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Taya2010 [7]
3 years ago
13

Find the next two terms in the given sequence, then write it in recursive form. A.) {7,12,17,22,27,...} B.) { 3,7,15,31,63,...}​

Mathematics
1 answer:
iren [92.7K]3 years ago
7 0

Answer:

A) a_n = 5n + 2

B) a_n = (2^(n + 1)) - 1

Step-by-step explanation:

A) The sequence is given as;

{7,12,17,22,27,...}

The differences are:

5,5,5,5.

This is an arithmetic sequence following the formula;

a_n = a_1 + (n - 1)d

d is 5

Thus;

a_n = a_1 + (n - 1)5

Now, a_1 = 7. Thus;

a_n = 7 + 5n - 5

a_n = 5n + 2

B) The sequence is given as;

{ 3,7,15,31,63,...}​

Now, let's write out the differences of this sequence:

Differences are:

4, 8, 16, 32

This shows that it is a geometric sequence with a common ratio of 2.

In the given sequence, a_1 = 3 and a_2 = 7 and a_3 = 15

Thus, a_2 = 2a_1 + 1

Also, a_(2 + 1) = 2a_2 + 1

Combining both equations, we can deduce that: a_(n + 1) = 2a_n + 1

Thus; a_n can be expressed as:

a_n = (2^(n + 1)) - 1

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The length of a rectangle is 22 centimeters and the width is
nataly862011 [7]

Answer:

78cm

Step-by-step explanation:

L₁/W₁ = L₂/W₂

22/4 = L₂/6

5.5*6=L₂

L₂=33cm

Perimeter of rectangle = 2L+2W

=2(33)+2(6)

=66+12

=78cm

7 0
2 years ago
100 Points PLEASE ANSWER ASP! Will Give BRAINLIST!
VikaD [51]

Let's work to solve this system of equations:

y = 2x ~~~~~~~~\gray{\text{Equation 1}}y=2x        Equation 1

x + y = 24 ~~~~~~~~\gray{\text{Equation 2}}x+y=24        Equation 2

The tricky thing is that there are two variables, xx and yy. If only we could get rid of one of the variables...

Here's an idea! Equation 11 tells us that \goldD{2x}2x and \goldD yy are equal. So let's plug in \goldD{2x}2x for \goldD yy in Equation 22 to get rid of the yy variable in that equation:

\begin{aligned} x + \goldD y &= 24 &\gray{\text{Equation 2}} \\\\ x + \goldD{2x} &= 24 &\gray{\text{Substitute 2x for y}}\end{aligned}  

x+y

x+2x

​    

=24

=24

​    

Equation 2

Substitute 2x for y

​  

Brilliant! Now we have an equation with just the xx variable that we know how to solve:

x+2x3x 3x3x=24=24=243=8Divide each side by 3

Nice! So we know that xx equals 88. But remember that we are looking for an ordered pair. We need a yy value as well. Let's use the first equation to find yy when xx equals 88:

\begin{aligned} y &= 2\blueD x &\gray{\text{Equation 1}} \\\\ y &= 2(\blueD8) &\gray{\text{Substitute 8 for x}}\\\\ \greenD y &\greenD= \greenD{16}\end{aligned}  

y

y

y

​    

=2x

=2(8)

=16

​    

Equation 1

Substitute 8 for x

​  

Sweet! So the solution to the system of equations is (\blueD8, \greenD{16})(8,16). It's always a good idea to check the solution back in the original equations just to be sure.

Let's check the first equation:

\begin{aligned} y &= 2x \\\\ \greenD{16} &\stackrel?= 2(\blueD{8}) &\gray{\text{Plug in x = 8 and y = 16}}\\\\ 16 &= 16 &\gray{\text{Yes!}}\end{aligned}  

y

16

16

​    

=2x

=

?

2(8)

=16

​    

Plug in x = 8 and y = 16

Yes!

​  

Let's check the second equation:

\begin{aligned} x +y &= 24 \\\\ \blueD{8} + \greenD{16} &\stackrel?= 24 &\gray{\text{Plug in x = 8 and y = 16}}\\\\ 24 &= 24 &\gray{\text{Yes!}}\end{aligned}  

x+y

8+16

24

​    

=24

=

?

24

=24

​    

Plug in x = 8 and y = 16

Yes!

​  

Great! (\blueD8, \greenD{16})(8,16) is indeed a solution. We must not have made any mistakes.

Your turn to solve a system of equations using substitution.

Use substitution to solve the following system of equations.

4x + y = 284x+y=28

y = 3xy=3x

4 0
3 years ago
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Which of the following units are most commonly used in the United States? Check all that apply. O A. Meters O B. Ounces C. Kilog
ArbitrLikvidat [17]

Answer:

I would say D. feet

4 0
3 years ago
Read 2 more answers
PLEASE HELP!!!!!!!!! LOOK AT PIC, THANKS!!!!!!
mario62 [17]

Answer:

F (x) = 1,6

Step-by-step explanation:

my answer is due to the reason that it is one of the three options and it should only in a way make sense that it is the right answer

3 0
2 years ago
PLEASE PLEASE PLEASEE PLEASEEEEESE HELPME!?!?!? IM SO BAD AT MATH PLEASE HELP!!!
Fiesta28 [93]
For this case we have the following function:
 f (x) = 0.01 * (2) ^ x

 By definition, the average rate of change is given by:
 AVR =  \frac{f(x2) - f(x1)}{x2 - x1}
 We evaluate the function for the given values:
 For x = 7:
 f (7) = 0.01 * (2) ^ 7

f (7) = 1.28
 For x = 14:
 f (14) = 0.01 * (2) ^ {14}  f (14) = 163.84
 Then, replacing values we have:
 AVR = \frac{163.84 - 1.28}{14 - 7}
 AVR = 23.22
 Answer:
 
the average rate of change from x = 7 to x = 14 is:
 
a. 23.22 
7 0
3 years ago
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