The first term of a geometric sequence is 8 and the fourth term is 216. what is the sum of the first 12 terms of the corresponding series?

Answers

Answer 1

The sum of the 12 terms of a geometric sequence with first term as 8 and fourth term as 216 is 2125760

Geometric sequence

The formula to solve geoemtric sequence is as follows:

aₙ = arⁿ⁻¹

where

a = first termn = number of termsr = common ratio

Therefore,

ar³ = 216

a = 8

Hence,

8r³ = 216

r³ = 216 / 8

r³ = 27

r = ∛27

r = 3

Therefore,

sum of 12 term = a(rⁿ - 1) / r - 1

S₁₂ = 8(3¹² - 1) / 3 - 1

S₁₂ = 8(531440)  / 2

S₁₂ = 4251520 / 2

S₁₂ = 2125760

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Related Questions

Consider this expression. select the correct statements. 8(4y + 7) + 9

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The provided algebraic expression 8(4y + 7) + 9 is a binomial expression, which has two terms in its simplified version.

What is polynomial?

Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).

Types of polynomial-

Monomial- Monomial type of polynomial contains only one term such as ax, by etc.Binomial-Binomial type of polynomial contains exactly two term such as ax+c, by+d etc.Trinomial-Trinomial type of polynomial contains three term.

The given expression in the problem is,

[tex]f(x)=8(4y + 7) + 9[/tex]

Solving it further,

[tex]f(y)=8(4y + 7) + 9\\f(y)=32y+56+9\\f(y)=32y+65[/tex]

The above polynomial has two terms. First is 32y and second one 65.

Hence, the provided algebraic expression 8(4y + 7) + 9 is a binomial expression, which has two terms in its simplified version.

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Elena is in her first year of college, living away from home on the college’s campus. her parents pay room and board, and she’s got loans, grants, and scholarship paying for tuition. she has her own checking and savings accounts and a 10-hour per week work study job. she doesn’t have any credit cards right now.

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Elena I say is living her dream and when she has a job, she can pay pack any loan that she has taken.

How is a student loan different from a scholarship?

A student loan  is known to be a type of loan that is taken by a student and it is one that must be paid back.

Note that a scholarship is a type of fund that is given to student and it is not one that needs to be paid back and as such Elena should make good use of what she has and come out with good grades in her studies.

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How does oiwa's work fit into the concepts of installation?

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The way that oiwa's work fit into the concepts of installation is that; He inflates 360 space to immerse the viewer in his drawings.

What is the concept of the story?

This question is taken from the life of a Japanese-Brazilian artist named Oscar Oiwa who created an incredible, immersive installation that brought canvas to life.

Oiwa worked only with simple black felt-tip pens and visualizes two opposite ideas or situations such as  light and shadow or hot and cold.

This method entails an all-encompassing stream of consciousness that collides inside a massive bubble.

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The supreme court cites these cases because it seeks to describe the unique

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Well this takes place when they erupted which left people Uniqlo in first cases

A heavy lab cart moves with kinetic energy kinit on a track and collides with a lighter lab cart that is initially at rest. the carts bounce off each other but the collision is not perfectly elastic, causing the two-cart system to lose kinetic energy klost . a student wonders if the fraction of kinetic energy lost from the two-cart system during the collision depends on the speed of the first cart before the collision and plans to perform an experiment.

Answers

The hypothesis; greater fraction of kinetic energy is lost from the system during the collision when the speed of the first cart is greater is; Correct

What is the Hypothesis of the Collision?

In an Inelastic Collision, energy is not conserved . Now, the loss of energy could be in the form of friction, vibrational energy, sound, heat energy, e.tc.

Now, for example frictional energy is proportional to the velocity. The, the greater the velocity, the greater the loss of energy. This is also true about  vibrational energy, sound, heat energy, e.tc.

Thus, we can conclude that the hypothesis is correct.

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Heather receives a phone call, in which an automated voice states that her credit card has been used fraudulently and that she must enter her 16-digit credit card number, using the keypad of her phone, to clear up the error. what should heather do next?

Answers

The next step which Heather should take is; to hang up and call her credit card company using the 1-800 number on the back of her card.

What is the position of the Character in the Passage?

From the story, we can see that Heather was a target of an attempted phone fraud whereby callers asked her to give her 16-digit credit card details such that the supposed error could be cleared up.

Now, It is pertinent to note that this information can be used to steal money from her checking account and Heather would best not give out such sensitive details over the phone, but call the company to see if the call was really from them.

Thus, the next step which Heather should take after she has gotten a fraudulent call asking for her credit card details is to hang up and call her credit card company using the 1-800 number on the back of her card to inquire  about the issue or report the attempted phone fraud.

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Which person has based their investment plan on high risk options brainly

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An example of peope whose investment plan on high risk options are those who deals on  Cryptocurrency or individual stocks.

Which is an high risk investment?

A high-risk investment is known to be a type of investment  where the likelihood of failed part of or all of the investment being lost, are said to be higher than the average.

Conclusively, Note that an example is Cryptoassets, Mini-bonds etc. are an example of high risk investment.

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A diagnosis of one type of cardiovascular disease does not necessarily indicate risk for another type.

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The statement 'a diagnosis of one type of cardiovascular disease does not necessarily indicate risk for another type' is TRUE.

What does 'diagnosis' mean?

The word diagnosis refers to the causes and/or problems that lead to a given health (disease) condition.

Cardiovascular diseases are multicausal, which means that these conditions can be caused by different health problems.

In conclusion, the statement 'a diagnosis of one type of cardiovascular disease does not necessarily indicate risk for another type' is TRUE.

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Researchers designed an experiment to test the hypothesis that the evolution of coloration in lice is driven by birds. researchers transferred 25 lice from a random sample of lice obtained from wild‑caught rock pigeons to each individual in groups of black pigeons and white pigeons. half of the pigeons from each color group were fitted with a harmless mouthpiece that stopped the beaks from entirely closing. the mouthpiece prevented pigeons from removing lice but did not affect the pigeons’ ability to feed. each pigeon was isolated and kept in identical environmental conditions for temperature, humidity, and amount of light. the lice have a generation time of 24 days. the researchers observed the phenotypes of the lice over a period of four years.

Answers

Phenotypic variation in louse body color in a population of lice would make it difficult for the louse to be spotted and picked off any pigeon's feathers.

What is phenotypic variation?

Phenotypic variation can be defined as the difference (variability) in the observable characters or attributes (phenotypes) of each organism in a specific population.

Based on the research, it is very important for phenotypic variation to exist in louse body color among other individuals in a population of lice because there are two different colors of pigeons, which would make it difficult for the louse to be spotted and picked off their feathers.

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For what purpose was the environmental protection agency established brainly

Answers

Answer:

The Environmental Protection Agency is an independent executive agency of the United States federal government tasked with environmental protection matters. President Richard Nixon proposed the establishment.

Explanation:

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Building sheep pens : darsh and darpan are fencing off a large rectangular area to build some temporary holding pens. to prep the males, females, and kids, they are separated into three smaller and equal-size pens partitioned

Answers

The larger rectangle will be a square with sides of 96 ft while the pens will have 96 ft of length and 31 ft of width

How to Maximize Area of rectangle?

The side lengths of the big rectangle are x and y and so we have the following expression for its area A:

A = x*y

This is tied to the constraint that the perimeter should not be larger than the available fencing , Thus;

2x + 2y = 384   (All the fencing is used to maximize the area)

y = (384 - 2x)/2

y = 192 - x

Put 192 - x for y in A to get;

A = x(192 - x)

A = 192x - x²

Completing the square gives;

A = 9216 - (x - 96)²

Thus;

A is maximum at;

x - 96 = 0

x = 96 ft

y = 192 - 96

y = 96 ft

Then since we maximised the area of the bigger rectangle , we have maximised the area of the smaller pens. The dimensions will be;

x_small = 96 ft /3

x_small = 31 ft

y_small = 96 ft

Complete question is;

Building sheep pens: It's time to drench the sheep again, so Chance and Chelsea-Lou are fencing off a large rectangular area to build some temporary holding pens. To prep the males, females, and lambs, they are separated into three smaller and equal-size pens partitioned within the large rectangle. If 384 ft of fencing is available and the maximum area is desired, what will be (a) the dimensions of the larger, outer rectangle? (b) the dimensions of the smaller holding pens?

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can someone write a 1200 word essay for my explaining why plants are important i dont really know how to do this and i need help.

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Answer:

Plants provide us with food, fiber, shelter, medicine, and fuel. The basic food for all organisms is

produced by green plants. In the process of food production, oxygen is released. This oxygen, which we

obtain from the air we breathe, is essential to life. The only source of food and oxygen are plants; no

animal alone can supply these. Shelter, in the form of wood for houses; and clothing, in the form of

cotton fibers, are obvious uses of plant materials. But we must not forget fuel, furniture, paper

products, certain medicines like aspirin, and many other products like perfume and chewing gum. To

these tangible aspects of the plant world we must also add the importance of beauty and relaxation

derived from plants. Since animals are surrounded by and dependent upon plants, the factors that

influence plant growth, structure, and distribution, affect the animal world as well.

Plant - Animal Relationships

Forests, lawns, streams, and marshes are all habitats that are easily recognized as unique biotic

communities. A community is a naturally occurring, interactive assemblage of plants and animals living

in the same environment. The interaction between plants and animals often exists out of the need for

food, protection, transportation, and reproduction. The different kinds of interaction possible between

organisms are extremely important in determining the abundance of species. If the interaction between

species is beneficial, it is described as mutualism. Some of the most complex mutualistic relationships

evolved between plants and pollinators. If the interaction proves disadvantageous, it is referred to as

competition. Commensal relationships, in which one species benefits and the other is unaffected, are

common between plants and animals. For example, when a bird builds a nest in a tree, the bird benefits

and the tree is (usually) unharmed. Other relationships may positively affect one population and be

detrimental to the other. Such relationships involve predation and parasitism. In predation, one

organism directly kills and consumes its prey. Parasitism differs in that parasites live on or in the prey,

but may not kill it outright. A good example of parasitism is mistletoe growing on a tree.

Ecosystems

An ecosystem is the biotic (living) and abiotic (nonliving) factors

of an ecological community considered together. Ecosystems contain

four components: the physical environment (abiotic), living things

(biotic), energy input and use, and nutrients that cycle between the

biotic and abiotic components. Based on this definition, ecosystems

can vary from large unbroken tracts of forest to small ephemeral ponds

to backyards.

Explanation:

Determine the ph of a 0. 22 m naf solution at 25°c. The ka of hf is 6. 8 × 10-4

Answers

The pH shows the degree of acidity or alkalinity of the solution. The pH of the solution is 1.92.

What is pH?

The term pH is defined as the hydrogen ion concentration of the solution. We have to set up the ICE table for this reaction as shown below;

             HF +  H2O ⇄  H3O^+  +   F^-

I           0.22                    0              0

C           -x                         +x             +x

E         0.22 - x                 x                x

Ka = [H3O^+] [F^-]/[HF]

6. 8 × 10^-4 = x^2/ 0.22 - x  

6. 8 × 10^-4(0.22 - x) = x^2

x^2 + 6. 8 × 10^-4x - 1.496 × 10^-4 = 0

x=0.012 M

Hence;

[H3O^+] = [F^-] = 0.012 M

pH = -log(0.012 M)

pH = 1.92

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Student grants that are based on one's personal background are known as ____
grants.

Answers

Answer:

student specific

Explanation:

Answer:

student specific

Explanation:

How will the decrease in the raccoon population affect the other populations?

Answers

The predator of the raccoon on the higher portion of the food chain will have a decrease in food availability so then their population will decrease.

Describe how homer develops odysseus's character throughout the passage. then analyze how his characterization of odysseus affects the way the audience relates to the character. be sure to use specific details from the text to support your ideas.

Answers

The description and analysis of how homer develops odysseus's character throughout the passage is; As detailed below

Describe the Character in the passage excerpt?

In the given excerpt, we see that Homer portrays Odysseus as a kind of guy with both brains and brands.

Now, Odysseus  is further described as being both physically adept as well as very intelligent and good with quick thinking in high pressure situations. However, Odysseus could sometimes be very foolish.

An example of Odysseus foolishness was when he taunted the Cyclops Pholyfemus. Thus, Odysseus is a very likeable character that people can easily relate to.

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What is the correct date format for mla citations?9 jan. 2014jan. 9, 20142014 jan. 92014 9 jan.

Answers

Answer:

A

Explanation:

9 Jan. 2014

Which mixture can be separated through filtration because one of the substances is insoluble in water? a

Answers

Answer:

Sand

Explanation:

The main difference between ponds and lakes is that ponds brainly

Answers

Answer:

A body of water is called a pond when it is small and enclosed, while a lake is large and open. There are many lakes in the world, even though there are more ponds than lakes

Explanation:

Which of these writing assignments suggests an informal style?

Answers

Answer:

What are the assignments?

Explanation:

Answer:

what are te assignments

Explanation:

so i can answer

Y = cot(x – 3) 3 units up 3 units down 3 units left 3 units right

Answers

Answer:

3 units right

Explanation:

Graph the trigonometric function using the amplitude, period, phase shift, and vertical shift.

Vertical Asymptotes: x = 3 + πn where n is an integer

Amplitude: None

Period: π

Phase Shift: 3 (3 to the right)

Vertical Shift: None

Answer:

D. 3 units right

Explanation:

Midwest sales, inc. has a stated written policy by which all similarly situated employees are to be paid the same salary. john doe (a male), a senior executive vice president for sales and marketing for midwest's zone a, is paid $100,000 a year by midwest. jane roe (a female), a senior executive vice president for sales and marketing for midwest's zone b is paid $95,000 a year by midwest. jane has worked for midwest two years longer than john. the descriptions of john and jane's respective jobs are identical. what is the most accurate statement concerning any legal challenge to the differential in pay between what midwest pays john and jane:

Answers

The most accurate statement concerning any legal challenge is that pay difference is unlawful unless Midwest can establish some significant difference between Zone A and Zone B.

Which legislation guided this practice?

Equal Pay Act of 1963 was the legislation that stated that both men and women must earn the same salary for similar jobs.

The legislation prohibited discimination of gender when establishing a person's salary.

However, there is an exception which is if work carried out in Zone A is much more demanding, challenging, difficult, important or relevant than the work carried out in Zone B, then, the company will be vindicated from any legal matter.

Thereforel the Option B is correct.

Missing options "a) The pay difference is not unlawful and cannot be challenged because there is less than a 10% pay difference between what Midwest pays John and Jane.b) The pay difference is unlawful, unless Midwest can establish some significant difference between Zone A and Zone B.c) The pay difference is not unlawful and cannot be challenged in this instance because the "seniority" defense allows for different pay for men and women even though they may be performing "substantially the same job".d) The pay difference is unlawful, not because of the gender difference between John and Jane, but because Midwest is violating its own stated pay policy.

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Now take a look at this first part of clinton’s speech. in this passage, clinton highlights his failures. challenges. successes.

Answers

Answer:

C. Successes

Explanation:

In the given Passage, we see that what Clinton was trying to do was to highlight his; Successes

What is the interpretation of the Passage?

The given passage as seen online is one about President Clinton's Administration.

Now, in the passage as seen online, some of his highlighted successes of his economic plan includes a balanced budget, a budget surplus, increased prosperity for Americans.

Now, he also had some achievements for his social agenda which were Family Medical Leave Act, Don't Ask, Don't Tell policy. background check requirement for gun purchase.

Thus, we can conclude that all he was trying to do in the first part of the speech was to highlight his successes.

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How do religious organisations support communities affected by gender-based violence brainly

Answers

The religious organizations are the groups that are formed for the development of the religious groups and the communities, however the gender based religious customs affects the violence in the group.

What is the role of gender in a religion?

The religion is given as the following of the customs and the practices by all. The religious practices are however different with the gender as well.

The support of the religious practices for a particular gender and the discrimination by the religious organizations adds to the religious violence.

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Dr. norton puts a cat in the room with karl and prevents karl from avoiding or escaping the cat until karl’s anxiety naturally dissipates. the treatment is called

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The treatment that Dr. Norton gives to address karl’s anxietyof Cats is referred to as; Flooding

What is the psychological disorder?

Karl’s fear of cats is classified as a generalized anxiety disorder.

An anxiety disorder is defined as a mental disorder whereby an individual responds to specific situations by showing excessive fear.

The symptoms of this anxiety disorders include, restlessness, tension, increased heart rate, hyperventilation and others.

This type of anxiety disorder can be treated by using using different means through psychotherapy means and in some cases through medication. However, the type of treatment used here is referred to as Flooding.

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What are the two major categories of leadership styles?

Answers

Answer:

instrumental and expressive

Explanation:

How does the strong nuclear force compare with the electrostatic force in the nucleus of an atom?

Answers

Answer:

Electrostatic force binds the negatively charged electrons to the positively charged atomic nucleus. The nucleons are bound to each other by means of Strong Nuclear Force that is more than 100 times stronger than the electrostatic force.

Answer the following question based on marguerite shuster's article "the mystery of original sin." according to shuster (who agreed with g. k. chesterton), the problem with the world is what?

Answers

God wants us to learn that having him at the center of our lives will always be best for us, no matter how big or small the decisions we face.

What is the main idea of the article?

Author Marguerite Shuster uses biblical argumentation to explain the dehumanization of the current world, relating her ideas to Genesis, a book of the Christian bible.

Therefore, the author draws a parallel between the problems faced by the world today and the need for individuals to turn to the Christian religion.

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For the galvanic (voltaic) cell fe(s) + mn²⁺(aq) ⟶ fe²⁺(aq) + mn(s) (e° = 0.77 v at 25°c), what is [fe²⁺] if [mn²⁺] = 0.050 m and e = 0.78 v? assume t is 298 k

Answers

The concentration of Iron in the galvanic (voltaic) cell Fe(s) + Mn²⁺(aq) ⟶ Fe²⁺(aq) + Mn(s) is 0.02297 M.

What is the Nernst Equation?

The Nernst equation enables us to identify the cell potential(voltage) in presence of non-standard conditions in a galvanic cell. It can be expressed by using the formula:

[tex]\mathbf{E_{cell} = E_o - \dfrac{0.059}{n} \times log \dfrac{[Fe^+]}{[Mn^{2+}]}}[/tex]

where;

n = Number of electrons = 2[tex]\mathbf{E_o}[/tex] = Initial voltage = 0.77 V[tex]\mathbf{E_{cell}}[/tex] = Cell voltage = 0.78 V[tex]\mathbf{[Mn^{2+}]}[/tex] = Manganese concentration = 0.050 M

Replacing the values into the above equation, we have:

[tex]\mathbf{0.78 = 0.77 - \dfrac{0.059}{2} \times log \dfrac{[Fe^{2+}]}{[0.050]}}[/tex]

[tex]\mathbf{0.78 -0.77= -0.0296\times log \dfrac{[Fe^{2+}]}{[0.050]}}[/tex]

[tex]\mathbf{log^{-1} (-0.3378) = \dfrac{[Fe^{2+}]}{[0.050]}}[/tex]

[tex]\mathbf{Fe^{2+} = (0.4594\times 0.050 )\ M}[/tex]

[tex]\mathbf{Fe^{2+} =0.02297 \ M }[/tex]

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Which property is characteristic of alkenes, alkynes, and aromatic hydrocarbons? their vapor pressures decrease as their size increases. their ph values are greater than 7. they are insoluble in water. they are soluble in water.

Answers

The property that is characteristic of alkenes, alkynes, and aromatic hydrocarbons is; C: they are insoluble in water

What are the properties of the compounds?

From density tables, we will discover that the density of alkynes is lower than the density of water. Likewise, the densities of alkenes and aromatic hydrocarbons are as well lower than the water.

Now those compounds are insoluble in water because they have non polar characteristics and are also lighter than water due to the fact that their density is lower than water and as such they are insoluble in water.

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Answer:

C. They are insoluble in water.

Explanation:

Correct on Edge 2022!!!

Good luck everyone, you got this! Have a great day!

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