Find an explicit formula for the geometric sequence \dfrac12\,,-4\,,\,32\,,-256,.. 2 1 ​ ,−4,32,−256,..start fraction, 1, divided by, 2, end fraction, comma, minus, 4, comma, 32, comma, minus, 256, comma, point, point. Note: the first term should be \textit{a(1)}a(1)start text, a, left parenthesis, 1, right parenthesis, end text. a(n)=a(n)=a, left parenthesis, n, right parenthesis, equals

Answers

Answer 1

Answer:

a(n)= 1/2 * (-8) n-1

Step-by-step explanation:

In a geometric sequence, the ratio between successive terms is constant. This means that we can move from any term to the next one by multiplying by a constant value. Let's calculate this ratio over the first few terms:

\dfrac{-256}{32}=\dfrac{32}{-4}=\dfrac{-4}{\frac12}=\blue{-8}  

32

−256

=  

−4

32

=  

2

1

 

−4

=−8start fraction, minus, 256, divided by, 32, end fraction, equals, start fraction, 32, divided by, minus, 4, end fraction, equals, start fraction, minus, 4, divided by, start fraction, 1, divided by, 2, end fraction, end fraction, equals, start color #6495ed, minus, 8, end color #6495ed

We see that the constant ratio between successive terms is \blue{-8}−8start color #6495ed, minus, 8, end color #6495ed. In other words, we can find any term by starting with the first term and multiplying by \blue{-8}−8start color #6495ed, minus, 8, end color #6495ed repeatedly until we get to the desired term.

Let's look at the first few terms expressed as products:

nn 111 222 333 444

h(n)\!\!\!\!\!h(n)h, left parenthesis, n, right parenthesis \red{\dfrac12}\cdot\!\!\!\left(\blue{-8}\right)^{\,\large0}\!\!\!\!\!\!  

2

1

⋅(−8)  

0

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, start superscript, 0, end superscript \red{\dfrac12}\cdot\!\!\!\left(\blue{-8}\right)^{\,\large1}\!\!\!\!\!\!  

2

1

⋅(−8)  

1

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, start superscript, 1, end superscript \red{\dfrac12}\cdot\!\!\!\left(\blue{-8}\right)^{\,\large2}\!\!\!\!\!\!  

2

1

⋅(−8)  

2

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, squared \red{\dfrac12}\cdot\!\!\!\left(\blue{-8}\right)^{\,\large3}  

2

1

⋅(−8)  

3

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, cubed

We can see that every term is the product of the first term, \red{\dfrac12}  

2

1

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, and a power of the constant ratio, \blue{-8}−8start color #6495ed, minus, 8, end color #6495ed. Note that this power is always one less than the term number nnn. This is because the first term is the product of itself and plainly 111, which is like taking the constant ratio to the zeroth power.

Thus, we arrive at the following explicit formula (Note that \red{\dfrac12}  

2

1

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030 is the first term and \blue{-8}−8start color #6495ed, minus, 8, end color #6495ed is the constant ratio):

a(n)=\red{\dfrac12}\cdot\left(\blue{-8}\right)^{\large{\,n-1}}a(n)=  

2

1

⋅(−8)  

n−1

a, left parenthesis, n, right parenthesis, equals, start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, start superscript, n, minus, 1, end superscript

Note that this solution strategy results in this formula; however, an equally correct solution can be written in other equivalent forms as well.


Related Questions

3. Find the product, using suitable properties :
a) 26 x (-48) + (-48) x (-36)
b) 625 x (-35) + (-625) x 65

please answer fast 10 marks

Answers

a) 26 x (-48) + (-48) x (-36) = ( –1248) + ( + 1728) = – 1248+ 1728 = 480

b) 625 x (-35) + (-625) x 65 = ( –21875) + ( –40625) = – 21875 –40625 = –62500

I hope I helped you^_^

Two similar polygons have areas of 4 square inches and 64 square inches.

The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .

Answers

Answer:

4

Step-by-step explanation:

The ratio of the area of similar figures is the ratio between corresponding sides squared. This means that 64/4 or 16 is the square of the ratio of corresponding sides. By taking the square root of 16, we get that ratio is 4.

if the ordered pairs (x-2,3y+1) and (y+1,x+3) are equal,find x and y
plz help me ​

Answers

x-2=y+1
x=y+3

3y+1=x+3
x=3y-2

3y-2=y+3
3y-y=5
2y=5
y=2.5

x=(2.5)+3
x=5.5

4.
Find the inverse of A if it has one, or state that the inverse does not exist.

Answers

Answer:

Hello,

[tex]\begin{bmatrix}\dfrac{-1}{5} &0\\\dfrac{-1}{10}&\dfrac{1}{4}\end{bmatrix}[/tex]

Step-by-step explanation:

See jointed file

The inverse of the matrix A is

[tex]A = \left[\begin{array}{cc}-5&-2\\0&4\end{array}\right][/tex]

What is a matrix?

A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.

We have,

[tex]A = \left[\begin{array}{cc}-5&0\\-2&4\end{array}\right][/tex]

The matrix A is a square matrix and its determinant is not zero.

So the inverse exist.

The inverse of matrix A.

We will change the rows into columns and columns into rows.

So,

[tex]A = \left[\begin{array}{cc}-5&-2\\0&4\end{array}\right][/tex]

Thus,

The inverse of the matrix A is given above.

Learn more about matrix here:

https://brainly.com/question/28180105

#SPJ2

HELP PLEASE !!


find the surface area of the cylinder and round it to the nearest tenth.​

Answers

Answer:

18.8

Step-by-step explanation:

Surface area=2*pi*r*(r+h)=2*pi*1*(3)=18.8

What is the value of a? Round to the nearest tenth.

Answers

Answer:

50 percent?

Step-by-step explanation:

Independent Practice


Which model is most appropriate for the set of points?

(–2, 5), (–1, –1), (0, –3), (1, –1), (2, 5)


A.
exponential


B.
linear


C.
quadratic

Answers

Quadratic because if you plot it on a graph it will look like a U

The vertex is 2,-4 what is the parabola equation

Answers

Answer:

y + 4 = (x - 2)^2

Step-by-step explanation:

The vertex form of the equation of a vertical parabola is

y - k = a(x - h)^2, where (h, k) represents the vertex and a is a scaling factor which stretches or compresses the parabola vertically.  If all we know is the vertex (2, -4), then the desired equation is:

y + 4 = a(x - 2)^2

If there is no vertical stretching or compression, then the equation becomes:

y + 4 = (x - 2)^2

Answer:

y = x² - 4x

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (2, - 4) , with a = 1 , the equation is

y = (x - 2)² - 4 ← expand using FOIL

 = x² - 4x + 4 - 4

y = x² - 4x ← equation of parabola

The population of a city is currently 45,000 and is declining at a rate of 2% each year. Give a formula for determining the total population after a period of t years.
Question 4 options:

A)

A = (45,000)e–0.02t

B)

A = 45,000 + e–0.02t

C)

A = (45,000)e0.02t

D)

A = 45,000 + e0.02t

Answers

Answer:

Step-by-step explanation:

The general form of this equation is

[tex]A=Pe^{rt}[/tex] where P is the initial population, e is Euler's number (a constant), r is the rate of decay, and t is the time in years.

Therefore, filling in:

[tex]A=45000e^{-.02t[/tex]

Y'ALL PLEASE HELP ME I WOULD GREATLY APPRECIATE IT!!!!!:)!!!!!!

Find the measure of angle TOS in the figure below. SHOW YOUR WORK SO I CAN SEE HOW YoU GOT IT!!!!

Answers

Step-by-step explanation:

<TOS=122° [being vertically opposite angle]

Answer:

angleTOS =122°

EXPLANATION:

[ If two straight lines intersect at point O, vertically opposite angles are equal]As vertically opposite angles are equal; Hence AngleTOS=QOR=122°

(y+2)(y^2-2y+4) ..........................

Answers

You can use the distributive property to multiply:

( y )( y² - 2y + 4 ) + ( 2 )( y² - 2y + 4) =

y³ - 2y² + 4y + 2y² - 4y + 8 =

y³ + 8

The -2y² and the 2y² cancel each other, and the 4y and -4y cancel each other out!

The answer is y^3 +8

Select the correct answer from each drop-down menu.
A company makes cylindrical vases. The capacity, in cubic centimeters, of a cylindrical vase the company produces is given by the
function C() = 6.2873 + 28.26x2, where x is the radius, in centimeters. The area of the circular base of a vase, in square
centimeters, is given by the function A () = 3.14.2
To find the height of the vase, divide
represents the height of the vase.
the expressions modeling functions C(x) and A(z). The expression

Answers

Answer:

divide, 2x+9

Step-by-step explanation:

got it right

The ratio of Mitchell's age to Connor's age is 8:5. In thirty years, the ratio of their ages will be 6:5. How much older is Mitchell than Connor now?

Answers

Answer:

9 years older

Step-by-step explanation:

The ratio of their ages is 8 : 5 = 8x : 5x ( x is a multiplier )

In 30 years their ages will be 8x + 30 and 5x + 30 and the ratio 6 : 5 , so

[tex]\frac{8x+30}{5x+30}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )

5(8x + 30) = 6(5x + 30) ← distribute parenthesis on both sides

40x + 150 = 30x + 180 ( subtract 30x from both sides )

10x + 150 = 180 ( subtract 150 from both sides )

10x = 30 ( divide both sides by 10 )

x = 3

Then

Michell is 8x = 8 × 3 = 24 years old

Connor is 5x = 5 × 3 = 15 years old

Mitchell is 24 - 15 = 9 years older than Connor

Ken needs a surgery on his foot. The estimated cost of the surgery is $5,000. The insurance policy provided by Ken's company has $500 deductible and 20% co-pay. How much will Ken have to pay for foot surgery?

Answers

9514 1404 393

Answer:

  $1400

Step-by-step explanation:

Ken will be required to pay the deductible and 20% of the remaining amount.

  Ken pays $500 + 0.20(5000 -500) = $500 +900

  Ken pays $1400

ac circular runway has a radius of 100 m.Find the distance covered by a person in one complete rotation .​

Answers

Answer:

628m

Step-by-step explanation:

Given radius=100m

distance=circumference

=2pie r

=2×22/7×100

=628m

please mark me brainliest

The area CA) of a Parallelogram is found by using this formula A = BH What is the area when b is 7cm and h is 3cm?​

Answers

Answer:

Area of parallelogram = 21

Step-by-step explanation:

A = BH

Plug in

A = 7×3

Solve

A = 21

The answer will be 21.

Find all three distinct roots for X³ =1. (two of them are complex mumber). And show that sum of all roots is zero.​

Answers

x ³ = 1

x ³ - 1 = 0

x ³ - 1³ = 0

Factorize the right side as a difference of cubes:

(x - 1) (x ² + x + 1) = 0

Then

x - 1 = 0   or   x ² + x + 1 = 0

The first equation yields x = 1 as a root.

For the other equation, rearrange and complete the square to get the other two roots,

x ² + x + 1/4 = -3/4

(x + 1/2)² = -3/4

x + 1/2 = ±√(-3/4) = ± i √3/2

x = -1/2 ± i √3/2

x = (-1 ± i √3)/2

Since complex roots occurs in conjugate pairs, taking the sum of these two roots eliminates the imaginary part:

(-1 + i √3)/2 + (-1 - i √3)/2 = (-1 - 1)/2 = -2/2 = -1

and adding to 1 indeed shows that the sum of roots is zero.

Please help me find x
Need help fast!!

Answers

Answer:

x = 100°

Step-by-step explanation:

p and q are parallel lines. Construct line 'l' parallel to p and q

a = 30°   {p// l  when parallel lines are intersected by transversal alternate interior angles are congruent}

c +110 = 180  {linear pair}

c = 180  - 110

c = 70°

b= c   {q // l  when parallel lines are intersected by transversal alternate interior angles are congruent}

b = 70°

x = a + b

x = 30° + 70°

x = 100°

Tuto
Combine any like terms in the expression. If there are no like terms, rewrite the expression.
8r + 9pg - pg - pq

Answers

Answer:

8r+8pg-pq

Step-by-step explanation:

The subtractable pg cancels out one of the 9 pg's. So 9 pg-1 pg= 8 pg

Hope this helps!


At Tubman Middle School, there are 6 English teachers and 5 science teachers. If each
student takes one English class and one science class how many possible combinations of
teachers are there?

Answers

There are 30 possible combinations of teachers.

Given that at Tubman Middle School, there are 6 English teachers and 5 science teachers, to determine, if each student takes one English class and one science class, how many possible combinations of teachers are there, the following calculation must be performed:

To calculate possible combinations, the number of options A must be multiplied by the number of options B. Thus, the calculation would be as follows.

6 x 5 = X30 = X

Therefore, there are 30 possible combinations of teachers.

Learn more about combinations in https://brainly.com/question/24180105.

The number of bags of Brand Y dog food sold on these five days was 175. Which bar represents the data for Day 5 for Brand Y?

Answers

Answer:

30

Step-by-step explanation:

Express 1.2, 2.25, 3.5, 4.06 as a fraction in its simplest form​

Answers

Answer:

1.2 = 12/10 = 6/5

2.25 = 225/100 = 9/4

3.5 = 35/10 = 7/2

4.06 = 406/100 = 203/50

The total cost of 2 bracelets and 3 necklaces is $15.50. The total cost of 4 bracelets and 1 necklace is $13.50. Let b represent the cost of each bracelet and n represent the cost of each necklace. This situation can be represented by the following system of equations.

{2b+3n=15.504b+n=13.50

What is the cost of one bracelet?

A
$2.50

B
$7.75

C
$5.00

D
$3.50

Answers

Answer:

A

$2.50

Step-by-step explanation:

b = cost of bracelet

n = cost of necklace

2b+3n = 15.50

4b+1n = 13.50

Multiply the first equation by -2

-4b -6n = -31

4b +n = 13.50

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

-5n = -17.50

Divide each side by -5

-5n/-5 = -17.5/-5

n = 3.50

Now we can find b

4b+n = 13.50

4b+3.50 = 13.50

4b+3.50-3.50 = 13.50 -3.50

4b = 10

Divide by 4

4b/4 = 10/4

b = 2.50

Answer ASAP please!
………

Answers

Answer:

47.746, answer choice C

Step-by-step explanation:

47.746

This year, a small business had a total revenue of $42,900 . If this is 35% less than their total revenue the previous year, what was their total revenue the previous year?

Answers

if this value 35% less than the total, we conclude that:

42,900 = 65%

1% = 660

100% = 66,000

if you want to check the value, just do 65% of 66000, which equals to 42,900

hope it helps :)

Which points are possible approximations for this system? Select two options.

Answers

Step-by-step explanation:

second: (2.2,-1.4)

third: (2.2,-1.35)

Step-by-step explanation:

hope it helps✨

Find the values of the missing sides. You must use exact answers! PLEASE HURRY AND HELP

Answers

Answer:

x=4sqrt3 a=4 b=3  ,y=8sqrt3 c=8 d=3

Step-by-step explanation:

because this is a 30-60-90 triangle, it is easy to find the side lengths. the longer leg is sqrt(3) times the shorter leg so x= 12/sqrt(3) or 4sqrt(3). the hypotenuse is 2 times the shorter leg so y= 8sqrt(3)

Can someone help me on any of the problems that are circled

Answers

15. Is $52.50 I think

Algebra 1 need help ASAP

Answers

Answer:

Step 1: 12-2a=3a-18

Step 2: 12-5a=-18

Step 3: -5a=-30

Step 4: a=6

I hope this helps!

pls ❤ and give brainliest pls

she bought 9 gallons of milk and no toilet tissue

Find the image of the given point
under the given translation.
P(-7,1) T(x,y) = (x + 9, y-3)
P' = ([?], []).

Answers

Answer:

P' = (2, -2)

Step-by-step explanation:

You have the x-value and the y-value of the pre-image, so all you have to do is plug that into the translation statement (x + 9 , y - 3).

Since x = -7 and y = 1 that would be (-7 + 9, 1 - 3), or (2, -2).

Other Questions
find the surface area of the cylinder and round to the nearest tenth of (3, -2) reflected across the line x = 1 is? The total number of branches in a tree diagram will be which of the following values?the probability of an event occurringthe denominator of a probabilitythe numerator of a probability what is the habitat of a bat, weaver bird, lizard, tilapia, rabbit and cactus plant WILL GIVE EXTRAPOINTS Read the following description:In a story, a prince must discover the source of a mysterious mist that is covering the kingdom, preventing crops from growing. The prince travels to the top of a mountain and discovers a lonely dragon whose tears are creating the mist. The dragon is gentle and kind, but the kingdom's residents fear him. The prince tells the people that the dragon is harmless. They befriend the dragon, the crops are saved, and the dragon becomes an official protector of the kingdom.What are two literary themes that can be identified in this description?A.The challenges of cooperation and the importance of economic successB.The difficulties of leadership and the importance of identifying others' skillsC.The importance of not prejudging others and the value of nonviolent solutionsD.The value of community and the dangers of standing out Which of the following is not a place where hydrogen can be found on Earth?A. Natural gas wellB. WaterC. MineD. Atmosphere From the list below, select the items that are classified as a materials activity. (You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer. Any boxes left with a question mark will be automatically graded as incorrect.) Raw materials used Raw materials beginning inventory Raw materials purchases Work in process beginning inventory Goods manufactured Direct labor used Factor overhead used 1. A consumer must decide between purchasing a new television or a new computer. What limited resource is responsible for this trade-off decision? A. The consumer has a different benefit from each possible product. B. The consumer has a limited amount of money available for purchases.2. What resources do consumers typically have in limited supply that forces them to make trade-off decisions in consumption?A. natural resources, land, and laborB. time, attention, and capitalC. time, money, and attentionD. money, labor, and capital A furniture store is having a sale on sofas and you're going to buy one. The advertisers know that buyers get to the store and that 1 out of 5 buyers change to a more expensive sofa than the one in the sale advertisement. Let X be the cost of the sofa. What is the average cost of a sofa if the advertised sofa is $250 and the more expensive sofa is $450 Analyze one of three poems - "The Lady of Shalott" by Alfred, Lord Tennyson,Sonnet 50 by William Shakespeare, or "Grievance" by Amy Lowell - and then write anew poem that uses the same meter, rhyme scheme, and form as the one youanalyzed. Your original poem should be at least two stanzas long (about 8 lines), orexactly 14 lines if you're writing a sonnet.Your assignment should include the following elements: An introduction paragraph with a hook and a thesis statement about the theme ofthe poem you've chosen to analyze An analysis paragraph that describes the rhyme scheme and meter of yourchosen poem 8 - 10 annotations that go into detail about the poetic elements in your chosenpoem An original poem that follows the same form (sonnet, ballad, or free verse) as thepoem you've chosen to analyze Which sentence describes existing cells?All cells, once formed, continue to live forever.All cells come from previously existing cells.All the cells that are on Earth have always been here.All cells develop from the remains of other cells. What is the Answer to: 120 Times 2/3 Whch part of reproductive system produces semen PLSS HELPPPP WILL GIVE BRAINLESSS A 22-foot ladder is resting against the side of a building. The bottom of the ladder is 3 feet from the building. Find the measure of the angle the ladder makes with the ground. Round your answer to the nearest tenth of a degree. what do you mean by scattering of light Mahmoud earns $450 per week plus a 20% commission as a car salesman. He wants hishourly salary to be at least $35. Simplify the expression 2x(4 + x - 9 + 3x)A. 8x - 10B. -2xC. -10xD. 8x - 10E. 8x - 10x 3x + ky = 8X 2ky = 5are simultaneous equations where k is a constant.b) Given that y = 1/2 determine the value of k. After getting RM24 from his mother, Samuel had 3 times as much as he had previously. How much did he have previously? Which statement is not true about the field of science?it is based on observations and explanations of the natural world.