Determine whether the statement is true or false. Justify your answer. For a geometric sequence in which the quotient of term $a_{7}$ and term $a_{5}$ is 16, the common ratio is 8.

Determine the number of ways in which a computer can randomly generate one or more such integers, or pairs of integers, from 1 through 15.

A pair of distinct integers whose sum is 20

Write the first five terms of the sequence. Determine whether or not the sequence is arithmetic. If it is, find the common difference. (Assume n begins with 1.) $a_{n}=8+13 n$

Use sigma notation to write the sum. Then use a graphing utility to find the sum. $\frac{1}{1 \cdot 3}-\frac{1}{2 \cdot 4}+\frac{1}{3 \cdot 5}-\frac{1}{4 \cdot 6}+\cdots-\frac{1}{10 \cdot 12}$

Determine whether or not the sequence is geometric. If it is, find the common ratio. $1,-\frac{1}{2}, \frac{1}{4},-\frac{1}{8}, \ldots$

The manufacturer of a new food processor plans to produce and sell 8000 units per year. Each year, $10 of all units sold become inoperative. So, 8000 units will be in use after 1 year,

Simplify the factorial expression. $\frac{(n+1) !}{(n-1) !}$

Determine the number of ways in which a computer can randomly generate one or more such integers, or pairs of integers, from 1 through 15. A pair of distinct integers whose sum is 8

Find the binomial coefficient.

$$\left(\begin{array}{c}{12} \\ {0}\end{array}\right)$$

Use sigma notation to write the sum. Then use a graphing utility to find the sum. $\frac{1}{1^{2}}-\frac{1}{2^{2}}+\frac{1}{3^{2}}-\frac{1}{4^{2}}+\cdots-\frac{1}{20^{2}}$

Use a graphing utility to graph f and g in the same viewing window. What is the relationship between the two graphs? Use the Binomial Theorem to write the polynomial function g in standard form.

$$\begin{array}{l} f(x)=x^{3}-4 x \\ g(x)=f(x+4) \end{array}$$

The sphere flake shown is a computer-generated fractal that was created by Eric Haines. The radius of the large sphere is 1 . Attached to the large sphere are nine spheres of radius $\frac{1}{3}$. Attached to each of the smaller spheres are nine spheres of radius $\frac{1}{9}$. This process is continued infinitely.

(a) Write a formula in series notation that gives the surface area of the sphere flake.

(b) Write a formula in series notation that gives the volume of the sphere flake.

(c) Determine if either the surface area or the volume of the sphere flake is finite or infinite. If either is finite, find the value.

Use sigma notation to write the sum. Then use a graphing utility to find the sum. $1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\cdot \cdot \cdot-\frac{1}{128}$

The table shows the mid-year populations $a_n$ of China (in millions) from 2002 through 2008.

(a) Use the exponential regression feature of a graphing utility to find a geometric sequence that models the data. Let $n$ represent the year, with $n=2$ corresponding to 2002.

(b) Use the sequence from part (a) to describe the rate at which the population of China is growing.

(c) Use the sequence from part (a) to predict the population of China in 2015. The U.S. Census Bureau predicts the population of China will be 1393.4 million in 2015. How does this value compare with your prediction?

(d) Use the sequence from part (a) to determine when the population of China will reach $1.35$ billion.

$$\begin{array}{|c|c|} \hline \text { Year } & \text { Population, } a_n \\ \hline 2002 & 1284.3 \\ 2003 & 1291.5 \\ 2004 & 1298.8 \\ 2005 & 1306.3 \\ 2006 & 1314.0 \\ 2007 & 1321.9 \\ 2008 & 1330.0 \\ \hline \end{array}$$