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For the following exercises, use the explicit formula to write the first five terms of the arithmetic sequence.

a n = 24 4 n

First five terms: 20 , 16 , 12 , 8 , 4.

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For the following exercises, write an explicit formula for each arithmetic sequence.

a n = { 3 , 5 , 7 , ... }

a n = 1 + 2 n

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a n = { 32 , 24 , 16 , ... }

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a n = { 5 95 195 ... }

a n = 105 + 100 n

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a n = { −17 −217 −417 , ... }

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a n = { 1.8 3.6 5.4 ... }

a n = 1.8 n

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a n = { −18.1 , −16.2 , −14.3 , ... }

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a n = { 15.8 , 18.5 , 21.2 , ... }

a n = 13.1 + 2.7 n

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a n = { 1 3 , 4 3 , −3 ... }

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a n = { 0 , 1 3 , 2 3 , ... }

a n = 1 3 n 1 3

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a n = { 5 , 10 3 , 5 3 , }

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For the following exercises, find the number of terms in the given finite arithmetic sequence.

a n = { 3 , 4 , 11 ... , 60 }

There are 10 terms in the sequence.

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a n = { 1.2 , 1.4 , 1.6 , ... , 3.8 }

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a n = { 1 2 , 2 , 7 2 , ... , 8 }

There are 6 terms in the sequence.

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Graphical

For the following exercises, determine whether the graph shown represents an arithmetic sequence.

Graph of a scattered plot with labeled points: (1, 1.5), (2, 2.25), (3, 3.375), (4, 5.0625), and (5, 7.5938). The x-axis is labeled n and the y-axis is labeled a_n.

The graph does not represent an arithmetic sequence.

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For the following exercises, use the information provided to graph the first 5 terms of the arithmetic sequence.

a 1 = 9 ; a n = a n 1 10

Graph of a scattered plot with labeled points: (1, 9), (2, -1), (3, -11), (4, -21), and (5, -31). The x-axis is labeled n and the y-axis is labeled a_n.
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Technology

For the following exercises, follow the steps to work with the arithmetic sequence a n = 3 n 2 using a graphing calculator:

  • Press [MODE]
    • Select SEQ in the fourth line
    • Select DOT in the fifth line
    • Press [ENTER]
  • Press [Y=]
    • n Min is the first counting number for the sequence. Set n Min = 1
    • u ( n ) is the pattern for the sequence. Set u ( n ) = 3 n 2
    • u ( n Min) is the first number in the sequence. Set u ( n Min) = 1
  • Press [2ND] then [WINDOW] to go to TBLSET
    • Set TblStart = 1
    • Set Δ Tbl = 1
    • Set Indpnt: Auto and Depend: Auto
  • Press [2ND] then [GRAPH] to go to the TABLE

What are the first seven terms shown in the column with the heading u ( n ) ?

1 , 4 , 7 , 10 , 13 , 16 , 19

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Use the scroll-down arrow to scroll to n = 50. What value is given for u ( n ) ?

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

Graph of a scattered plot with labeled points: (1, 1), (2, 4), (3, 7), (4, 10), and (5, 13). The x-axis is labeled n and the y-axis is labeled a_n.
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For the following exercises, follow the steps given above to work with the arithmetic sequence a n = 1 2 n + 5 using a graphing calculator.

What are the first seven terms shown in the column with the heading u ( n ) in the TABLE feature?

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Graph the sequence as it appears on the graphing calculator. Be sure to adjust the WINDOW settings as needed.

Graph of a scattered plot with labeled points: (1, 5.5), (2, 6), (3, 6.5), (4, 7), and (5, 7.5). The x-axis is labeled n and the y-axis is labeled a_n.
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Extensions

Give two examples of arithmetic sequences whose 4 th terms are 9.

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Give two examples of arithmetic sequences whose 10 th terms are 206.

Answers will vary. Examples: a n = 20.6 n and a n = 2 + 20.4 n.

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Find the 5 th term of the arithmetic sequence { 9 b , 5 b , b , } .

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Find the 11 th term of the arithmetic sequence { 3 a 2 b , a + 2 b , a + 6 b } .

a 11 = 17 a + 38 b

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At which term does the sequence { 5.4 , 14.5 , 23.6 , ... } exceed 151?

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At which term does the sequence { 17 3 , 31 6 , 14 3 , ... } begin to have negative values?

The sequence begins to have negative values at the 13 th term, a 13 = 1 3

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For which terms does the finite arithmetic sequence { 5 2 , 19 8 , 9 4 , ... , 1 8 } have integer values?

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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: 3 , 0 , 3 , 6 a 31 = 87

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Write an arithmetic sequence using an explicit formula. Show the first 4 terms, and then find the 28 th term.

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Questions & Answers

find the value of 2x=32
Felix Reply
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
use the y -intercept and slope to sketch the graph of the equation y=6x
Only Reply
how do we prove the quadratic formular
Seidu Reply
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
Shirley Reply
thank you help me with how to prove the quadratic equation
Seidu
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Opoku
what is math number
Tric Reply
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
Alfred Reply
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Kala Reply
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
Moses Reply
12, 17, 22.... 25th term
Alexandra Reply
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Shirleen Reply
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
hi vedant can u help me with some assignments
Solomon
find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma
Practice Key Terms 2

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Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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