The sum of the first 8 terms of a GP is five times the sum of first 4 terms. Find the common ratio.​

Answers

Answer 1

Answer:

1

Step-by-step explanation:

Sum of nth term of a GP is expressed as;

Sn = a(r^n-1)/r-1

The sum of the first 8 terms of a GP is expressed as;

S8 = a(r^8 - 1)/r-1

The sum of first 4 terms is expressed as;

S4 = a(r^4 - 1)/r-1

If the sum of the first 8 terms of a GP is five times the sum of first 4 terms then

S8 = 5S4

a(r^8 - 1)/r-1 = 5[a(r^4 - 1)/r-1]

r^8 - 1 = 5(r^4 - 1)

r^8 - 1 = 5r^4 - 5

r^8 - 5r^4 = -5+1

r^4(r^4 - 5) = -4

r^4 - 5 = -4

r^4 = -4+5

r^4 = 1

r = 1

Hence the common ratio is 1


Related Questions

help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

Option C it is sure

,

A

trust me looooooooooll

IMPORTANT!! in a unit circle, what is the relationship between arc length and central angle?

Answers

The measure of an arc refers to the arc length divided by the radius of the circle. The arc measure equals the corresponding central angle measure, in radians. That's why radians are natural: a central angle of one radian will span an arc exactly one radius long.

5TH GRADE MATH GIVING BRAINLIESTT

Answers

Answer:

graph A

Step-by-step explanation:

When the cost is at 4 dollars, the feet is at 1. Hope this helps!

Answer:

A

Step-by-step explanation:

The only number that comes across 4x and 1y is a.

in the pond were 240 little fish and 90 big fish. what was the ratio of big fish to little fish

Answers

Answer:

266.66666667%

Step-by-step explanation:

240 / 90 = 266.666666666667%

What is the square root of 10 plus 25 minus 5 times 20

Answers

Answer: √

10

75

Step-by-step explanation:

Answer:

463.245553

Step-by-step explanation:

3.16227766+25-5 times 20

Gabby's dad drives a dump truck for a construction company. Last week, he came to Gabby's class for Career Day and talked about how math is used in his job. As an example, he told the class the bed of his truck is shaped like a rectangular prism with a volume of 24 cubic meters. The bed is 4 meters long and 2 meters deep.
How wide is the bed of the truck?


PLEASE HELP!!!!!!!!!!

Answers

Answer:

3 meters wide

Step-by-step explanation:

if the volume is 24 and the bed is 4 meters long and 2 meters deep, just multiply 4 x 2 =8 then find what number multiplies with 8 to get 24 which is: 3

A function is given: f (x) = 2x + 3
What is the value of f(-2)?

Answers

Answer:

f(-2) = -1

Step-by-step explanation:

-2 is x, so replace x as -2 into the equation

f (-2) = 2(-2) + 3

f (-2) = -4 + 3

f (-2) = -1

A collection of all points in the plane of the form (x, f(x)) is the graph of a function f. The graph of f is defined as the graph of the equation y = f(x).

Find function:

[tex]\to f (x) = 2x + 3[/tex]

[tex]\to f(-2) =?[/tex]

Putting the value "-2 " into the above given method:

⇒  f(-2) = 2(-2) + 3

⇒  f(-2) = -4 + 3

⇒  f(-2) = -1

Please find the graph file.

Find out more about the value of x here:

brainly.com/question/9916945

Solve: -2x - 5 = -3
plz help me hurry

Answers

Answer:

x=-1

Step-by-step explanation:

-2x - 5 = -3

add 5 to both sides

-2x = 2

divide both sides by -2

x = -1

Answer:

x = -1

Step-by-step explanation:

-2x - 5 = -3

Same to both sides:

-2x = -3 + 5

Simplify:

-2x = 2

Divide by -2 on each side to isolate x:

x = -1

Let me know if you have any questions

2(3x-9)=2x+10 what's x

Answers

Answer:

x = 7

Step-by-step explanation:

2(3x-9)=2x+10

6x - 18 = 2x + 10

4x = 28

x = 7

Answer:

x = 7

Step-by-step explanation:

In order to find the value of x, isolate it in the equation.

1) First, distribute the 2 to the terms inside the set of parentheses.

[tex]2 (3x - 9) = 2x + 10 \\6x - 18 = 2x + 10 \\[/tex]

2) Next, move all the x terms to one side and all the other terms to the other side. Subtract both sides by 2x and add both sides by 18.

[tex]6x - 18 = 2x + 10 \\4x = 28[/tex]

2) Divide both sides by 4 to finally isolate x.

[tex]4x = 28 \\x = 7[/tex]

Thus, x = 7.

Ms. Day went shopping last week and spent a total of $120. Blankets cost her $16 while pillows cost her $10. Altogether, she bought 9 items. How many of each item did Ms. Day end up buying?

Answers

Answer:

Ms. Day bought 5 blankets and 4 pillows.

Step-by-step explanation:

Let [tex]x[/tex] denotes number of blankets and [tex]y[/tex] denotes number of pillows.

Blankets cost her $16 while pillows cost her $10 and Ms. Day spent a total of $120.

[tex]16x+10y=120[/tex]

Divide this equation by 2.

[tex]8x+5y=60\,\,...(i)[/tex]

Ms. Day bought 9 items.

[tex]x+y=9[/tex]

Multiply this equation by 5.

[tex]5x+5y=45\,\,...(ii)[/tex]

Subtract [tex](ii)[/tex] from [tex](i)[/tex]

[tex]3x=15\\x=5[/tex]

Put [tex]x=5[/tex] in [tex]x+y=9[/tex]

[tex]5+y=9\\y=9-5\\y=4[/tex]

Therefore,

Ms. Day bought 5 blankets and 4 pillows.

What scale factor was applied to the first rectangle to get the resulting image?

Answers

Answer: Another way to look at it is that the rectangle was reduced in a factor of 5 (1/0.2=5)

don't forget to drop a heart hope it helped

Step-by-step explanation:

Answer: 1/0.2=5

Step-by-step explanation:

I hope this helps if you guys need a reach out to me :)

Inverse of f(n)=-2n^3-3

Answers

Pizza is great, yes very good

Solve. Then, rewrite the complete number sentence in decimal form

Answers

Step-by-step explanation:

a)

6.9+1.1= 8

b)

9.9+2.45=12.35

[tex]12 \frac{35}{100} [/tex]

c)

2.4+8.9=11.3

[tex]11 \frac{3}{10} [/tex]

d)

6.37+7.7=14.07

[tex]14 \frac{7}{100} [/tex]

Hola alguien puede ayudarme a resolver estos ejercicios por favor Ejercicios de intervalos 1.- Escribe en todas las formas posibles los siguientes intervalos y semirrectas: a) { x / –2 ≤ x < 3} b) Números mayores que –1 c) (–[infinity], –5] d) Números mayores o iguales que –7 y menores que 19. e) Números mayores que 9 y menores que 5.

Answers

Answer:

Tenemos 3 formas de escribir cada intervalo, una es con solo texto, la otra es usando los símbolos { <, >, ≤, ≥ }, y la última es con intervalos, donde:

( se usa para " < x "

) se usa para " > x "

[ se usa para  " ≤ x "

] se usa para   " ≥ x "

a) -2 ≤ x ≤3

Esto se escribe como:

"números mayores o iguales que -2 y menores o iguales que 3"

y

[-2, 3]

b) Números mayores que –1

Las otras formas de escribir esto son:

-1 < x

y no tenemos limite mayor, entonces:

(-1, ∞)

con -∞ y ∞ siempre se usan los símbolos ( o )  

c) (–[infinity], –5]  

Las otras notaciones son:

"Un numero menor o igual que -5"

x ≤ -5

d)  Números mayores o iguales que –7 y menores que 19

Las otras notaciones son:

-7 ≤ x < 19

[-7, 19)

e) Números mayores que 9 y menores que 5.

Las otras formas de escribir esto son:

5 < x < 9

(5, 9)

A family of four bought 6 bags of peanuts to share equally. If
each bag contained 36 peanuts, how many did each family
member receive?

Answers

Answer:

54

Step-by-step explanation: 36 * 6 = 216

216 divided by 4 = 54

a(b - 4) + c(b - 4)
can someone help me please!!!​

Answers

Answer:

(b−4)(a+c)

Step-by-step explanation:

Answer:

ab-4a+cb-4c

Step-by-step explanation:

a(b-4)+c(b-4)

ab-4a+cb-4c

x + y = 400
10x + 5y = 2750

Answers

Answer:

fart

Step-by-step explanation:

X = 150
Y = 250
150 + 250 = 400
10(150) + 5(250) = 2750
1500 + 1250 = 2750


Find the highest common factor of 35 and 8C.

Answers

Answer:

Factors of 35 = 1, 5, 7 and 35

Factors of 8= 1, 2, 4, 8.

common = 1


Simplify the expression.

4(5x + 2) + 7x + 6 =
12x + 8
27x + 14
27x + 8
27 + 14x

Answers

Answer: =27x+14

Step-by-step explanation: hope this help :)

Let's simplify step-by-step.

4(5x+2)+7x+6

Distribute:

=(4)(5x)+(4)(2)+7x+6

=20x+8+7x+6

Combine Like Terms:

=20x+8+7x+6

=(20x+7x)+(8+6)

=27x+14

Answer:

=27x+14

The sum of two numbers is 15. Four times the smaller number is 60 less than twice the larger number. What is the larger number?

Answers

Answer:

just put the words into math:

x+y=15

4x = 2y-60

Now just solve the system for y.

Help ASAP I’ll give you brainlest

Answers

Answer:

5.33 OR 5 1/3

Step-by-step explanation:

3 x 2³ ÷ 2 x 4 -1 +2

3 x 8 ÷ 2 x 4 -1 + 2

24 ÷ 8 +1

24 ÷ 9

2.66 OR 2 2/3

If $18\sqrt 8-8\sqrt{18}=\sqrt n, what is n?

Answers

Answer:

288 trust me it is 100% right I tried it as an answer an got it right.

Step-by-step explanation:

Answer:

288

Step-by-step explanation:

From the first two parts of the problem, we have

18√8 - 8√18 = 36√2 - 24√2

                    = (36 - 24)√2

                    = 12√2.

Thus, we wish to solve for n in the equation 12√2 = √n. In other words, we want to know what number 12√2 is the square root of. Any nonnegative number is the square root of its own square, so

n = (12√2)²

  = 12²(√2)²

  = 144 ∙ 2

  = 288.

Which table and graph represent the equation y = 3X?
—————————
a.table B and graph A
b.table B and Graph B
c.table A and graph B
d.table A and graph A

Answers

Answer:

d. table A and graph A

Step-by-step explanation:

y=3x

y = 3X is represented by graph B .

y = 3X is represented by table A .

Hence option C is correct .

Given, Equation : y = 3X

Now, to get the values of y substitute x.

Firstly table A:

y = 3X

x = 1 : y = 3

x = 2 : y = 6

x = 3 : y = 9

Thus table A represents the equation .

Next graph B :

Starting point of graph B is origin.

Coordinates of origin : (0,0)

Equation of graph B : y = 3X

Thus graph B represents the equation .

Therefore option C is correct .

Know more about equations,

https://brainly.com/question/27598076

#SPJ6

She measured the circumference of the globe along the equator to be 12π centimeters. Which of the following measures is closest to the volume of Tiffany’s globe?

Answers

Answer:

117 i think not sure

Step-by-step explanation:

Use place value to convert 1.18 to a fraction SELECT ALL CORRECT ANSWERS
A. 1 15/100
B. 1 15/1000
C. 1 9/50
D. 1 9/500

Answers

Answer:

c. 1 9/50

Step-by-step explanation:

1.18= 59 = 1 9/50

---

50

Forgive me if i am wronge

what is2/3b - 1/4b? Please help- also has to be simplified

Answers

Answer:5/12b

Step-by-step explanation:

Answer:

5/12b

Step-by-step explanation:

2/3= 8/12

1/4= 3/12

8/12-3/12= 5/12 then put the b at the end,

5/12b

5/12 is already in simplest form

Im giving brainiest to the person who answers it first. Thank you!

Answers

Answer: Oscer

Step-by-step explanation:

What is the difference?
5X
X-2
x + 4
2x
9x2 + 2x + 8
2 x(x - 2)
7x²+8
2 x(x - 2)
9x2–2x+8
2 x(x-2)
7x²-8
2X(x-2)

Answers

Answer:

Are these the option or what what this suppose to be ??????

Q A clothing company uses 280 pounds to make 70 shirts at this rate how many buttons with the clothing company used to make 460 shirts

Answers

Answer:

1840

Step-by-step explanation:

The number of buttons used in making 1 shirt = 280/70 = 4 buttons

the number of buttons used in making 460 shirts = 460 x 4 = 1840 buttons

Which correctly explains the number of solutions of the following system of linear
equations?
y = 6x + 2
y=6x - 2
No answer text provided.
Infinitely Many Solutions
One Solution
No Solution

Answers

Answer:

No solution

Step-by-step explanation:

Hope this Helped

Other Questions
A light house worker is tracking a boat that is 5 km south of her. She is also tracking a boatthat is 6 km from the tower located 70 east of north. To the nearest kilometer, howfar apart are the two boats?A. 7 kmB. 9 kmC. 8 kmD. 16 kM Please guys I need help The Holocaust is only one story of genocide. Name at least 3 more places we have seen Genocide in recent years. What are the characteristics of electromagnetic waves? if you were a member of national planning commission, what projects would you run in your province What does the graph show about the importance ofclean air?O People have a lower risk of aying from COPD whencompared to acute lower respiratory infections.O The health risk is the highest for getting lung cancerwhen people are exposed to indoor air pollutionO Most people will die from the negative health effectsassociated with stroke as indoor dirty air builds upO The risk of developing acute lower respiratoryinfection and ischemic heart disease is the samewhen exposed to indoor air pollution Solve the given equation 7/10X=4 3/5 What is the measure of Angles are not necessarily drawn to scale. the nth term of a sequence is given by an+bn where a and b are integers the 2nd term of the sequence is 2 4th term of the sequence is 20. find the 6th term of the sequence What policy was the US demonstrating with its series of neutrality acts? (5.1.A) A. Policy of peacetime military drafting B. Policy of isolationism C. Policy of embargo against Axis powers D. Policy of deporting communists HELP HELP I NEED HELP ASAP The visible color spectrum comes from _________.A. White light B. White paintC. White marshmallow creme Need help asap !!!!! its math! WI GIVE BRAINLIEST AND A FOLLOW AND PLEASE SHOW HOW U GOT THE ANSWER Quick QUESTION:33 1/3 as a fraction 3/4x+3-6/2x-1 algebric fractions What information about the organisms best helps the scientists to determine the evolutionary relationships among them?Anatomical featuresReproductive strategiesDNA SequencesHabitat types Determine a quadratic equation in standard form that has each pair of roots. X=52/3 HELP ASAP PLS. Which of the following best describes the relationship between air temperature and relative humidity?A. Cold air cannot hold any water vapor.B. Warm air can hold less water vapor than cold air.C. Cold air can hold less water vapor than warm air.D. Warm air and water vapor are measured in degrees Celsius (C). At year-end, salaries expense of $17,000 has been incurred by the company but is not yet paid to employees. Salaries payable Step 1: Determine what the current account balance equals. Step 2: Determine what the current account balance should equal. Step 3: Record the December 31 adjusting entry to get from step 1 to step 2 b. At its December 31 year-end, the company owes $325 of interest on a line-of-credit loan. That interest will not be paid until sometime in January of the next year. Interest payable Step 1: Determine what the current account balance equals. Step 2: Determine what the current account balance should equal. Step 3: Record the December 31 adjusting entry to get from step 1 to step 2. c. At its December 31 year-end, the company holds a mortgage payable that has incurred $950 in annual interest that is neither recorded nor paid. The company intends to pay the interest on January 7 of the next year. Interest payable Step 1: Determine what the current account balance equals. Step 2: Determine what the current account balance should equal. Step 3: Record the December 31 adjusting entry to get from step 1 to step 2. What type of work did women in America commonly perform in the early 1800s? A. Teaching at colleges and law schoolsB. Campaigning for candidates and organizing political campaigns C. Cooking, washing, and mending clothes for there familiesD. Practicing medicine and dentistry QUICK SOMEONE HELP ME Ms. Mathews wants to put a fence around the north, south and east sides if her square garden. The garden has an area of 100ft2. How much fencing does she need? twice the square root of a number is 12