Please i need an answer urgently. Sum of 3 terms are 252, first term is 192. Find common ratio

Please I Need An Answer Urgently. Sum Of 3 Terms Are 252, First Term Is 192. Find Common Ratio

Answers

Answer 1

Answer:

[tex]r=\frac{1}{4}\\\\r=-\frac{5}{4}[/tex]

Step-by-step explanation:

Geometric Sequences

The geometric sequence is given as:

[tex]a_1, a_1r, a_1r^2, a_1r^3,..., a_1r^{n-1}[/tex]

Where n is the number of the term, n≥1, and r is the common ratio.

The sum of n terms of the geometric sequence is given by:

[tex]\displaystyle S_n=a_1\frac{r^n-1}{r-1}[/tex]

We are given: S3=252, a1=192, thus substuting:

[tex]\displaystyle 252=192\frac{r^3-1}{r-1}[/tex]

Dividing by 12:

[tex]\displaystyle 21=16\frac{r^3-1}{r-1}[/tex]

Recall that:

[tex]r^3-1=(r-1)(r^2+r+1)[/tex]

Substituting:

[tex]\displaystyle 21=16\frac{(r-1)(r^2+r+1)}{r-1}[/tex]

Simplifying:

[tex]21=16(r^2+r+1)=16r^2+16r+16[/tex]

Rearranging:

[tex]16r^2+16r+16-21=0[/tex]

16r^2+16r-5=0

Rewriting:

[tex]16r^2-4r+20r-5=0[/tex]

Factoring:

[tex]4r(4r-1)+5(4r-1)=0[/tex]

[tex](4r-1)(4r+5)=0[/tex]

Solving:

[tex]r=\frac{1}{4}\\\\r=-\frac{5}{4}[/tex]

Both solutions are valid


Related Questions

Luke ate a snack with 91 total calories. If the chips he ate were 41.2 calories,how many calories were in the rest of his snack?

Answers

Answer:

49.8 calories were left!!!

Step-by-step explanation: Just subtract 91-41.2!

evaluate the expression 9!/6!

A: 54,000
B: 2!
C: 3/2
D: 504

Answers

Answer: D) 504

Step-by-step explanation:

9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

6! = 6 x 5 x 4 x 3 x 2 x 1

Using this, we can rewrite the initial expression as:

9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 / 6 x 5 x 4 x 3 x 2 x 1

We can see that 6 x 5 x 4 x 3 x 2 x 1 is in both the numerator and the denominator, so we can cancel it out, leaving us with 9 x 8 x 7 which equals 504.

The answer is D because it is 504

Help me please 40 points for this math question

Answers

Answer: The answer is C

Step-by-step explanation:

It’s C because I just had that question and I got it right

Which of these expressions is equivalent to -2(x−5)?
-2x−5
-2x+5
-2x+10
-2x−10

Answers

Answer:

c. -2x+10

Step-by-step explanation:

distributive property

(-2)x-(-2)5= -2x-(-10)

keep change change

-2x+10

where the answer is -2x+10

Answer:

-2x-10

Step-by-step explanation: so WE CAN SLOVE THIS EQUATION BY distrubutive property, -2 times x = -2x, we got 1 part of the equation. Now we distrubute -2 and -5.

-2 x -5 = -10.

So we get = -2x-10

Here is a picture of a circle. Each square represents 1 square unit.
Explain why the area of the circle is less than 4 square units.

Answers

Answer:

No picture?

Step-by-step explanation:

i need a picture to anwser

−5w−2w+3w=9 whats w
help

Answers

Answer: w = -9/4

Step-by-step explanation:

The original price of the shirt is $50 but you paid $30 for it on sale what was the percentage change in price

Answers

40% was the percentage change in price.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, The original price of the shirt is $50 but you paid $30 for it on sale

From the general formula of percentage change:

Percentage change = change in value / original value * 100

In our case,

Original value = 50

Change in values = 50 - 30

Change in values = 20

Percentage change = 20/50 * 100

Percentage change = 40

Therefore,  the percentage change in price was 40%.

Learn more about percentages here:

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At an expected rate of return of 7% compounded semi-annually, what is the expected percentage growth of a portfolio after 4 years?

Answers

Answer:

The expected growth is 17.2%

Step-by-step explanation:

Let us have a present initial value of 500

we then proceed to get the value after 4 years

We use the compound interest formula to get the amount

That will be;

A = P( 1 + r/n)^nt

P = 500

r = 4% = 4/100 = 0.04

n is 2: semi annually means twice per year

t is 4

So

using the formula, we have that;

P = 500(1 + 0.04/2)^(2 * 4)

= 500(1.02)^8

= 586 approximately

So the percentage growth rate is as follows

(586-500)/500 * 100

= 86/500 * 100 = 17.2%

A puppy's weight increases by 15% each week for the first 6 months. The puppy currently weighs 3.7 pounds. Which expression will not calculate how much the puppy will weigh in 1 week?

Answers

Answer:

y=3.7+0.15(1)

Step-by-step explanation:

Note we are not given the options to choose from in this question, let us solve for the answer directly

Step one:

given data

The puppy's weight increases by 15% each week for the first 6 months

=0.15

The puppy currently weighs 3.7 pounds

Step two:

let the number of weeks be x

and the weight after x weeks be y

so

y= 3.7+0.15x

after 1 week the expression to calculate the weight is

y=3.7+0.15(1)

Zoe invest $600 in college savings account. The account earns 5.7% interest compounded quarterly. How many years will it take for Zoe's account to reach $7,000?

Answers

Answer:

43.407 years

Step-by-step explanation:

Zoe invest $600 in college savings account. The account earns 5.7% interest compounded quarterly. How many years will it take for Zoe's account to reach $7,000?

We are asked to find time t in a compound interest formula

The formula is given as:

t = log(A/P) / n[log(1 + r/n)]

A = Total amount = $7000

P = Principal = $600

n = number of times interest is compounded = Quarterly =4

r = Interest rate = 5.7% = 0.057

Hence,

t = log(7000/600) /4[log (1 + 0.057/4)]

t = 43.407 years

Complete the proof that AFGH isn't similar to AJIH.

Answers

Sides FH and HJ are not congruent

Divide. Write your answer in fraction form.

(5x+ + 18x+ 15) / (x+2)

Answers

Answer:

what? it seems like you just spammed anything from the web O_o

Step-by-step explanation:

M is the midpoint of AN, A has coordinates
(7,-4), and M has coordinates (3,2). Find
the coordinates of N.
Explain??

Answers

(7+x)/2= 3

7+x=6

x=(-1,0)

(-4+y)/2= 2

-4+y=4

y=(0,8)

Therefore, N has coordinates (-1,8)

Is the quotient for 36 ÷ 0.6 greater than or less than 36? Explain your answer

Answers

Answer: Greater than

Step-by-step explanation:

36/0.6 = 60

60 is more than 36

It is 60 so it’s greater than

Last year, Mr. Smith's biology class averaged 73 on their first test. This year, his new class averaged 87 on the same
test. Based on these results, is it reasonable to conclude that this year's class is more intelligent?
Yes, a grade of 87 is higher than a grade of 73.
Yes, the study was done in an academic setting.
No, the experiment was not double-blind.
No, there was no use of a placebo in the experiment.
No, there may be other differences between the two years besides the grades.

Answers

E. No, there may be other differences between the two years besides the grades.

This is because every kid is different and Mr. Smith might have just gotten a better group of kids the second year. This is just one factor of many viable options.

May I have brainliest please? :)

PLZZZ HELPPP!!!!!!!!!!

Answers

Hello!

[tex]\large\boxed{2x + y = 3}[/tex]

Begin by finding the slope that would be perpendicular to the given equation.

A perpendicular line has a slope that is the opposite reciprocal of the original. Therefore:

1/2 --> -2

Find the answer choice that contains a slope of -2 when rewritten in the form y = mx + b:

Choice 1:

x + 2y = 2

Move x to the other side:

2y = -x + 2

Divide both sides by 2:

y = -1/2x + 1. This choice is incorrect.

Choice 2:

x - 2y = -12

Move x to the other side:

-2y = -x - 12

Divide both sides by -2:

y = 1/2x + 6. This choice is incorrect.

Choice 3:

2x + y = 3

Move 2x to the other side:

y = -2x + 3. This contains a slope of -2, which is correct.

Choice 4:

y - 2x = -5

Move -2x to the opposite side:

y = 2x - 5. This contains a slope of positive 2, so it is incorrect.

The correct answer is 2x + y = 3.

Answer:

D. y-2x=-5

Step-by-step explanation:

Algebra 2. solve each equation. remember to check for extraneous solutions
(p-2)/(p-4)=(p^2-6P)/(P-4) - (P+5)

Answers

Answer:

p=11/4

Step-by-step explanation:

Solve the rational equation by combining expressions and isolating the variable  p .

Solve: 3,125 = 5–10 + 3x

Answers

Answer:

x = 3130/3

Step-by-step explanation:

3125 -5 +10 = 3X

3130 = 3x

x = 3130/3   or 1043 1/3

From the sum of 2x-y+z and 2y -10, subtract 4x-2y-11​

Answers

ans: -2x + 3y + z + 1
the working is below :)

Answer:

-2x + 3y + z + 1

Step-by-step explanation:

A recipe calls for 2 cups of water for every 3 cups of flour. How much water is needed if you use 12 cups of flour?

Answers

Answer:

8

Step-by-step explanation:

Answer:

8 cups of water

Step-by-step explanation:

2 cups of water = 3 cups of flour

x cups of water = 12 cups of flour

12/3=4

2x4= 8

Tom has already baked 4 cakes, and he can bake 1 cake with each additional stick of butter he buys. How many additional sticks of butter does Tom need in order to bake a total of 42 cakes?

Answer in the number of additional sticks of butter.

Answers

Answer:

since it takes 1 additional stick to bake a cake,then it takes 84 additional sticks to bake 42 cakes

what is the slope of points (3,5) and (-1,-7)

Answers

Answer:

slope is 3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Given: Quadrilaterals ABCD ~ EFGH , with measure of angle A = 47 degrees, measure of angle B = 39 degrees, and measure of angle C = 112 degrees. Find: Measure of angle F and measure of angle H.

Answers

Answer:

The answer is below

Step-by-step explanation:

Two polygons are said to be congruent if they have the same size and shape that is their corresponding angles and sides are equal.

Hence since Quadrilaterals ABCD is congruent to EFGH, then their corresponding angles and sides are equal.

In quadrilateral ABCD:

∠A + ∠B + ∠C + ∠D = 360° (sum of angles in a quadrilateral)

Substituting:

47 + 39 + 112 + ∠D = 360

∠D + 198 = 360

∠D = 360 - 198

∠D = 162°

The image of Quadrilaterals ABCD and EFGH is not given but let us assume that they have the same orientation, hence:

∠A = ∠E = 47°

∠B = ∠F = 39°

∠C = ∠G = 112°

∠D = ∠H = 162°

Find the period of the graph shown below.

Answers

Answer:

π/2

Step-by-step explanation:

Find the period of the graph shown below.

Total time to complete one oscillation is called the period.

The total number of oscillations in the graph is 7 oscillations:

Hence;

7 oscillations = 3π + π/2 = 7π/2

To get the period, we want to know thw angle it takes to complete just one oscillation that is;

1 oscillation = x

Divide both equations:

7/1 = (7π/2)/x

7x = 7π/2

14x = 7π

x = 7π/14

x = π/2

Hence the period of the wave is π/2

After visiting the Titanic, Captain Brain and Mr. Pinky are taking the Alvin submarine back to the surface of the water. They start 2000 meters below the surface of the water, and ascend at 57 meters per hour.

Answers

Answer:

35.09hours

Step-by-step explanation:

Since we are not told what to find, we can as well look for the time it took to ascend

Given

Distance below surface of water = 2000m

Speed = 57m/hr

Required

Time

Using the formula;

Speed = Distance/Time

Time = Distance/Speed

Time = 2000/57

Time = 35.09hours

Hence it took 35.09hours to ascend

What are the coordinates of the z- and y-intercepts in the equation 14x+ 8y=-56?

Answers

Answer:

Idkasd

Step-by-step explanation:

Keep trying

Answer:

the x-intercept is (-4,0)

the y-intercept is (0,-7)

Sorry for annoying you guys just need answers

Answers

What type of math is this??? Geometry? Algebra?

Select the correct answer.
Mateo teaches a continuing education class at the library on Tuesday nights. He estimates that 75% of his students are satisfied or very satisfied with the class.

Last week, he asked a random sample of students to take a survey on their experience in the class. However, the results showed that only 70% indicated that they are satisfied or very satisfied with the class. He decides to randomly survey more of his students. How will Mateo know whether his model is valid or not?

A.
It is valid if the result from all the surveys and the model get closer together.
B.
It is impossible to determine whether the model is valid.
C.
It is valid if the result from all the surveys and the model stay the same.
D.
It is valid if the result from all the surveys and the model get farther apart.

Answers

Answer:

A

Step-by-step explanation:

Getting closer together means that both are becoming more accurate.

A valid model is such model whose calculated value approximates to the actual value. If it doesn't approximate to the actual value, it must be close to the actual value.

The model is valid if the results from the survey are close enough, together.

Given that:

[tex]p_1 = 75\%[/tex] -- the actual estimation of satisfied students

[tex]p_2 = 70\%[/tex] -- the second estimation of satisfied students

For a model to be valid, the calculated value must be close to the actual value.

If after Mateo's survey of more students, the result of satisfied or very satisfied students is still close to 75%, then Mateo's model is valid.

If otherwise, then the model is invalid.

Read more at:

https://brainly.com/question/731147

PLEASE HELPPPPPP I NEED IT DONE BY 3 OR 4

Answers

Hi so I’m not that smart but if I had to answer that i would probably put the third one. Sorry if that’s wrong

sin∅=√3-1/2 find approximate value of sec∅(sec∅+tan∅)/1+tan²∅​

Answers

Answer:

The approximate value of [tex]f(\theta) = \frac{\sec \theta \cdot (\sec \theta+\tan \theta)}{1+\tan^{2}\theta}[/tex] is 1.366.

Step-by-step explanation:

Let [tex]f(\theta) = \frac{\sec \theta \cdot (\sec \theta+\tan \theta)}{1+\tan^{2}\theta}[/tex], we proceed to simplify the formula until a form based exclusively in sines and cosines is found. From Trigonometry, we shall use the following identities:

[tex]\sec \theta = \frac{1}{\cos \theta}[/tex] (1)

[tex]\tan\theta = \frac{\sin\theta}{\cos \theta}[/tex] (2)

[tex]\cos^{2}+\sin^{2} = 1[/tex] (3)

Then, we simplify the given formula:

[tex]f(\theta) = \frac{\left(\frac{1}{\cos \theta} \right)\cdot \left(\frac{1}{\cos \theta}+\frac{\sin \theta}{\cos \theta}\right) }{1+\frac{\sin^{2}\theta}{\cos^{2}\theta} }[/tex]

[tex]f(\theta) = \frac{\left(\frac{1}{\cos^{2} \theta} \right)\cdot (1+\sin \theta)}{\frac{\sin^{2}\theta + \cos^2{\theta}}{\cos^{2}\theta} }[/tex]

[tex]f(\theta) = \frac{\left(\frac{1}{\cos^{2}\theta}\right)\cdot (1+\sin \theta)}{\frac{1}{\cos^{2}\theta} }[/tex]

[tex]f(\theta) = 1+\sin \theta[/tex]

If we know that [tex]\sin \theta =\frac{\sqrt{3}-1}{2}[/tex], then the approximate value of the given function is:

[tex]f(\theta) = 1 +\frac{\sqrt{3}-1}{2}[/tex]

[tex]f(\theta) = \frac{\sqrt{3}+1}{2}[/tex]

[tex]f(\theta) \approx 1.366[/tex]

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