the sum of the first six terms of a G.P is 9 times the sum of the first three terms . what is the first term ?​

Answers

Answer 1

Without any more information, the first term can be any number.

Let a be the first term in the geometric progression, and let r be the common ratio between consecutive terms. Then

a + ar + ar ² + ar ³ + ar ⁴ + ar ⁵ = 9 (a + ar + ar ²)

ar ³ + ar ⁴ + ar ⁵ = 8 (a + ar + ar ²)

r ³ + r ⁴ + r ⁵ = 8 (1 + r + r ²)

r ³ (1 + r + r ²) = 8 (1 + r + r ²)

r ³ = 8

r = 2

Now with this ratio, the sum of the first six terms is

a (1 + r + r ² + r ³ + r ⁴ + r ⁵) = a (1 - r ⁶)/(1 - r) = 63a

while the sum of the first three terms is

a (1 + r + r ²) = a (1 - r ³)/(1 - r) = 7a

and of course 63a = 9 • 7a, and this is true for any a.


Related Questions

Leshonda had been working at her job for almost twenty years. She felt like she worked overtime more often than not (more than 50% of the time) and deserved a raise, so she randomly selected 50 paychecks (each for one week of work) and found that she had worked overtime in 32 of those weeks. Use a TI-83, TI-83 plus, or TI-84 calculator to test whether Leshonda worked overtime more often than not. Identify the p-value, rounding to three decimal places.

Answers

Answer:

Z statistic = 1.980

Pvalue = 0.024

Step-by-step explanation:

Sample size (n) = number of paychecks = 50

Number of overtime (x) = 32

Let Number of overtime = o

Claim : Overtime work is done more than 50% of the time ;

Null hypothesis:H0: o = 0.5

Alternative hypothesis : H1: o > 0.5

Using the T84 calculator :

Selecting the 1 proportion test under the Stat menu:

p0 = 50% = 0.5

x = 32 ; n = 50 ; >p0

The z test statistic value obtained is 1.980 (3 decimal places)

The P value = 0.024 (3 decimal places)

At α = 0.05 ;

P value < α ; therefore we reject the null

Hence, overtime work is done more than 50% of the time.

What is the slope of a line that passes through the following points (4, 6) and (2, 0)?

Answers

Answer:

3

Step-by-step explanation:

Step-by-step explanation:

formula to fine slope

m=tan()=y2-y1/x2-x1

Sophia had 63¢ until she spent 5 nickels. How much money does Sophia have now?

Answers

Answer:

38 cents

Step-by-step explanation:

5x5=25

63-25=38

Please help and explain how you got the answer. Im giving out brainliest. || Q3

Answers

Answer:6:8

Step-by-step explanation:

The Answer to the problem is is 6:8

What is the answer to this?

Answers

Answer:

dfgv nm./

Step-by-step explanation:

Point R on the coordinate grid below shows the location of a car in a parking lot. A second car needs to park 6 units above R to leave room for a utility truck. What are the coordinates of the location of the second car?

Image of a coordinate grid with point R R located at negative 1, negative 3.
(3 points)

(−1, −3)
(−1, 3)
(5, −3)
(5, 3)

Answers

Answer:

Point R is located at the point (-1,-3)

The car needs to park 6 units above point R.

When you are moving something up or down on the coordinate grid, you are affecting the y- axis. So to find the coordinates we would keep the x value and add 6 to the y value.

Coordinates of the second car

(-1, -3 +6)

(-1 , 3)

The answer to this question is B

Adding a positive to a negative is the same as subtracting.

EX:

We were adding 6 and -3

Adding 6 and -3 is the same as subtracting 3 from 6.

Either way we get the same answer.

B is your answer

Hope this helps!

The Quality Control Department employs five technicians during the day shift Listed below is the number of times each technician instructed the production foreman to shut down the manufacturing process last week.

Technician Shutdown
Taylor 4
Hurley 3
Gupta 5
Rousche 6
Huang 3

Required:
a. How many samples, without replacement, of size two are possible?
b. Compute the mean of the sample means and compare it to the population mean. (Round your answers to 1 decimal place.)

Answers

Solution :

Number of different samples of two technicians possible is = 10, as 2 technicians are to be chosen from a total of 5 technicians.

a). Therefore, 10 different samples are possible of size two.

b).

        Sample                    Shut down         Mean

1. Taylor, Hurley                 4, 3                    3.5

2. Taylor, Gupta                 4, 5                    4.5

3. Taylor, Rousche             4,6                      5

4. Taylor, Huang                4, 3                    3.5

5. Hurley, Gupta                 3,5                       4

6. Hurley, Rousche             3,6                      4.5

7. Hurley, Huang                 3,3                       3

8. Gupta, Rousche              5,6                       5.5

9. Gupta, Huang                  5,3                       4

10. Rousche, Huang            6,3                      4.5  

                                                                        42

Now mean of sample means  [tex]$=\frac{42}{10}$[/tex]    = 4.2

Mean of population is = [tex]$\frac{4+3+5+6+3}{5}$[/tex]    = 4.2

Thus both the means are equal.

Ellen collected 88 empty cans to recycle,and Carl collected 72 cans. They packed an equal number of cans into each of two boxes to the recycling center

Answers

ellen had 44 per box and carl had 36 per box

but if they had only two boxes altogether then each box had 80 cans in it

What is the value of the expression below? 3x + (12 - 3) - x, when x = 2.5 A. 13 B. 14 C. 15 D. 19

Answers

Answer:

The answer to this question is: (B)

Which is "14"

Step-by-step explanation:

Substitute the value of the variable into the equation and simplify.

HOPE this helped if so PLEASE leave a "Rating" and a "LIke" and PLEASE mark me brainliest if I have the best answer! THANKS! :))))

i need also need help with this ​

Answers

Answer:

umm you need help with what

Step-by-step explanation:

there is no question

lb = 64 oz Helppppppppppppp me
[tex]5[/tex]

Answers

Answer:

no u

Step-by-step explanation: no no no no no no no no no


12. A company advertises on a website. A worker tracked the number of visits to the
website and the number of clicks on the advertisement. The table shows the data
for several days. A linear function can be used to model the data.
Website Advertisement
Number of Visits
to Website, X
Number of Clicks
on Advertisement, y
14
153
629
38
471
30
914
53
307
21
1,045
60
510
32
1,106
63
Based on the table, what is the best prediction of the number of clicks on the
advertisement if 1,500 people visit the website?

Answers

Answer:

The answer is 83

Step-by-step explanation:

It's a build up of a continental slope

Im in 8th grade and hope this helped

find the amount accumlatrd after investing a principal P for t years at an interest rate compound annuay. P= $12,000 r=7.5% t=7 ​

Answers

Answer:

A = $19,908.59

Step-by-step explanation:

Compound Interest

Compound interest occurs when the interest earned in a given period is reinvested rather than paying it out. The interest in the next period is then earned on the principal sum plus previously accumulated interest.

The formula is:

[tex]{\displaystyle A=P\left(1+{\frac {r}{k}}\right)^{kt}}[/tex]

Where:

A = final amount

P = initial principal balance

r = interest rate

k = number of times interest applied per time period

t = number of time periods elapsed

We are given the following data:

P = $12,000

r = 7.5% = 7.5/100 = 0.075

t = 7

k = 1 since there is only on compounding per year.

Applying the formula:

[tex]{\displaystyle A=\$12,000\left(1+{\frac {0.075}{1}}\right)^{7}}[/tex]

[tex]{\displaystyle A=\$12,000\left(1.075\right)^{7}}[/tex]

A = $19,908.59

does anyone know the answer ?

Answers

Answer:

your answer is D.

Step-by-step explanation:

when the square of r crosses over the square will become square-root

A= πr^2

r=√π/A

when A crosses over it has to be under.

True or false
do all states have an income tax?

Answers

Answer:

All states have a state income tax. The amount of tax withheld generally depends on the level of income and the number of exemptions claimed.

this answer would be true

11) It takes you 15 minutes to frost a 2 layer cake. You and a friend have 100 1 point
cakes to frost for the church bake sale. How many hours will it take the two
of you to frost all of the cakes if you work at the same time rate? Hint: It
takes you 15 minutes to frost one cake, you can frost 4 cakes in 1 hr. *
B. 8 hours
O c. 12.5 hours

Answers

Answer:

12.5 hours

Step-by-step explanation:

100/4=25

25/2=12.5

HELP IM IN CLASS DOING IT RIGHT NOW The absolute value of any number is always positive. True False

Answers

Answer:

True

Step-by-step explanation:

Answer:

[tex] \huge\purple{TRUE}[/tex]

Step-by-step explanation:

The absolute value of any number is always positive.

A dozen is how much in maths?

Answers

A dozen is 12 in maths..

Answer:

well for me it's

Step-by-step explanation:

12

But a german dozen is 13

please give me brainlest

x + 5y = 8
3x = 24 - 157

Answers

Answer:

x = [tex]-\frac{133}{3}[/tex], y = [tex]\frac{157}{15}[/tex]

Step-by-step explanation:

x + 5y = 8

3x = 24 - 157

3x = 24 - 157

3x = -133

x = [tex]-\frac{133}{3}[/tex]

x + 5y = 8

[tex]-\frac{133}{3}[/tex] + 5y = 8

5y = [tex]\frac{157}{3}[/tex]

y = [tex]\frac{157}{15}[/tex]

What is the volume of the rectangular prism below?



A

16 cubic units


B

20 cubic units


C

23 cubic units


D

32 cubic units

Answers

Answer:

D- 32 cubic units

Step-by-step explanation:

count each side and then multiple the numbers

A regression model to predict Y, the state-by-state 2005 burglary crime rate per 100,000 people, used the following four state predictors: X1 5 median age in 2005, X2 5 number of 2005 bank- ruptcies per 1,000 people, X3 5 2004 federal expenditures per capita, and X4 5 2005 high school graduation percentage. (a) Write the fitted regression equation. (b) Interpret each coef- ficient. (c) Would the intercept seem to have meaning in this regression

Answers

Answer:

hello your question is incomplete attached below is the complete question

Answer :

a) attached below

b) Agemed ; 2005 median age of population

Fedspend ; 2004 federal spending per capita for all functions

HSGrad% ; 2005 public high school graduation rate

Bankrupt ; 2005 corporate or individual bankruptcies filed per 1,000 population

c) No

Step-by-step explanation:

A) Fitted regression equation

attached below is the excel procedure and the answer related to the question

b) Interpret each coefficient

Agemed ; 2005 median age of population

Fedspend ; 2004 federal spending per capita for all functions

HSGrad% ; 2005 public high school graduation rate

Bankrupt ; 2005 corporate or individual bankruptcies filed per 1,000 population

C) would the intercept seem to have meaning in this regression

The intercept wouldn't have a meaning in this regression

what is the value of x in the eqation 5[x-6] = 2 [x+3]

Answers

Answer:

x = 12

Step-by-step explanation:

5x - 30 = 2x + 6

3x = 36

x = 12

Answer:

x=12

Step-by-step explanation:

1) distribute values:

5x-30=2x+6

2) add 30 to both sides

5x=2x+36

3) subtract 2x from both sides

3x=36

4) divide by 3

x=12

What is the y-value of the solution of the system of equations given below?
3x + 2y = -6
y = 2x + 4

Answers

Point form: (-2, 0)
Equation form: x=2, y=0

can anybody help me and explain how to calculate it?​

Answers

Answer:

[tex]\frac{\pi }{4}[/tex]

Step-by-step explanation:

1. note, that

[tex]arcsin\frac{1}{2}=\frac{\pi}{6};arcsin\frac{\sqrt{2}}{2}=\frac{\pi}{4};arcsin1=\frac{\pi }{2};arcsin\frac{\sqrt{3}}{2}=\frac{\pi}{3}[/tex]

2. after the substitution:

[tex]\frac{\pi}{6}+\frac{\pi }{4}- \frac{\pi }{2} + \frac{\pi }{3}=\frac{\pi }{4}.[/tex]

A math quiz has 10 questions and is scoreout of 100. Each question is worth the same. The function S (q) represents the quiz score, S, in terms of the number of correctly answered questions, q. Determine whether each statement below is true or false. Select True or False for each stateent.

Answers

Answer:

False

True

True

False

Step-by-step explanation:

got it right on the test

I need help with this

Answers

Answer:

A

Step-by-step explanation:

process of elimination... :D

the answer below thanks

Answers

Answer:

The equation of the circle having centre (-5,-9) and radius r=3  is

x² + 10 x +y² + 14 y + 65 = 0

Step-by-step explanation:

Explanation:-

From graph  The centre of the circle  C( -5 , -7)

The radius of the circle r = 3cm from the centre of the given circle

The equation of the circle



From graph the centre ( h, k) = ( -5,-7) and r = 3cm

                 [tex](x-(-5))^2+(y-(-7))^2 = 3^2[/tex]

                x² + 10 x +25 +y² + 14 y + 49 =9

              x² + 10 x +25 +y² + 14 y + 49 -9=0

 The equation of the circle

                x² + 10 x  +y² + 14 y + 65 = 0  

 



                     

Assume that you have a choice between a manufacturing job and a sales job. The annual earnings from the manufacturing job will have a normal distribution with a mean of $40 000 and a standard deviation of $9 000. The annual earnings from the sales job will have a normal distribution with a mean of $35 000 and a standard deviation of $9 000. What is the probability that you would earn more than $45 000 per year if you select one or the other

Answers

Answer:

0.42124

Step-by-step explanation:

Manufacturing job :

Mean (m) = 40,000

Standard deviation (s) = 9000

Sales job :

Mean (m) = 35000

Standard deviation (s) = 9000

Probability of earning more than 45000 if one or the other job is selected;

Obtaining the standardized scores and probability for each :

Z = (x - m) / s

P(x > 45000)

Z = (45000 - 40000) / 9000 = 0.5555

= 0.56

P(Z > 0.56) = 0.28774(Z probability calculator)

For sales :

P(x > 45000)

Z = (45000 - 35000) / 9000 = 1.1111111

= 1.11

P(Z > 1.11) = 0.1335 (Z probability calculator)

0.28774 + 0.1335 = 0.42124

0.25 of 40 plz plz help

Answers

Percentage Calculator: What is 0.25 percent of 40? = 0.1.

What is -23/6 - 7/3
A-37/6
B-30/9
C-16/6
D37/6​

Answers

Answer:

A

Step-by-step explanation:

i solved it

Other Questions
this is kinda confusing can someone help explain!! Suppose you deposit $2,500 in a savings account that pays you 5% interest per year.a. How many years will it take for you to double your money?b. How many years will it take for your account to reach $8,000? Las caracetrsticas que mejor describen a Santiago Nasar son las siguientes excepto...a) es violento.b) es bebedor y parrandero.c) es joven, rico, bilinge, y bien parecido.d) la gusta la caza y maneja muy bien las armas.e) ama los caballos y es mujeriego. Evaluate the function f (x) = 3x2 5 when x = 11. Active12Which of the following are forms of asexual reproduction? Select three options.zygote formationbinary fissionfertilizationfragmentationsporulation a. Harry started a new job where he earns the same amount every hour. Last week, he worked 9 hours and earned $108. Write the linear equation for this situation, where y represents the money earned, in dollars, and I represents the number of hours worked. Write a version of the sequential search algorithm that can be used to search a sorted list. Write a program to test the sequential search algorithm. Use either the function bubbleSort or insertionSort to sort the list before the search. Your program should prompt the user to enter 10 digits and then prompt the user to enter a digit to search - if the list contains this digit, output its position to the console: Katelynn has 24$ and jalicia has 30 divided what is | -5 | + 7 what did bohr consider electrons as?A. Discrete particlesB. Continuous particlesC. Particles with zero energy D. None of the above Which type of economic system allows people to own private property and profit from what they sell? Question 4 (1 point)If non-disjunction occurred during meiosis II, would any of the resulting cells end upbeing haploid?NO or YES 20 points!! Write an essay on the industry on which you want to focus. Research and discuss the kinds of jobs that are available in that industry, the average wage, the economys effect on the industry, and so on. How should you begin your speech?a. with your thesis statementb. with details and explanations of your topicc. with an attention-grabbing openerd. with a call to action that motivates the audience What did the Spanish accomplish Peter and Judy together earn $5060 per month. Their mortgage payment is $1265pr month. What percentage of their household income goes toward paying themortgage? A ps4 uses uses 8.8 watts when on stand by mode. If electricty in your area costs 0.10$ kwh, how much would this cost? At what rate does magma deep below Earth's surface cool? What size of crystal results from magma cooling deep below Earth's surface?O A. Slowly, large crystals formB Quickly, large crystals formC. Slowly, small crystals formD. Quickly, small crystals form Decide if each function below can be represented by y = 3x 2. Select Yes or No for each function PLEASE HELP !!Limerick Poetry!Now, create your own humorous limerick. Make sure that you use the correct rhyme scheme and rhythmical pattern.HINT: Many limericks begin with "There was a . . . " because it fits well with the rhythm.Rhyme Scheme: AABBALines 1, 2, and 5 = 3 accented syllablesLines 3 and 4 = 2 accented syllables