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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

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
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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