The fifth term of a geometric sequence is 781. 25. Each term of the sequence is of the value of the following term. Which recursive formula represents the situation?.

Answers

Answer 1

Answer: an = 5an-1

Explanation: Given fifth term of a geometric sequence is 781.25.

a5 = 781

Also, each previous term is 1/5 of the value of the current term.

Therefore, common ratio would be 5.

But we just need to find the recursive formula .

Recursive formula of a geometric sequence is given by

Plugging value of r in above formula, we get

Therefore, recursive formula would be   represents the situation.

Answer 2

The recursive formula that represents the situation is: [tex]t_n = a^{(3/4)} * 781.25^{(1/4)} * n^{(1/4)}[/tex].

What is recursive formula?

A recursive formula is one that defines any term in a sequence in terms of the term(s) before it.

Let the first term of the geometric sequence be 'a' and the common ratio be 'r'.

We are given that the fifth term is 781.25, so we can write:

a * [tex]r^4[/tex] = 781.25

We also know that each term is the value of the following term, so we can write the recursive formula:

t_n = r * t_(n-1)

Where t_n is the nth term of the sequence and t_(n-1) is the previous term.

To express the recursive formula in terms of 'a' and 'r', we can use the formula for the nth term of a geometric sequence:

[tex]t_n = a * r^{(n-1)[/tex]

Substituting the recursive formula, we get:

[tex]r * t_{(n-1)} = a * r^{(n-1)[/tex]

Dividing both sides by r^(n-1), we get:

[tex]t_{(n-1)} = a * r^{(n-2)[/tex]

So the recursive formula in terms of 'a' and 'r' is:

t_n = r * t_(n-1)

[tex]= r * (a * r^{(n-2)})\\\\= a * r^{(n-1)[/tex]

Now we can substitute the value of the fifth term (781.25) to solve for 'a' and 'r':

a * [tex]r^4[/tex] = 781.25

Dividing both sides by a, we get:

[tex]r^4[/tex]= 781.25/a

Taking the fourth root of both sides, we get:

r = [tex](781.25/a)^{(1/4)[/tex]

Substituting this value of 'r' into the recursive formula, we get:

[tex]t_n = a * ((781.25/a)^{(1/4)}){^(n-1)}\\\\= a^{(3/4)} * 781.25^{(1/4)} * n^{(1/4)}[/tex]

Therefore, the recursive formula that represents the situation is:

t_n = a^(3/4) * 781.25^(1/4) * n^(1/4)

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Related Questions

In sentence 6 (reproduced below), the writer is considering deleting the underlined text. However, strong evidence indicates that this event did not inspire the poem and that the author was in fact sarah josepha hale, not roulstone. Should the writer keep or delete the underlined text?.

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Based on the information given, the correct option will be C. Keep it, because it previews the way the rest of the passage will support the thesis about Hale's authorship with evidence.

From the question, it was stated that one should show what the author should do with the underlined text.

The underlined text is important as it gives a preview of the passage. It's also used as supporting evidence to the claim of Hale.

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What is silhak? a. The most sacred of all korean instruments b. A truly korean style that emphasizes the study of things korean c. A traditional korean male hat d. The korean word for picnic.

Answers

Answer: B

Explanation:

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Answer:

The answer is B

Explanation:

I got it right on my test have a lovely day!

A binary number is to be transformed by appending three 0s to the end of the number. For example, 11101 is transformed to 11101000. Which of the following correctly describes the relationship between the transformed number and the original number?.

Answers

Numbers can be converted from one base to another base. a. The transformed number is 8 times the value of the original number.

Given that:

Three 0s are appended to a binary digit to get a new binary digit.

Using the given values, the transformation can be illustrated as follows:

Where:

represents the three appended 0s.

In binary  represents 8 in decimal.

So, the above illustration can be expressed as:

This means that the new or transformed number is 8 times the original number.

The chemical equation below shows the combustion of methane (ch4). Ch4 + 2o2 right arrow. Co2 + 2h2o the molar mass of oxygen gas (o2) is 32. 00 g/mol. The molar mass of carbon dioxide (co2) is 44. 01 g/mol. What mass of co2, in grams, will form when 8. 94 g o2 completely react?.

Answers

Taking into account the reaction stoichiometry, 6.15 grams of CO₂ are formed when 8.94 grams of O₂ reacts completely.

In first place, the balanced reaction is:

CH₄ + 2 O₂  → CO₂ + 2 H₂O

By reaction stoichiometry (that is, the relationship between the amount of reagents and products in a chemical reaction), the following amounts of moles of each compound participate in the reaction:

CH₄: 1 mole O₂: 2 moles CO₂: 1 mole H₂O: 2 moles

The molar mass of the compounds is:  

CH₄: 16.04 g/mole O₂: 32 g/moleCO₂: 44.01 g/moleH₂O: 18 g/mole

Then, by reaction stoichiometry, the following mass quantities of each compound participate in the reaction:

CH₄: 1 mole× 16.04 g/mole= 16.04 gramsO₂: 2 moles× 32 g/mole= 64 gramsCO₂: 1 mole× 44.01 g/mole= 44.01 gramsH₂O: 2 moles× 18 g/mole= 36 grams

Then the following rule of three can be applied: if by reaction stoichiometry 64 grams of O₂ form 44.01 grams of CO₂, 8.94 grams of O₂ form how much mass of CO₂?

[tex]mass of CO_{2} =\frac{8.94 grams of O_{2} x44.01 grams of CO_{2} }{64 grams of O_{2}}[/tex]

mass of CO₂= 6.15 grams

Finally, 6.15 grams of CO₂ are formed when 8.94 grams of O₂ reacts completely.

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The formula for density is given by p equals startfraction m over v endfraction, where p is density, m is mass and v is volume. If a substance has a mass of 27. 82 grams and a volume of 3. 6 ml, what is the most accurate density of the substance in g/ml? 7. 7 7. 7278 7. 73 0. 1.

Answers

Explanation:

so, we need to do the division :

27.82 g / 3.6 ml = 7.727777778... g/ml

so, 7.7278 is the rounded correct answer.

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Explanation:

The crew of a garbage truck takes 5 hours to empty all the bins in one neighborhood on pickup day. The city assigned a second garbage truck to this neighborhood. During their training, it took the crew from the second truck 8 hours to empty all the bins. A table showing rate in part per hour, time in hours, and part of bins emptied. The first row shows first truck and has, startfraction 1 over 5 endfraction, t, and startfraction 1 over 5 endfraction times t. The second row shows second truck and has, startfraction 1 over 8 endfraction, t, and startfraction 1 over 8 endfraction times t. When the two crews start working together, what part of all the garbage bins will the first garbage truck empty? 0. 6 0. 5 0. 7 0. 4.

Answers

When the two crews start working together, the part of all the garbage bins that the first garbage truck will empty is; A: 0.6

We are told that the first truck empties all bins in 5 hours. Thus;

Rate of first truck per hour = ¹/₅

Second truck empties all bins in 8 hours. Thus;

Rate of second truck per hour = ¹/₈

If both trucks work together, their rate per hour is;

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The part that the first garbage truck will empty when they both work together = ¹/₅t = ¹/₅ * ⁴⁰/₁₃

⇒ Approximately 0.6

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0.6

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Answers

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Answers

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There are different ways to support a claim. The description of Elisa’s daily routine support the author’s claim that It provides anecdotal evidence of a teenage fast food employee living like an adult.

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its A

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Answer:

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Answer: irrigation

Explanation:

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Answers

Explanation:

Risk Return relationship

Answer:

Whole test

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Answers

Answer: b

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The Wollstonecraft’s purpose in citing Rousseau’s theory is to disprove his theory. The correct option is B.

What is Rousseau’s theory?

Rousseau believed that modern man's enslavement to his own needs was to blame for a wide range of societal ills, including exploitation and dominance over others, as well as low self-esteem and depression.

Rousseau believed that the freedom of all citizens was the most important goal of good government.

History conjecture and moral psychology Rousseau repeatedly asserts that his worldview is centered on a single idea, namely, that humans are good by nature but corrupted by society.

Jean-Jacques Rousseau, born in Geneva in 1712, was a major political thinker of the 18th century. The purpose of Wollstonecraft citing Rousseau's theory is to refute it.

Thus, the correct option is B.

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Meiosis contributes to the process of reproduction by producing what type of cell?.

Answers

Meiosis contributes to the process of reproduction by producing gamete cells.

A recipe says to use 3 cups of flour to make 48 cookies.

Answers

Answer: The constant of proportionality that relates the number of cups with x and the number of cookies with y is 16

The given parameters are:

Cups (x) = 3

Cookies (y) = 48

Represent the number of cups with x and the number of cookies with y.

So, the constant of proportionality (k) is calculated using:

The above equation becomes

Divide 48 by 3

Hence, the constant of proportionality is 16

Explanation:

In what way is flick sticking his tongue on the flagpole an example of negative reinforcement?.

Answers

Sticking the tongue on the flagpole is an example of negative reinforcement because it produces an unpleasant sensation. In consequence, this behavior will be avoided in the future.

Negative reinforcement refers to a phenomenon that allows teaching a particular behavior.

Negative reinforcement occurs when an uncomfortable and/or unpleasant situation is taken away as a reaction to a particular stimulus.

This process (negative reinforcement) involves discarding the negative situation in order to strengthen a particular behavior.

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Select the correct answer from each drop-down menu. Scientists that reducing the consumption of substances that emit harmful gases would reduce pollution. Jonathan was irritated by the noise made by the loud musical procession on the street. The poor farmer was in for a pleasant surprise when he stumbled upon a pot of gold buried in his yard.

Answers

1. Scientists conjectured that reducing the consumption of substances that emit harmful gases would reduce pollution.

2. Jonathan was irritated by the incessant noise made by the loud musical procession on the street.

3. The poor farmer was in for a pleasant surprise when he fortuitously stumbled upon a pot of gold buried in his yard.

In this exercise, you're required to fill in the gap (blank) in the given sentences with the most appropriate word as follows:

1. Scientists conjectured that reducing the consumption of substances that emit harmful gases would reduce pollution.

A conjecture is a noun and it can be defined as an opinion or conclusion that is formed without sufficient evidence, fact or proof. Thus, a conjecture is formed on on the basis of an inconclusive or incomplete information.

2. Jonathan was irritated by the incessant noise made by the loud musical procession on the street.

Incessant is an adjective and it can be defined as an unpleasant thing that happens continuously without interruption. Thus, it is a word that is used to describe something that is ceaseless, unending or happens without stopping.

3. The poor farmer was in for a pleasant surprise when he fortuitously stumbled upon a pot of gold buried in his yard.

Fortuitously is an adverb and it is used it describe a situation or an event that happened by chance or accidentally rather than happening intentionally.

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Answer:

1. Scientists conjectured that reducing the consumption of substances that emit harmful gases would reduce pollution.

2. Jonathan was irritated by the incessant noise made by the loud musical procession on the street.

3. The poor farmer was in for a pleasant surprise when he fortuitously stumbled upon a pot of gold buried in his yard.

Explanation:

In the photoelectric effect a photon with an energy of 5. 3.

Answers

In the photoelectric effect a photon with an energy of 5.3

Which statement best describes a theme of the text? the government is always the highest law of the land. Religious law is above or greater than man's law. The laws of the government are sometimes correct and sometimes incorrect. One must be willing to accept punishment for breaking laws.

Answers

A theme simply means the main idea or the underlying meaning that a writer explores in a novel or literary work.

Your information is incomplete as you didn't provide the text. Therefore, an overview of a theme will be given. A theme is the central topic, subject, or message that's within a narrative.

The theme of a story can be conveyed by using the characters, dialogue, plot, settings, etc that's in the story. For the reader to understand the theme, it's important for one to understand what the story is about.

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