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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

what is math number
Tric Reply
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
hi
Adu
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10
Augustine
how do they get the third part x = (32)5/4
kinnecy Reply
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
AJ
how
Sheref
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
hi
Ayuba
Hello
opoku
hi
Ali
greetings from Iran
Ali
salut. from Algeria
Bach
hi
Nharnhar
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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