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Thepotemich [5.8K]
3 years ago
9

In an arithmetic sequence, a_17 = -40 and a_28 = -73. Please explain how to use this information to write a recursive formula fo

r this sequence!
Mathematics
1 answer:
Vinvika [58]3 years ago
7 0

An arithmetic sequence

a_1,a_2,a_3,\ldots,a_n,\ldots

is one in which consecutive terms of the sequence differ by a fixed number, call it <em>d</em>. This means that, given the first term a_1, we can build the sequence by simply adding <em>d</em> :

a_2=a_1+d

a_3=a_2+d

a_4=a_3+d

and so on, the general pattern governed by the recursive rule,

a_n=a_{n-1}+d

We can exploit this rule in order to write any term of the sequence in terms of the first one. For example,

a_3=a_2+d=(a_1+d)+d=a_1+2d

a_4=a_3+d=(a_1+2d)+d=a_1+3d

and so on up to

a_n=a_1+(n-1)d

In this case, we're not given the first term right away, but the 17th. But this isn't a problem; we can use the same exploit to get

a_{18}=a_{17}+d

a_{19}=a_{17}+2d

a_{20}=a_{17}+3d

and so on, up to the next term we know,

a_{28}=a_{17}+11d=-40+11d

(Notice how the subscript of <em>a</em> on the right and the coefficient of <em>d</em> add up to the subscript of <em>a</em> on the left.)

The 28th term is -73, so we can solve for <em>d</em> :

-73=-40+11d\implies -33=11d\implies d=-3

To get the first term of the sequence, we use the rule found above and either of the known values of the sequence. For instance,

a_{17}=a_1+16d\implies-40=a_1-16\cdot3\implies a_1=8

Then the recursive rule for this particular sequence is

\begin{cases}a_1=8\\a_n=a_{n-1}-3&\text{for }n>1\end{cases}

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Gala2k [10]

Answer:

(x,y)→(y,-x)

Step-by-step explanation:

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B(5,4)

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Rule:

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so the rule is

(x,y)→(y,-x)

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2 years ago
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The Solution:

Given:

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10 months ago
. The mean width of 12 iPads is 5.1 inches. The mean width of 8 Kindles is 4.8 inches. a. What is the total width of the iPads?
UkoKoshka [18]

Answer:

a) 61.2, b) 38.4 and c) 4.98

Step-by-step explanation:

Given:

The mean width of 12 I-Pads is 5.1 inches.

The mean width of 8 Kindles is 4.8 inches.

Question asked:

a. What is the total width of the I-Pads?

b. What is the total width of the Kindles?

c. What is the mean width of the 12 I-Pads and 8 Kindles?

Solution:

<u>As we know:</u>

<u />Mean =\frac{Sum\ of\ observations}{Number\ of\ observations}\\ \\ Mean\ width =\frac{Sum\ of\ width\ of\ all \ I-pad}{Number \  of\ I-pad}

5.1=\frac{Sum\ of\ width\ of\ all\ I-pad}{12} \\ \\ By \ cross\ multiplication\\ \\ Sum\ of\ width\ of\ all\ I-pad}=5.1\times1 2\\ \\ Sum\ of\ width\ of\ all\ I-pad}= 61.2

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Mean\ width =\frac{Sum\ of\ width\ of\ all\ Kindles}{Number \  of\ Kindles}

4.8=\frac{Sum\ of\ width\ of\ all\Kindles}{8} \\ \\ By \ cross\ multiplication\\ \\ Sum\ of\ width\ of\ all \ Kindles=4.8\times8\\ \\ Sum\ of\ width\ of \ all\ Kindles}=38.4

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Combined mean of width of the 12 I-Pads and 8 Kindles = Combined width of both I-pad and Kindles \div Combined number of observations

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Scilla [17]
Hello There!

Follow through these steps:
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76 + 85 + 86 = 247
308 - 247 = 61.

She needs to score 61.

Hope This Helps You!
Good Luck :) 

- Hannah ❤
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