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3 years ago

5

you want to create a rectangular display of 50 quarters with the same amount of quarters in each row. how many ways can you arra

nge your display?

2 answers:

oksian1 [2.3K]3 years ago

8 0

10 and 5
50 and 1
2 and 25

Over [174]3 years ago

6 0

You can make:
1 row of 50
2 rows of 25
5 rows of 10
10 rows of 5
25 rows of 2
and 50 rows of 1

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Answer:

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3 years ago

4. A geometric sequence is defined recursively by a(1) = 40 and a(n)= a(n-1)

Anarel [89]

The complete question is:

A geometric sequence is defined recursively by

$a_{(1)}=40\text{ and }a_n=(-1/2)a_{(n-1)}$

(a) Write out the first four terms of this sequence.

(b) Is the 9th term of this sequence larger or smaller than 1/10? Show the calculation that you use to determine your answer.

Answer:

<u>The 9th term is larger than 1/10.</u>

Explanation:

You are given the first term, $a_(1)=40$ , and the recursive formula

$a_{(n)}=(-1/2)a_{(n-1}$

Thus, you can find the sequence of terms by multiplying each term by the constant ratio, (-1/2).

<u>(a) First four terms of the sequence</u>

$a_{(1)}=40\\ \\ a_{(2)}=40\times (-1/2)=-20\\ \\ a_{(3)}=-20\times (-1/2)=10\\\\ a_{(4)}=10\times (-1/2)=-5$

Those are the first four terms.

<u>(b) 9th term</u>

You can write the explicit formula of the sequence as:

$a_{(n)}=a_{(1)}\times r^{(n-1)}\\ \\ a_{(n)}=40(-1/2)^{(n-1)}$

Thus, for the 9th term, n = 9, and the term is:

$a_{(9)}=40\times (-1/2)^{(9-1)}\\ \\ a_{(9)}=40\times(-1/2)^8\\ \\ a_{(9)}=40\times(1/256)=0.1526$

Since 1/10 = 0.1, and 0.1 < 0.1526, the 9th term is larger than 1/10.

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3 years ago