Arithmetic Sequences

What is an arithmetic sequence?

How do we determine whether a sequence is arithmetic?

Describe how linear functions and arithmetic sequences are similar. How are they different?

$\left\{0,\frac{1}{2},1,\frac{3}{2},2,\mathrm{...}\right\}$

$\{4,16,64,256,1024,\mathrm{...}\}$

$a_1=0$ , $d=\frac{2}{3}$

$a_{13}=-60,a_{33}=-160$

First term is 4, common difference is 5, find the 4^th term.

First term is 6, common difference is 7, find the 6^th term.

Find the first term or $a_1$ of an arithmetic sequence if $a_6=12$ and $a_{14}=28.$

Find the first term or $a_1$ of an arithmetic sequence if $a_8=40$ and $a_{23}=115.$

Find the first term or $a_1$ of an arithmetic sequence if $a_{11}=11$ and $a_{21}=16.$

$a_3=-17.1$ and $a_{10}=-\mathrm{15.7.}$ Find $a_{21}.$

$a_1=-19;\text{<msub> <mi>a</mi> <mi>n</mi> </msub> <mo>=</mo><msub> <mi>a</mi> <mrow> <mi>n</mi><mo>−</mo><mn>1</mn> </mrow> </msub> <mo>−</mo><mn>1.4</mn>}$

$a=\{17,26,35,\mathrm{...}\}$

$a=\{12,17,22,\mathrm{...}\}$

$a=\{8.9,10.3,11.7,\mathrm{...}\}$

$a=\left\{\frac{1}{5},\frac{9}{20},\frac{7}{10},\mathrm{...}\right\}$

$a=\left\{\frac{1}{6},-\frac{11}{12},-2,\mathrm{...}\right\}$

$a=\left\{4\text{, }11\text{, }18\text{, }\mathrm{...}\right\};$ Find the 14^th term.

$a_n=24-4n$

$a=\{3,5,7,\mathrm{...}\}$

$a=\{-5\text{, }95\text{, }195\text{, }\mathrm{...}\}$

$a=\left\{1.8\text{, }3.6\text{, }5.4\text{, }\mathrm{...}\right\}$

$a=\{15.8,18.5,21.2,\mathrm{...}\}$

$a=\left\{0,\frac{1}{3},\frac{2}{3},\mathrm{...}\right\}$

$a=\{3\text{,}-4\text{,}-11\text{, }\mathrm{...}\text{,}-60\}$

$a=\left\{\frac{1}{2},2,\frac{7}{2},\mathrm{...},8\right\}$

$a_1=9;a_n=a_{n-1}-10$

What are the first seven terms shown in the column with the heading $u(n)\text{?}$

Press [WINDOW]. Set $n\text{Min}=1$, $n\text{Max}=5$, $x\text{Min}=0$, $x\text{Max}=6$, $y\text{Min}=-1$, and $y\text{Max}=14.$ Then press [GRAPH]. Graph the sequence as it appears on the graphing calculator.

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 10^th terms are $206.$

Find the 11^th term of the arithmetic sequence $\{3a-2b,a+2b,-a+6b\dots \}.$

At which term does the sequence $\left\{\frac{17}{3},\frac{31}{6},\frac{14}{3},\mathrm{...}\right\}$ begin to have negative values?

Write an arithmetic sequence using a recursive formula. Show the first 4 terms, and then find the 31^st term.