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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

show that the set of all natural number form semi group under the composition of addition
Nikhil Reply
explain and give four Example hyperbolic function
Lukman Reply
_3_2_1
felecia
⅗ ⅔½
felecia
_½+⅔-¾
felecia
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
SABAL Reply
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
Pawel
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
Pawel
ok
Ifeanyi
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
x*x=2
felecia
2+2x=
felecia
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
mariel Reply
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
Harshika Reply
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
Shirley Reply
please can go further on polynomials quadratic
Abdullahi
hi mam
Mark
I need quadratic equation link to Alpa Beta
Abdullahi Reply
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
yes i wantt to review
Mark
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
please help me prove quadratic formula
Darius
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
may God blessed u for that. Please I want u to help me in sets.
Opoku
what is math number
Tric Reply
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
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
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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