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What are the main differences between using a recursive formula and using an explicit formula to describe an arithmetic sequence?

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Describe how linear functions and arithmetic sequences are similar. How are they different?

Both arithmetic sequences and linear functions have a constant rate of change. They are different because their domains are not the same; linear functions are defined for all real numbers, and arithmetic sequences are defined for natural numbers or a subset of the natural numbers.

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Algebraic

For the following exercises, find the common difference for the arithmetic sequence provided.

{ 5 , 11 , 17 , 23 , 29 , ... }

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{ 0 , 1 2 , 1 , 3 2 , 2 , ... }

The common difference is 1 2

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For the following exercises, determine whether the sequence is arithmetic. If so find the common difference.

{ 11.4 , 9.3 , 7.2 , 5.1 , 3 , ... }

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{ 4 , 16 , 64 , 256 , 1024 , ... }

The sequence is not arithmetic because 16 4 64 16.

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For the following exercises, write the first five terms of the arithmetic sequence given the first term and common difference.

a 1 = 0 , d = 2 3

0 , 2 3 , 4 3 , 2 , 8 3

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For the following exercises, write the first five terms of the arithmetic series given two terms.

a 1 = 17 , a 7 = 31

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a 13 = 60 , a 33 = 160

0 , 5 , 10 , 15 , 20

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For the following exercises, find the specified term for the arithmetic sequence given the first term and common difference.

First term is 3, common difference is 4, find the 5 th term.

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First term is 4, common difference is 5, find the 4 th term.

a 4 = 19

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First term is 5, common difference is 6, find the 8 th term.

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First term is 6, common difference is 7, find the 6 th term.

a 6 = 41

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First term is 7, common difference is 8, find the 7 th term.

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For the following exercises, find the first term given two terms from an arithmetic sequence.

Find the first term or a 1 of an arithmetic sequence if a 6 = 12 and a 14 = 28.

a 1 = 2

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Find the first term or a 1 of an arithmetic sequence if a 7 = 21 and a 15 = 42.

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Find the first term or a 1 of an arithmetic sequence if a 8 = 40 and a 23 = 115.

a 1 = 5

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Find the first term or a 1 of an arithmetic sequence if a 9 = 54 and a 17 = 102.

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Find the first term or a 1 of an arithmetic sequence if a 11 = 11 and a 21 = 16.

a 1 = 6

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For the following exercises, find the specified term given two terms from an arithmetic sequence.

a 1 = 33 and a 7 = 15. Find a 4 .

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a 3 = 17.1 and a 10 = 15.7. Find a 21 .

a 21 = 13.5

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

a 1 = 39 ;   a n = a n 1 3

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a 1 = 19 ;   a n = a n 1 1.4

19 , 20.4 , 21.8 , 23.2 , 24.6

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For the following exercises, write a recursive formula for each arithmetic sequence.

a n = { 40 , 60 , 80 , ... }

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a n = { 17 , 26 , 35 , ... }

a 1 = 17 ;   a n = a n 1 + 9 n 2

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a n = { 1 , 2 , 5 , ... }

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a n = { 12 , 17 , 22 , ... }

a 1 = 12 ;   a n = a n 1 + 5 n 2

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a n = { 15 , 7 , 1 , ... }

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a n = { 8.9 , 10.3 , 11.7 , ... }

a 1 = 8.9 ;   a n = a n 1 + 1.4 n 2

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a n = { 0.52 , 1.02 , 1.52 , ... }

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a n = { 1 5 , 9 20 , 7 10 , ... }

a 1 = 1 5 ;   a n = a n 1 + 1 4 n 2

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a n = { 1 2 , 5 4 , 2 , ... }

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a n = { 1 6 , 11 12 , 2 , ... }

1 = 1 6 ;   a n = a n 1 13 12 n 2

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For the following exercises, write a recursive formula for the given arithmetic sequence, and then find the specified term.

a n = { 7 4 1 ... } ; Find the 17 th term.

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a n = { 4 11 18 ... } ; Find the 14 th term.

a 1 = 4 ;   a n = a n 1 + 7 ;   a 14 = 95

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a n = { 2 6 10 ... } ; Find the 12 th term.

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Questions & Answers

hello, I am happy to help!
Shirley Reply
please can go further on polynomials quadratic
Abdullahi
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
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
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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