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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 the function of sine with respect of cosine , graphically
Karl Reply
tangent bruh
Steve
cosx.cos2x.cos4x.cos8x
Aashish Reply
sinx sin2x is linearly dependent
cr Reply
what is a reciprocal
Ajibola Reply
The reciprocal of a number is 1 divided by a number. eg the reciprocal of 10 is 1/10 which is 0.1
Shemmy
 Reciprocal is a pair of numbers that, when multiplied together, equal to 1. Example; the reciprocal of 3 is ⅓, because 3 multiplied by ⅓ is equal to 1
Jeza
each term in a sequence below is five times the previous term what is the eighth term in the sequence
Funmilola Reply
I don't understand how radicals works pls
Kenny Reply
How look for the general solution of a trig function
collins Reply
stock therom F=(x2+y2) i-2xy J jaha x=a y=o y=b
Saurabh Reply
sinx sin2x is linearly dependent
cr
root under 3-root under 2 by 5 y square
Himanshu Reply
The sum of the first n terms of a certain series is 2^n-1, Show that , this series is Geometric and Find the formula of the n^th
amani Reply
cosA\1+sinA=secA-tanA
Aasik Reply
Wrong question
Saad
why two x + seven is equal to nineteen.
Kingsley Reply
The numbers cannot be combined with the x
Othman
2x + 7 =19
humberto
2x +7=19. 2x=19 - 7 2x=12 x=6
Yvonne
because x is 6
SAIDI
what is the best practice that will address the issue on this topic? anyone who can help me. i'm working on my action research.
Melanie Reply
simplify each radical by removing as many factors as possible (a) √75
Jason Reply
how is infinity bidder from undefined?
Karl Reply
Practice Key Terms 2

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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