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Section 1

Sequences and Series

Write out the first five terms of each sequence.$$a_{n}=n+1$$

Write out the first five terms of each sequence.$$a_{n}=n+4$$

Write out the first five terms of each sequence.$$a_{n}=\frac{n+3}{n}$$

Write out the first five terms of each sequence.$$a_{n}=\frac{n+2}{n}$$

Write out the first five terms of each sequence.$$a_{n}=3^{n}$$

Write out the first five terms of each sequence.$$a_{n}=2^{n}$$

Write out the first five terms of each sequence.$$a_{n}=\frac{1}{n^{2}}$$

Write out the first five terms of each sequence.$$a_{n}=\frac{-2}{n^{2}}$$

Write out the first five terms of each sequence.$$a_{n}=5(-1)^{n-1}$$

Write out the first five terms of each sequence.$$a_{n}=6(-1)^{n+1}$$

Write out the first five terms of each sequence.$$a_{n}=n-\frac{1}{n}$$

Write out the first five terms of each sequence.$$a_{n}=n+\frac{4}{n}$$

Find the indicated term for each sequence.$$a_{n}=-9 n+2 ; \quad a_{8}$$

Find the indicated term for each sequence.$$a_{n}=3 n-7 ; \quad a_{12}$$

Find the indicated term for each sequence.$$a_{n}=\frac{3 n+7}{2 n-5} ; \quad a_{14}$$

Find the indicated term for each sequence.$$a_{n}=\frac{5 n-9}{3 n+8} ; \quad a_{16}$$

Find the indicated term for each sequence.$$a_{n}=(n+1)(2 n+3) ; \quad a_{8}$$

Find the indicated term for each sequence.$$a_{n}=(5 n-2)(3 n+1) ; \quad a_{10}$$

Find a general term $a_{n}$ for the given terms of each sequence.$$4,8,12,16, \dots$$

Find a general term $a_{n}$ for the given terms of each sequence.$$7,14,21,28, \dots$$

Find a general term $a_{n}$ for the given terms of each sequence.$$-8,-16,-24,-32, \dots$$

Find a general term $a_{n}$ for the given terms of each sequence.$$-10,-20,-30,-40, \dots$$

Find a general term $a_{n}$ for the given terms of each sequence.$$\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \frac{1}{81}, \ldots$$

Find a general term $a_{n}$ for the given terms of each sequence.$$\frac{2}{5}, \frac{2}{25}, \frac{2}{125}, \frac{2}{625}, \dots$$

Find a general term $a_{n}$ for the given terms of each sequence.$$\frac{2}{5}, \frac{3}{6}, \frac{4}{7}, \frac{5}{8}, \ldots$$

Find a general term $a_{n}$ for the given terms of each sequence.$$\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \ldots$$

Solve each applied problem by writing the first few terms of a sequence.Horacio Loschak borrows $\$ 1000$ and agrees to pay $\$ 100$ plus interest of $1 \%$ on the unpaid balance each month. Find the payments for the first six months and the remaining debt at the end of that period.

Solve each applied problem by writing the first few terms of a sequence.Leslie Maruri is offered a new modeling job with a salary of $20,000+2500 n$ dollars per year at the end of the $n$ th year. Write a sequence showing her salary at the end of each of the first 5 yr. If she continues in this way, what will her salary be at the end of the tenth year?

Solve each applied problem by writing the first few terms of a sequence.Suppose that an automobile loses $\frac{1}{5}$ of its value each year; that is, at the end of any given year, the value is $\frac{4}{5}$ of the value at the beginning of that year. If a car costs $\$ 20,000$ new, what is its value at the end of 5 yr, to the nearest dollar?

Solve each applied problem by writing the first few terms of a sequence.A certain car loses $\frac{1}{2}$ of its value each year. If this car cost $\$ 40,000$ new, what is its value at the end of 6 yr?

Write out each series and evaluate it.$$\sum_{i=1}^{5}(i+3)$$

Write out each series and evaluate it.$$\sum_{i=1}^{6}(i+9)$$

Write out each series and evaluate it.$$\sum_{i=1}^{3}\left(i^{2}+2\right)$$

Write out each series and evaluate it.$$\sum_{i=1}^{4}\left(i^{3}+3\right)$$

Write out each series and evaluate it.$$\sum_{i=1}^{6}(-1)^{i}$$

Write out each series and evaluate it.$$\sum_{i=1}^{5}(-1)^{i} \cdot i$$

Write out each series and evaluate it.$$\sum_{i=3}^{7}(i-3)(i+2)$$

Write out each series and evaluate it.$$\sum_{i=2}^{6}(i+3)(i-4)$$

Write each series with summation notation.$$3+4+5+6+7$$

Write each series with summation notation.$$7+8+9+10+11$$

Write each series with summation notation.$$-2+4-8+16-32$$

Write each series with summation notation.$$-1+2-3+4-5+6$$

Write each series with summation notation.$$1+4+9+16$$

Write each series with summation notation.$$1+16+81+256$$

Explain the basic difference between a sequence and a series.

Consider the following statement.For the sequence defined by $a_{n}=2 n+4,$ find $a_{1 / 2}$

Find the arithmetic mean for each collection of numbers.$$8,11,14,9,7,6,8$$

Find the arithmetic mean for each collection of numbers.$$10,12,8,19,23,12$$

Find the arithmetic mean for each collection of numbers.$$5,9,8,2,4,7,3,2,0$$

Find the arithmetic mean for each collection of numbers.$$2,1,4,8,3,7,10,8,0$$

Solve each problem.The number of mutual funds operating in the United States available to investors each year during the period 2004 through 2008 is given in the table.$$\begin{array}{c|c}{} & {\text { Number of }} \\ \text { Year } & \text{Funds Available} \\\hline{2004} & {8041} \\{2005} & {7975} \\{2006} & {8117} \\{2007} & {8024} \\{2008} & {8022} \\\hline\end{array}$$To the nearest whole number, what was the average number of funds available per year during the given period?

Solve each problem.The total assets of mutual funds operating in the United States, in billions of dollars, for each year during the period 2004 through 2008 are shown in the table. What were the average assets per year during this period?$$\begin{array}{|c|c|}\hline \text { Year } & {\text { Assets (in billions of dollars) }} \\{2004} & {8107} \\{2005} & {8905} \\{2006} & {10,397} \\{2007} & {12,000} \\{2008} & {9601} \\\hline\end{array}$$

Find the values of a and d by solving each system.$$\begin{array}{l}{a+3 d=12} \\{a+8 d=22}\end{array}$$

Find the values of a and d by solving each system.$$\begin{array}{l}{a+7 d=12} \\{a+2 d=7}\end{array}$$

Evaluate $a+(n-1) d$ for $a=-2, n=5,$ and $d=3$