circle. center \((0,0),\) radius 3

Suppose you turn the water on in an empty bathtub with vertical sides. After 20 s, the water has reached a level of 1.15 in. You then leave the room. You want to turn the water off when the level in the bathtub is 8.5 in. How many minutes later should you return? (Hint: Begin by identifying two terms of an arithmetic sequence.)

Write an equation of the circle with the given center and radius. Graph the circle. center \((-3,1),\) radius 5

Write an equation of the circle with the given center and radius. Graph the circle. center \((1,1),\) radius 2

The arithmetic mean of two terms in an arithmetic sequence is \(-6 .\) One term is \(-20 .\) Find the other term.

Find the vertical asymptotes of each function. $$ y=\frac{x-3}{x+3} $$

Find the vertical asymptotes of each function. $$ y=\frac{x-3}{x+1} $$

In an arithmetic sequence with \(a_{1}=2\) and \(d=-2,\) which term is \(-82 ?\)

Find the vertical asymptotes of each function. $$ y=\frac{x-3}{x(x-1)} $$

Given two terms of each arithmetic sequence, find \(a_{1}\) and \(d\). \(a_{4}=8\) and \(a_{7}=20\)

Given two terms of each arithmetic sequence, find \(a_{1}\) and \(d\). \(a_{10}=17\) and \(a_{14}=34\)

Given two terms of each arithmetic sequence, find \(a_{1}\) and \(d\). \(a_{4}=-2.4\) and \(a_{6}=2\)

Find the indicated term of each arithmetic series. \(a_{1}=k+7, d=2 k-5 ; a_{11}\)

Which arithmetic sequence includes the term 27\(?\) I. \(a_{1}=7, a_{n}=a_{n-1}+5\) \(\quad\) II. \(a_{n}=3+(n-1) 4\) \(\quad\) III. \(a_{n}=57-6 n\) F. I only G. I and II only H. II and III only J. \(1,11,\) and 111

What is the 30 th term of the sequence \(7,16,25,34, \ldots ?\) F. 277 G. 270 H. 268 J. 261

Find the 100 th term of the arithmetic sequence \(3,10,17,24,31, \ldots\) Explain your steps.

Decide whether each formula is explicit or recursive. Then find the first five terms of each sequence. \(a_{n}=3 n(n+1)\)

Decide whether each formula is explicit or recursive. Then find the first five terms of each sequence. \(a_{1}=-121, a_{n}=a_{n-1}+13\)

Find the foci of each ellipse. \(\frac{x^{2}}{36}+\frac{y^{2}}{4}=1\)

Find the foci of each ellipse. \(\frac{(x-1)^{2}}{64}+\frac{(y-3)^{2}}{25}=1\)