Contents

Preface
1Foundations
- Introduction
- 1.1Use the Language of Algebra
- 1.2Integers
- 1.3Fractions
- 1.4Decimals
- 1.5Properties of Real Numbers
- Chapter Review
  Key Terms
  Key Concepts
- Exercises
  Review Exercises
  Practice Test
2Solving Linear Equations
3Graphs and Functions
4Systems of Linear Equations
5Polynomials and Polynomial Functions
6Factoring
7Rational Expressions and Functions
8Roots and Radicals
9Quadratic Equations and Functions
10Exponential and Logarithmic Functions
11Conics
12Sequences, Series and Binomial Theorem
- Introduction
- 12.1Sequences
- 12.2Arithmetic Sequences
- 12.3Geometric Sequences and Series
- 12.4Binomial Theorem
- Chapter Review
  Key Terms
Answer Key
Index

Practice Test

In the following exercises, write the first five terms of the sequence whose general term is given.

320.

$a_{n} = \frac{5 n - 3}{3^{n}} a_{n} = \frac{5 n - 3}{3^{n}}$

$a_{n} = \frac{(n + 2)!}{(n + 3)!} a_{n} = \frac{(n + 2)!}{(n + 3)!}$

322.

Find a general term for the sequence, $- \frac{2}{3}, - \frac{4}{5}, - \frac{6}{7}, - \frac{8}{9}, - \frac{10}{11}, … - \frac{2}{3}, - \frac{4}{5}, - \frac{6}{7}, - \frac{8}{9}, - \frac{10}{11}, …$

323.

Expand the partial sum and find its value. $\sum_{i = 1}^{4} {(−4)}^{i} \sum_{i = 1}^{4} {(−4)}^{i}$

324.

Write the following using summation notation. $−1 + \frac{1}{4} - \frac{1}{9} + \frac{1}{16} - \frac{1}{25} −1 + \frac{1}{4} - \frac{1}{9} + \frac{1}{16} - \frac{1}{25}$

325.

Write the first five terms of the arithmetic sequence with the given first term and common difference. $a_{1} = −13 a_{1} = −13$ and $d = 3 d = 3$

326.

Find the twentieth term of an arithmetic sequence where the first term is two and the common difference is $−7 . −7 .$

327.

Find the twenty-third term of an arithmetic sequence whose seventh term is $1111$ and common difference is three. Then find a formula for the general term.

328.

Find the first term and common difference of an arithmetic sequence whose ninth term is $−1 −1$ and the sixteenth term is $−15 . −15 .$ Then find a formula for the general term.

329.

Find the sum of the first 25 terms of the arithmetic sequence, $5, 9, 13, 17, 21, … 5, 9, 13, 17, 21, …$

330.

Find the sum of the first 50 terms of the arithmetic sequence whose general term is $a_{n} = −3 n + 100 . a_{n} = −3 n + 100 .$

331.

Find the sum. $\sum_{i = 1}^{40} (5 i - 21) \sum_{i = 1}^{40} (5 i - 21)$

In the following exercises, determine if the sequence is arithmetic, geometric, or neither. If arithmetic, then find the common difference. If geometric, then find the common ratio.

332.

$14, 3, −8, −19, −30, −41, … 14, 3, −8, −19, −30, −41, …$

333.

$324, 108, 36, 12, 4, \frac{4}{3}, … 324, 108, 36, 12, 4, \frac{4}{3}, …$

334.

Write the first five terms of the geometric sequence with the given first term and common ratio. $a_{1} = 6 a_{1} = 6$ and $r = −2 r = −2$

335.

In the geometric sequence whose first term and common ratio are $a_{1} = 5 a_{1} = 5$ and $r = 4, r = 4,$ find $a_{11} . a_{11} .$

336.

Find $a_{10} a_{10}$ of the geometric sequence, $1250, 250, 50, 10, 2, \frac{2}{5}, … . 1250, 250, 50, 10, 2, \frac{2}{5}, … .$ Then find a formula for the general term.

337.

Find the sum of the first thirteen terms of the geometric sequence, $2, −6, 18, −54, 162, −486 … 2, −6, 18, −54, 162, −486 …$

In the following exercises, find the sum.

338.

$\sum_{i = 1}^{9} 5 {(2)}^{i} \sum_{i = 1}^{9} 5 {(2)}^{i}$

339.

$1 - \frac{1}{5} + \frac{1}{25} - \frac{1}{125} + \frac{1}{625} - \frac{1}{3125} + … 1 - \frac{1}{5} + \frac{1}{25} - \frac{1}{125} + \frac{1}{625} - \frac{1}{3125} + …$

340.

Write the repeating decimal as a fraction. $0. \overset{—}{81} 0. \overset{—}{81}$

341.

Dave just got his first full-time job after graduating from high school at age 18. He decided to invest $450 per month in an IRA (an annuity). The interest on the annuity is 6% which is compounded monthly. How much will be in Adam’s account when he retires at his sixty-fifth birthday?

342.

Expand the binomial using Pascal’s Triangle. ${(m - 2 n)}^{5} {(m - 2 n)}^{5}$

343.

Evaluate each binomial coefficient. ⓐ $(\begin{matrix} 8 \\ 1 \end{matrix}) (\begin{matrix} 8 \\ 1 \end{matrix})$
ⓑ $(\begin{matrix} 16 \\ 16 \end{matrix}) (\begin{matrix} 16 \\ 16 \end{matrix})$ ⓒ $(\begin{matrix} 12 \\ 0 \end{matrix}) (\begin{matrix} 12 \\ 0 \end{matrix})$ ⓓ $(\begin{matrix} 10 \\ 6 \end{matrix}) (\begin{matrix} 10 \\ 6 \end{matrix})$

344.

Expand the binomial using the Binomial Theorem. ${(4 x + 5 y)}^{3} {(4 x + 5 y)}^{3}$