Mathematics: What number completes the pattern 3, 9,_ , 243

What number completes the pattern 3, 9,_ , 243, №11244367, 17.02.2021 09:50

Mathematics

If x = 1, 2, 3, 4, . . which pattern of y-values completes a linear function? a y = 0, 1, 8, 27, . . b y = 1, 2, 4, 7, . . c y = 1, 3, 9, 27, . . d y = 2, 5, 8, 11, . .

Step-by-step answer

P Answered by PhD

1

The answer for the question above is the option D, which is: D y=2, 5, 8, 11,...
The explanation for this answer is shown below:
As you can see, the option D, y=2, 5, 8, 11,...increase with a constant factor of 3, and the other options do not increase with a constant factor, therefore, they are not linear functions.
Finally, keeping the information above on mind, you have that the linear function is the following: f(x)=3x-1.

Mathematics

If x = 1, 2, 3, 4, . . which pattern of y-values completes a linear function? a y = 0, 1, 8, 27, . . b y = 1, 2, 4, 7, . . c y = 1, 3, 9, 27, . . d y = 2, 5, 8, 11, . .

Step-by-step answer

P Answered by PhD

1

The answer for the question above is the option D, which is: D y=2, 5, 8, 11,...
The explanation for this answer is shown below:
As you can see, the option D, y=2, 5, 8, 11,...increase with a constant factor of 3, and the other options do not increase with a constant factor, therefore, they are not linear functions.
Finally, keeping the information above on mind, you have that the linear function is the following: f(x)=3x-1.

Mathematics

Part 1.] match these items. 1.) the positive integers 2.) an ordering of quantities 3.) 2, 4, 8, 16, . ., 256 4.) 1, 3, 5, 7, . . 5.) no first term is available a.) an example of a finite sequence b.) a sequence c.) the reason the numbers . . -4, -2, 0, 2, 4, . . are not a sequence d.) the natural numbers e.) an example of an infinite sequence part 2.] write the first five terms of the sequence. [tex] a_{n}= n^{2}+2[/tex] a.] 3,6,11,18,27 b.] 3,6,9,12,15 c.] 2,3,6,11,18 part 3.] write the first five terms of the sequence. [tex] a_{n}= -1( frac{1}{3})^{n-1}[/tex]

Step-by-step answer

P Answered by Specialist

43

Part 1
1) The positive integers -----------> D.) The natural numbers
2.) An ordering of quantities  -----------> B.) A sequence
3.) 2, 4, 8, 16, . . ., 256   ----------->  A.) An example of a finite sequence
4.) 1, 3, 5, 7, . . .   ----------->  E.) An example of an infinite sequence
5.) No first term is available ----------->  C.) The reason the numbers . . . -4, -2, 0, 2, 4, . . . are not a sequence
Part 2
$a_n=n^2+2\\ a_1=1+2=3\\ a_2=4+2=6\\ a_3=9+2=11\\ a_4=16+2=18\\ a_5=25+2=27$
The answers is A.
Part 3
$a_n=-1(\frac{1}{3})^{n-1} \\ a_1=-1(\frac{1}{3})^{1-1}=-1\\ a_2=-1(\frac{1}{3})^{2-1}=-\frac{1}{3}\\ a_3=-1(\frac{1}{3})^{3-1}=--\frac{1}{9}\\ a_4=-1(\frac{1}{3})^{4-1}=--\frac{1}{27}\\ a_5=-1(\frac{1}{3})^{5-1}=--\frac{1}{81}\\$
The answers is B.
Part 4
The pattern in this sequence is:
$a_n=2a^nb^{n-1}$
Let's list first six terms:
$a_n=2a^nb^{n-1}\\
a_1=2a^1b^0=2a\\
a_2=2a^2b^1=2a^2b\\
a_3=2a^3b^2\\
a_4=2a^4b^3\\
a_5=2a^5b^4\\
a_6=2a^6b^5\\$
This is a infinite sequence. The patern is obvious and we could find any term within the sequence.

Mathematics

Part 1.] match these items. 1.) the positive integers 2.) an ordering of quantities 3.) 2, 4, 8, 16, . ., 256 4.) 1, 3, 5, 7, . . 5.) no first term is available a.) an example of a finite sequence b.) a sequence c.) the reason the numbers . . -4, -2, 0, 2, 4, . . are not a sequence d.) the natural numbers e.) an example of an infinite sequence part 2.] write the first five terms of the sequence. [tex] a_{n}= n^{2}+2[/tex] a.] 3,6,11,18,27 b.] 3,6,9,12,15 c.] 2,3,6,11,18 part 3.] write the first five terms of the sequence. [tex] a_{n}= -1( frac{1}{3})^{n-1}[/tex]

Step-by-step answer

P Answered by Specialist

43

Part 1
1) The positive integers -----------> D.) The natural numbers
2.) An ordering of quantities  -----------> B.) A sequence
3.) 2, 4, 8, 16, . . ., 256   ----------->  A.) An example of a finite sequence
4.) 1, 3, 5, 7, . . .   ----------->  E.) An example of an infinite sequence
5.) No first term is available ----------->  C.) The reason the numbers . . . -4, -2, 0, 2, 4, . . . are not a sequence
Part 2
$a_n=n^2+2\\ a_1=1+2=3\\ a_2=4+2=6\\ a_3=9+2=11\\ a_4=16+2=18\\ a_5=25+2=27$
The answers is A.
Part 3
$a_n=-1(\frac{1}{3})^{n-1} \\ a_1=-1(\frac{1}{3})^{1-1}=-1\\ a_2=-1(\frac{1}{3})^{2-1}=-\frac{1}{3}\\ a_3=-1(\frac{1}{3})^{3-1}=--\frac{1}{9}\\ a_4=-1(\frac{1}{3})^{4-1}=--\frac{1}{27}\\ a_5=-1(\frac{1}{3})^{5-1}=--\frac{1}{81}\\$
The answers is B.
Part 4
The pattern in this sequence is:
$a_n=2a^nb^{n-1}$
Let's list first six terms:
$a_n=2a^nb^{n-1}\\
a_1=2a^1b^0=2a\\
a_2=2a^2b^1=2a^2b\\
a_3=2a^3b^2\\
a_4=2a^4b^3\\
a_5=2a^5b^4\\
a_6=2a^6b^5\\$
This is a infinite sequence. The patern is obvious and we could find any term within the sequence.

Mathematics

Complete each pattern. 1/3,2/6,3/9,4/ 1/2,2/4,3/6,4/8,5/ ,6/

Step-by-step answer

P Answered by PhD

1

1/3, 2/6, 3/9, 4/You see the pattern? The denominator is by 3's. You can also see it as 1*3=3, 2*3=6, 3*3=6, then 4*3=12

So, the last fraction would be 4/12.

1/2, 2/4, 3/6, 4/8, 5/ , 6/ The denominator is by 2's.
1*2=2, 2*2=4, 3*2=6, 4*2=8, 5*2=10,6*2=12

So, the last two fractions would be 5/10, and 6/12.

Mathematics

Complete each pattern. 1/3,2/6,3/9,4/ 1/2,2/4,3/6,4/8,5/ ,6/

Step-by-step answer

P Answered by PhD

1

1/3, 2/6, 3/9, 4/You see the pattern? The denominator is by 3's. You can also see it as 1*3=3, 2*3=6, 3*3=6, then 4*3=12

So, the last fraction would be 4/12.

1/2, 2/4, 3/6, 4/8, 5/ , 6/ The denominator is by 2's.
1*2=2, 2*2=4, 3*2=6, 4*2=8, 5*2=10,6*2=12

So, the last two fractions would be 5/10, and 6/12.

Mathematics

Complete the pattern 1/27, 1/9, 1/3, 1

Step-by-step answer

P Answered by PhD

1. Let the $n^{th}$ term of the sequence be $u_{n}$

2. The first term $u_{1}$ =1/27, second term $u_{2}$ =1/9 and so on

3. so

$u_{1}= \frac{1}{27}= \frac{1}{ 3^{3} }= 3^{-3}$

$u_{2}= \frac{1}{9}= \frac{1}{ 3^{2} }= 3^{-2}$

$u_{3}= \frac{1}{3}= \frac{1}{ 3^{1} }= 3^{-1}$

$u_{4}= 3^{0}$

so by now it is clear that the general rule is $u_{n}= 3^{n-4}$

so the next term, $u_{4}$ is $u_{5}= 3^{5-4}=3^{1}=3$

Mathematics

Complete the pattern 1/27, 1/9, 1/3, 1

Step-by-step answer

P Answered by PhD

1. Let the $n^{th}$ term of the sequence be $u_{n}$

2. The first term $u_{1}$ =1/27, second term $u_{2}$ =1/9 and so on

3. so

$u_{1}= \frac{1}{27}= \frac{1}{ 3^{3} }= 3^{-3}$

$u_{2}= \frac{1}{9}= \frac{1}{ 3^{2} }= 3^{-2}$

$u_{3}= \frac{1}{3}= \frac{1}{ 3^{1} }= 3^{-1}$

$u_{4}= 3^{0}$

so by now it is clear that the general rule is $u_{n}= 3^{n-4}$

so the next term, $u_{4}$ is $u_{5}= 3^{5-4}=3^{1}=3$

Mathematics

Complete the patterns of the equivalent ratios by filling in the gaps. 27:9 _ : 7 15:5 9 : _ 3 : _

Step-by-step answer

P Answered by PhD

1

21:3
9:3
3:1

there all a 3:1 ratio

Mathematics

Weight (g) words, not numbers, deso 1-14. k (for example, write, double the previo vious number copy and complete each sequence below. using we how the patterns work. (for example, write. “t a. 1,3,6, 10,- - b. 1, 2, 3, 5, d. 8,7,5,2,_ c. e. 1,3,9, 27, 49, 47, 52, 50, 55, 12 core connections, course

Step-by-step answer

P Answered by PhD

a) add n+1 to the previous term

b) add the previous two terms

d) subtract n+1 from the previous term

e) multiply the previous term by 3

f) subtract 2 from previous term then add 5 to the next term

Step-by-step explanation:

a) 1, 3, 6, 10

∨ ∨ ∨

+2 +3 +4 The next term is 10 +5 = 15

b) 1, 2, 3, 5

∨ ∨ ∨

=3 =5 =8 The next term is 5 + 8 = 13

d) 8, 7, 5, 2

∨ ∨ ∨

-1 -2 -3 zThe next term is 2 - 4 = -2

e) 1, 3, 9, 27

∨ ∨ ∨

×3 ×3 ×3 The next term is 27 × 3 = 81

f) 49, 47, 52, 50, 55

∨ ∨ ∨ ∨

-2 +5 -2 +5 The next term is 55 - 2 = 53

The following term is 53 + 5 = 58

What number completes the pattern 3, 9,_ , 243

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