Determine if the sequence is geometric . If it is , find the common ratio , the explicit formula and the recursive formula .


1. -40 , 20 , -100 , 500


2. 4 , 20 , 100 , 500


3. 4 , 24 , 144, 864


5. 3 , -12 , 48 , -192

Answers

Answer 1

Step-by-step explanation:

if it is a geometric sequence, then

sn = sn-1 × r

with r being the common ratio.

1.

s2 = s1 × r

20 = -40 × r

r = 20/-40 = -1/2

but the same r has to apply to all other terms, if it is geometric.

s3 = s2 × r

-100 = 20 × -1/2 = -10

this is wrong, so, it is not geometric.

2.

s2 = s1 × r

20 = 4 × r

r = 20/4 = 5

but the same r has to apply to all other terms, if it is geometric.

s3 = s2 × r

100 = 20 × 5 = 100

s4 = s3 × r

500 = 100 × 5 = 500

this is all correct, so, it is geometric.

sn = sn-1 × 5

sn = s1 × 5^(n-1) = 4 × 5^(n-1)

3.

s2 = s1 × r

24 = 4 × r

r = 24/4 = 6

but the same r has to apply to all other terms, if it is geometric.

s3 = s2 × r

144 = 24 × 6 = 144

s4 = s3 × r

864 = 144 × 6 = 864

this is all correct, so, it is geometric.

sn = sn-1 × 6

sn = s1 × 6^(n-1) = 4 × 6^(n-1)

5.

s2 = s1 × r

-12 = 3 × r

r = -12/3 = -4

but the same r has to apply to all other terms, if it is geometric.

s3 = s2 × r

48 = -12 × -4 = 48

s4 = s3 × r

-192 = 48 × -4 = -192

this is all correct, so, it is geometric.

sn = sn-1 × -4

sn = s1 × (-4)^(n-1) = 3 × (-4)^(n-1)


Related Questions

Determine whether each graph shows a positive correlation, a negative
correlation, or no correlation. If there is a positive or negative correlation,
describe its meaning in the situation.

Answers

Answer:

Positive correlation.

Step-by-step explanation:

From the graph we can see overall increasing trend.

It means there is a positive correlation.

The meaning of this is the more time you spend on study the better test score you get.

Answer:

Negative correlation

Step-by-step explanation:

As TV hours increase, exercise

hours decrease.

PLEASE HELP ME!!!
Which expression has a value of 8?

a: 10−(−2)

b: (−10)−(−2)

c:(−2)−(−10)

d: (−2)−10

Answers

Answer:

c:(-2)-(-10)

Step-by-step explanation:

When two minus symbols are next to each other in an expression, they become a plus sign.

a: 10-(-2)

   10+2

     12

b: (-10)-(-2)

     -10+2

        -8

c: (-2)-(-10)

     -2+10

        8

d: (-2)-10

      -12

C.

-2 - -10= 8

The negative stays the same. The two dashes in between 2 and 10 become pluses.

10 - 2 = 8

The bigger number positive or negative is the dominant passing down their + or - to the value.

Answer as soon as possible I’ll give 5 stars!!!

Answers

Answer:

B

Step-by-step explanation:

2 times x is 2x

2*8=16

its B

Hey there!

2(x + 8)

DISTRIBUTE 2 WITHIN THE PARENTHESES

= 2(x) + 2(8)

= 2x + 16

Therefore, your answer should be: 2x + 16

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

A group hiked 3 7/10 miles on the Blue Trail and then 4 3/4 miles on the White Trail. What is the total distance the group hiked?

Answers

Answer:

8 9/20

Step-by-step explanation:

Just add them which would give you 169/20 and then simplify it which would be 8 9/20.

Help help math please I don’t understand

Answers

Answer:

45°

Step-by-step explanation:

it's a mirror angle to the known angle

what is the value of x in x(a+b)=b(c-x)​

Answers

Answer:

x = [tex]\frac{bc}{a+2b}[/tex]

Step-by-step explanation:

x(a + b) = b(c - x) ← distribute parenthesis on both sides

ax + bx = bc - bx ( add bx to both sides )

ax + 2bx = bc ← factor out x from each term on the left side

x(a + 2b) = bc ← divide both sides by (a + 2b)

x = [tex]\frac{bc}{a+2b}[/tex]

MODELING REAL LIFE The table shows the amount y (in fluid Ounces) of carpet cleaner in a tank after x minutes of
cleaning.
x ll y
5 ll 108
10 ll 88
15 ll 68
a. Write an equation that represents the amount of cleaner in the tank after x minutes.

b. How much cleaner is in the tank when the cleaning begins?

C. After how many minutes is the tank empty?

Answers

Answer:

a. Write an equation that represents the amount of cleaner in the tank after x minutes

y= -4x + 128

b. How much cleaner is in the tank when the cleaning begins?

128

c. After how many minutes is the tank empty?

The tank is empty in 32 minutes

3. Write an equation in slope-intercept form for the line with a slope of 5/4 and a
y-intercept of 2.

Answers

Answer:

y = [tex]\frac{5}{4}[/tex] x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = [tex]\frac{5}{4}[/tex] and c = 2 , then

y = [tex]\frac{5}{4}[/tex] x + 2 ← equation of line

What is the total holiday debt (no less than $500) that you are trying to pay off and what did you purchase
to accrue (accumulate) that debt?

Answers

Step-by-step explanation:

What is the total holiday debt (no less than $500) that you are trying to pay off and what did you purchase

to accrue (accumulate) that debt?

help pls mwah <3 i also give brainliest

Answers

Answer:

i think it is 0.7 correct me if i am wrong i am in the 6th grade

Step-by-step explanation:

Answer:

y=3/4x

Step-by-step explanation:

From the origin (0,0) count the rise to the next point (3) and then the run (4) leaving you with 3/4 as your slope.

Hope that helps


A small tree was planted at a height of 5 feet. The tree has been planted for 16 months, and is now 48.2 feet tall. Which equation
could be used to find x, the average number of feet the tree grew each month?

Answers

Answer:

Use the equation for Average Rate of Change which will give you 2.7 feet per month

Step-by-step explanation:

The equation is:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Now insert your values:

[tex]\frac{48.2-5}{16-0}[/tex]

The answer is: 2.7 feet per month

Step-by-step explanation:

how much did it grow per month ?

well, it grew from 5 to 48.2 ft in 16 months.

that means it grew 48.2 - 5 = 43.2 ft.

per month that is 43.2/16 = 2.6875 ft per month.

so, the equation would look like

x = (48.2 - 5)/16

State the postulate or theorem you would use to prove each pair of triangles congruent.
a) SSS
b) SAS
c) ASA
d) AAS
e) HL
f) Not possible

Answers

Answer:

  f) Not possible

Step-by-step explanation:

The triangles can be shown to be similar by SAS, but the corresponding sides are not marked as congruent. With the given information, it is not possible to show the triangles are congruent.

I WILL GIVE BRAINLEST AND 50 POINTS
Katrina was training for a race. The line plot below shows the number of miles Katrina ran last week.



3. How many times did Katrina run 1 mile?

Answers

Answer:

Katrina ran 1 mile 3 times! I hope this helps you!

please help, theres a picture

Answers

Answer:

C 1/-3

Step-by-step explanation:

To find the slope I found two-point of the graph that were easy to point out and used rise over run to determine the slope!

In this case, rise was one because it went from -1 to 0 and run was -3 because it went from 0 to -3

Hope this helps!!

Please tell me if I have messed up!!

I enjoy learning form my mistakes:)

*Also if I am correct could you please mark me brainliest? I am trying to level up!!

The line is on -3 and -1 so I think the answer is -1/3 .

Which of the following satisfy x ≥ 4.1? Select all that apply.
x = 4
x = 3.5
x = 4.5
x = 4.1​

Answers

Answer:

x = 4.5

x = 4.1

Step-by-step explanation:

Which function has a greater rate of change?

Answers

Answer:

A

Step-by-step explanation:

Because

Answer:

Step-by-step explanation:

it’s a

Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows:

x 1 2 3 4
p(x) 0.4 0.3 0.2 0.1

Answers

The required linear equation representing the distribution is

p(x) = -0.1x + 0.5

From the table given, we can generate the equation for the distribution.

Expressing as a coordinate form (x, p(x)). We can use the coordinate points (1, 0.4) and (2, 0.3)

The linear expression will be in the form p(x) = mx + b

m is the rate of change:b is the intercept

Gete the rate of change:

m = 0.3-0.4/2-1

m = -0.1/1

m = -0.1

Get the intercept.

0.4 = -0.1(1) + b

0.4  = -0.1  + b

b = 0.4 + 0.1

b = 0.5

Hence the required linear equation representing the distribution is

p(x) = -0.1x + 0.5

Learn more on linear equation here: https://brainly.com/question/18176080

What’s the formula for the series -5,10,-20,40

Answers

Answer:

Stare at it long enough. You will notice that with each step you double the value, and change sign. It makes it a geometric sequence of ratio -2. At this point you have two ways of writing down:

Option 1: Ricorsively, the first term is -5, then the next term is -2 times the previous one:

[tex]\left \{ {{a_0=-5} \atop {a_{n+1}=-2a_n}} \right.[/tex]

Option 2: In closed form, remembering that the n-th term in a geometric sequence is the starting term times the n-th power of the ratio:

[tex]a_n=-5 (-2)^n[/tex]

Either work, depending on what you need to use it for.

A pirate was digging a hole on an island to bury his treasure. If he is able to dig a hole into the sand at 2 feet per minute, what integer would represent how deep the would be after 7 minutes?

Answers

Answer:

2(7) = 14 ft.

Step-by-step explanation:

That pirate must be a beast! or have an excavator.

A dairy needs 364 gallons of milk containing 6% butterfat. How many gallons each of milk containing 7% butterfat and milk containing 3% butterfat must be used to obtain the desired 364 gallons?

Answers

Answer:

Step-by-step explanation:

Let x be gallons of 7%

Let y be gallons of 3%

364 = x + y

y = 364 - x

364(0.06) = x(0.07) + y(0.03)

364(6) = x(7) + y(3)

364(6) = 7x + 3y

364(6) = 7x + 3(364 - x)

364(6 - 3) = 7x - 3x

364(3) = 4x

x = 273

y = 364 - 273 = 91

273 gallons of 7%

91    gallons of 3%

please help ill mark brainliestO​

Answers

Answer:

AA, SAS, SSS

Step-by-step explanation:

These three theorems can be used to find similar triangles.

Integrate:Cos 7x/(1+sin**2(7x))​

Answers

Answer:

7x/1+7sin(2)x

Step-by-step explanation:

squared root of -100 = ____ + ____^i

Answers

Step-by-step explanation:

thats way of multiplication not 56

Answer:

√−100 = 0 + 10 i

Step-by-step explanation:

What is the vertical shift for the absolute value function below. Explain how you know using complete sentences. Include the direction and number of units of the shift. f(x)=9|x+1|+2

Answers

The vertical shift of the function [tex]f(x) = 9|x + 1| + 2[/tex] is 2 units up

The absolute function is given as:

[tex]f(x) = 9|x + 1| + 2[/tex]

An absolute function is represented as:

[tex]f(x) = a|x - h| + k[/tex]

Where k represents the vertical shift.

By comparison, the value of k is:

[tex]k = 2[/tex]

This means that the vertical shift is 2 units

Hence, the vertical shift of the function [tex]f(x) = 9|x + 1| + 2[/tex] is 2 units up

Read more about absolute value function at:

https://brainly.com/question/25971887

can someone help me with this i’ll give you 25 points

Answers

Answer:

Um.... Wouldn't angle 1 just be 180-17 which is 163. Angle 3 would be equal to angle 1 so also 163. Angle 4 and angle 2 are equal to 17.

Step-by-step explanation:

Answer:

angle1 = 163°

angle2 = given in diagram

angle 3 = alternating angle 1, so 163°

angle 4 = alternating angle 2, so 17°

Step-by-step explanation:

noticing that the two lines intercept each other at the centre, making angles going around that interception point add up to 360° (you can use this information to check the answers).

an angle on a straight line is always 180°, so given that angle2 is 17°, you can already do 180 - 17 to get an easy answer to angle 1 and 3.

The ages of the students in a statistics class are listed below. If the 18-year-old student has a birthday and turns 19, how will it affect the mean and median ages of the class?

Ages: 14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18

A
Both the mean age and the median age will increase.

B
The mean age will increase, and the median age will remain the same.

C
The mean age will remain the same, and the median age will increase.

D
The mean age will remain the same, and the median age will decrease.

Answers

A is believe I’m not 100% sure

The mean age will increase, and the median age will remain the same.

Option B is the correct answer.

What is a mean?

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

Ages:

14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18

The mean of the ages.

= (14 + 15 + 15 + 16 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 17 + 18) / 13

= 211/13

= 16.23

The median of the ages.

= 16

Now,

18 becomes 19.

14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 19.

Mean = 212/13 = 16.3

Median = 16

Thus,

The mean age is increased.

The median is the same.

Learn more about mean here:

https://brainly.com/question/23263573

#SPJ2

Please help solve for a in the equation in the photo

Answers

[tex]\huge\bf Question:—[/tex]

[tex] \sf \longmapsto \: g=a(4− {d}^{2} )[/tex]

[tex]\huge\bf Solution:—[/tex]

[tex] \underline{\bf \: Flip \: the \: equation:—}[/tex]

[tex] \sf \longmapsto \: −a {d}^{2} +4a=g[/tex]

[tex] \underline{\bf \: Factor \: out \: variable \: (a):—}[/tex]

[tex] \sf \longmapsto \: a(− {d}^{2} +4)=g[/tex]

[tex]\underline{ \bf \: Divide \: both \: sides \: by -d^2+4 :—} [/tex]

[tex]\sf \longmapsto \: \dfrac{a( - {d}^{2} + 4) }{ { - d ^2+ 4}^{} } = \dfrac{g}{{ - d ^2+ 4}^{}} [/tex]

[tex]\sf \longmapsto \:1 a = \dfrac{g}{{ - d^2 + 4}^{}} [/tex]

[tex]\underline{\bf Answer:—}[/tex]

[tex]\boxed{ \bf \: a = \dfrac{g}{ - d^2 + {4}^{} } }[/tex]

Answer:

[tex]\boxed{\boxed{\sf a=\cfrac{G}{4-d^2} }}[/tex]

Step-by-step explanation:

[tex]\sf G=a(4-d^2)[/tex]

Use the Distributive Property to multiply a by (4-d^2):

[tex]\sf G=4a-ad^2[/tex]

Now, we'll swap sides so that all variable terms are on the left hand side.

[tex]\sf 4a-ad^2=G[/tex]

Combine like terms:

[tex]\sf (4-d^2)\:a =G[/tex]

Divide both sides by 4-d^2:

[tex]\sf \cfrac{(4-d^2)a}{4-d^2} =\cfrac{G}{4-d^2}[/tex]

Dividing by 4-d^2 undoes the multiplication by 4-d^2.

[tex]\sf a=\cfrac{G}{4-d^2}[/tex]

_______________________________________

Hep help help help help math math

Answers

Answer:

5(37)+10

10(17.5)+5

Step-by-step explanation:

5x+10=180

-10 -10

5x=170

divide by 5

x=37

---------------------

10x+5=180

-5 -5

10x=175

divide by 10

x=17.5

Quadratic functions 30pt

Answers

Answer:

y= -x -3

Step-by-step explanation:

A perpendicular bisector of a line cuts through the line at its midpoint perpendicularly (90°).

Let's find the slope of the line segment.

\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }slope=x1−x2y1−y2

Slope of line segment

= \frac{4 - ( - 8)}{5 - ( - 7)}=5−(−7)4−(−8)

= \frac{4 + 8}{5 + 7}=5+74+8

= \frac{12}{12}=1212

= 1

The product of the slopes of 2 perpendicular lines is -1.

Let the slope of the perpendicular bisector be m.

m(1)= -1

m= -1

y= -x +c

To find the value of c, substitute a pair of coordinates in which the line passes through into the above equation.

Since the perpendicular bisector cuts through the midpoint of the line segment, let's find the coordinates of this midpoint.

\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}midpoint=(2x1+x2,2y1+y2)

Midpoint of line segment

= ( \frac{5 - 7}{2} , \frac{4 - 8}{2} )=(25−7,24−8)

= ( \frac{ - 2}{2} , \frac{ - 4}{2} )=(2−2,2−4)

= (-1, -2)

y= -x +c

When x= -1, y= -2,

-2= -(-1) +c

-2= 1 +c

c= -2 -1

c= -3

Thus, the equation of the perpendicular bisector is y= -x -3.

Simplify the expression 7h+​(−8.3d​)−13+6d−2.9h.

Answers

Answer:−2.3d+4.1h−13

Step-by-step explanation:

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