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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

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
Naveen
what is subgroup
Purshotam Reply
Prove that: (2cos&+1)(2cos&-1)(2cos2&-1)=2cos4&+1
Macmillan Reply
e power cos hyperbolic (x+iy)
Vinay Reply
10y
Michael
tan hyperbolic inverse (x+iy)=alpha +i bita
Payal Reply
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
Trilochan Reply
what is complex numbers
Ayushi Reply
Please you teach
Dua
Yes
ahmed
Thank you
Dua
give me treganamentry question
Anshuman Reply
Solve 2cos x + 3sin x = 0.5
shobana 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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