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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

the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply
1+cos²A/cos²A=2cosec²A-1
Ramesh Reply
test for convergence the series 1+x/2+2!/9x3
success Reply
a man walks up 200 meters along a straight road whose inclination is 30 degree.How high above the starting level is he?
Lhorren Reply
100 meters
Kuldeep
Find that number sum and product of all the divisors of 360
jancy Reply
answer
Ajith
exponential series
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what is subgroup
Purshotam Reply
Prove that: (2cos&+1)(2cos&-1)(2cos2&-1)=2cos4&+1
Macmillan Reply
e power cos hyperbolic (x+iy)
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10y
Michael
tan hyperbolic inverse (x+iy)=alpha +i bita
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prove that cos(π/6-a)*cos(π/3+b)-sin(π/6-a)*sin(π/3+b)=sin(a-b)
Tejas Reply
why {2kπ} union {kπ}={kπ}?
Huy Reply
why is {2kπ} union {kπ}={kπ}? when k belong to integer
Huy
if 9 sin theta + 40 cos theta = 41,prove that:41 cos theta = 41
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what is complex numbers
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Solve 2cos x + 3sin x = 0.5
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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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