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For the following exercises, use the explicit formula to write the first five terms of the arithmetic sequence.
${a}_{n}=\frac{1}{2}n-\frac{1}{2}$
For the following exercises, write an explicit formula for each arithmetic sequence.
${a}_{n}=\{32,24,16,\mathrm{...}\}$
${a}_{n}=\{-5\text{,}95\text{,}195\text{,}\mathrm{...}\}$
${a}_{n}=-105+100n$
${a}_{n}=\left\{\mathrm{-17}\text{,}\mathrm{-217}\text{,}\mathrm{-417}\text{,}\mathrm{...}\right\}$
${a}_{n}=\left\{1.8\text{,}3.6\text{,}5.4\text{,}\mathrm{...}\right\}$
${a}_{n}=1.8n$
${a}_{n}=\{\mathrm{-18.1},\mathrm{-16.2},\mathrm{-14.3},\mathrm{...}\}$
${a}_{n}=\{15.8,18.5,21.2,\mathrm{...}\}$
${a}_{n}=13.1+2.7n$
${a}_{n}=\left\{\frac{1}{3},-\frac{4}{3},\mathrm{-3}\text{,}\mathrm{...}\right\}$
${a}_{n}=\left\{0,\frac{1}{3},\frac{2}{3},\mathrm{...}\right\}$
${a}_{n}=\frac{1}{3}n-\frac{1}{3}$
${a}_{n}=\left\{-5,-\frac{10}{3},-\frac{5}{3},\dots \right\}$
For the following exercises, find the number of terms in the given finite arithmetic sequence.
${a}_{n}=\{3\text{,}-4\text{,}-11\text{,}\mathrm{...}\text{,}-60\}$
There are 10 terms in the sequence.
${a}_{n}=\{1.2,1.4,1.6,\mathrm{...},3.8\}$
${a}_{n}=\left\{\frac{1}{2},2,\frac{7}{2},\mathrm{...},8\right\}$
There are 6 terms in the sequence.
For the following exercises, determine whether the graph shown represents an arithmetic sequence.
For the following exercises, use the information provided to graph the first 5 terms of the arithmetic sequence.
${a}_{1}=0,d=4$
${a}_{n}=-12+5n$
For the following exercises, follow the steps to work with the arithmetic sequence ${a}_{n}=3n-2$ using a graphing calculator:
What are the first seven terms shown in the column with the heading $u(n)\text{?}$
$1,4,7,10,13,16,19$
Use the scroll-down arrow to scroll to $n=50.$ What value is given for $u(n)\text{?}$
Press [WINDOW] . Set $\text{\hspace{0.17em}}n\text{Min}=1,n\text{Max}=5,x\text{Min}=0,x\text{Max}=6,y\text{Min}=-1,\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}y\text{Max}=14.\text{\hspace{0.17em}}$ Then press [GRAPH] . Graph the sequence as it appears on the graphing calculator.
For the following exercises, follow the steps given above to work with the arithmetic sequence ${a}_{n}=\frac{1}{2}n+5$ using a graphing calculator.
What are the first seven terms shown in the column with the heading $\text{\hspace{0.17em}}u(n)\text{\hspace{0.17em}}$ in the TABLE feature?
Graph the sequence as it appears on the graphing calculator. Be sure to adjust the WINDOW settings as needed.
Give two examples of arithmetic sequences whose 4 ^{th} terms are $9.$
Give two examples of arithmetic sequences whose 10 ^{th} terms are $206.$
Answers will vary. Examples: ${a}_{n}=20.6n$ and ${a}_{n}=2+20.4\mathrm{n.}$
Find the 5 ^{th} term of the arithmetic sequence $\{9b,5b,b,\dots \}.$
Find the 11 ^{th} term of the arithmetic sequence $\{3a-2b,a+2b,-a+6b\dots \}.$
${a}_{11}=-17a+38b$
At which term does the sequence $\{5.4,14.5,23.6,\mathrm{...}\}$ exceed 151?
At which term does the sequence $\left\{\frac{17}{3},\frac{31}{6},\frac{14}{3},\mathrm{...}\right\}$ begin to have negative values?
The sequence begins to have negative values at the 13 ^{th} term, ${a}_{13}=-\frac{1}{3}$
For which terms does the finite arithmetic sequence $\left\{\frac{5}{2},\frac{19}{8},\frac{9}{4},\mathrm{...},\frac{1}{8}\right\}$ have integer values?
Write an arithmetic sequence using a recursive formula. Show the first 4 terms, and then find the 31 ^{st} term.
Answers will vary. Check to see that the sequence is arithmetic. Example: Recursive formula: ${a}_{1}=3,{a}_{n}={a}_{n-1}-3.$ First 4 terms: $\begin{array}{ll}3,0,-3,-6\hfill & {a}_{31}=-87\hfill \end{array}$
Write an arithmetic sequence using an explicit formula. Show the first 4 terms, and then find the 28 ^{th} term.
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