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

E
С
70
A
D
B
What is mZDEA?
OA) 20°
OB) 70°
OC) 90°
OD) 180°

Answers

I would say 180 but its just a guess
90 degrees it is a right angle

Help please answer fast!!!

Answers

Answer: -3.5

Step-by-step explanation:

tell if im wrong

Answer:it would be 7.5

Step-by-step explanation:-2.5 + 2.5 = 0 0+2.5=2.5 2.5+2.5=4.5 so it would be 2.5+2.5+2.5=7.5

Kiran's family took a road trip to Niagara Falls. Kiran slept through the last 62% of the trip. If the total length of the trip was 1000 miles, how many miles had they traveled when Kiran fell asleep?

Answers

Answer:

380 miles

Step-by-step explanation:

First, find 62% of 1,000:

1,000 • .62 = 620 miles

Next, subtract 620 from 1,000:

1,000 - 620 = 380 miles

The family had traveled 380 miles before Kiran fell asleep

(need help fast)
Which of the following is an open statement?

A)

An angle that measures 95° is an obtuse angle.

B)

An angle that measures 95° is an acute angle.

C)

An angle that measures 40° is an acute angle.

D)

∠XYZ is an acute angle.

Answers

Answer:

D) is the right answer.

Hope it helps!

Thanks!

Answer:

I believe the correct answer is C) An angle that measures 40° is an acute angle. I'm not 100% sure if this is the correct answer.

plss help me il mark you brainly

Answers

Answer:

thisl give u extra credit: 2.29*20 = 45.80 and 3.49*35 = 122.15.

Step-by-step explanation:

Answer:

1. 78.54 (area)

2. 25.13 (circumference)

3. 4.5 (radius)

4. 13 (diameter)

Step-by-step explanation:

1. Carlos tiene un terreno de 30.000 m2, él
vende 3/5 del total del terreno y recibe por
la venta $27.000.000.000; en 1/3 del
terreno restante va a construir una piscina
que tiene de profundidad desde 1,2 metros
hasta 1,8 m en forma descendente; en el
resto del terreno va a construir una casa.
De la información, se puede decir que Carlos
vendió cada m2 por un valor de
A. $1.500.000
B. $1.800.000
C. $2.100.000
D. $2.400.000
PROCEDIMIENTO:

Answers

Answer:

d)şıtkı abi nasıl bilemesin

La opción correcta es A. Carlos vendió cada m2 a $1.500.000.

Dado que Carlos tiene un terreno de 30.000 m2, y vendió 3/5 del total del terreno y recibió por la venta $27.000.000.000; para determinar el valor en que Carlos vendió cada m2 se debe realizar el siguiente cálculo:

27.000.000.000 / (30.000 x 3/5) = X27.000.000.000 / 18.000 = X1.500.000 = X

Por lo tanto, Carlos vendió cada m2 a $1.500.000.

Aprende más en https://brainly.com/question/9283173

14 = -2s -8
Solve for s

Answers

Answer:

s = -11

Step-by-step explanation:

14 = -2s - 8

22 = -2s

2s = -22

s = -11

14= -2s -8

+8 +8 Add 8 to both sides to isolate -2s

22= -2s

--- ----

-2 -2 Divide -2 by both sides

-11=s This is the answer.

properties of rectangle
and your free fire id

Answers

Answer:

i am not play free fire

muje school dhyan nahi ate eseleye

Please help. I don’t know what to do.

Answers

Answer:

83

Step-by-step explanation:

The sum of the interior angles of any closed figure will always equal 360º, so what you need to do is add:

109+90+78=?

This will in turn give you 277.

Subtract 277 from 360, and boom, 83 degrees.

What is the quotient of 9−x^2 divided by 3x and x^2+6x+9 divided by 3x?

Answers

Answer:

44 rem

Step-by-step explanation:

Sorry i dont have an explanation

plato de Leonardo tiene 0.2 kg de arroz y el de su hermana Leticia tiene 0.3 kg si quieren que los dos tengan lo mismo y los juntan para después repartirse los en partes iguales cuánto tendrá cada plato​

Answers

Answer:

0.5 kg

Step-by-step explanation:

estimate the difference
7 3/4 subtracted by 2 2/5
show your work

Answers

7 3/4 - 2 2/5
(7-2)+(3/4-2/5)
5+7/20

5 and 7/20 or 5.35

Answer:

5 7/20

Step-by-step explanation:

basically, you are going to want to turn these into improper fractions

7 3/4 = 28/4 + 3/4

        = 31/4  (no further simplification)

2 2/5 = 10/5 + 2/5

         = 12/5

now get common denominator to subtract

31/4 - 12/5

155/20 - 48/20 = 107/20

if you want this back into mixed fraction then convert

107/20 = 5 7/20

If someone can help that would be great

Answers

Answer:

x = 16

Step-by-step explanation:

For the triangle to be isosceles then AB = CB , that is

5x - 9 = 4x + 7 ( subtract 4x from both sides )

x - 9 = 7 ( add 9 to both sides )

x = 16

write : what’s the algebraic expression for the difference of 9 and x

Answers

Answer:

9-x

Step-by-step explanation:

ez dub

Answer:

9-x

Step-by-step explanation:

the difference of (tells you to subtract) 9 and x (9-x)

hope this helps have a blessed

Given g(x) = -5x+ 2, find g(4).
Answer:

Answers

Answer:

-18

Step-by-step explanation:

g(x)=-5x+2

g(4)=-5(4)+2=-20+2=-18

Answer:

-18

Step-by-step explanation:

Mr. Scott is planning a party for 78 people. Each table seats 8 people. He divides to find the number of tables he needs to seat everyone
9r6
878
-72
6

Answers

What is the equation

a x + b y is equal to 12​

Answers

Answer:

y= -a*x + 12

b b

Step-by-step explanation:

ax+by=12 (subtract "ax" from both sides so that the one on the left will become zero and we will have "by" )

by= -ax+12(divide both side by "by" so that we will have the equation as "y=mx+b")

finally the result will be:

y= -a*x + 12

b b

Help, I'm bad at math XD

Answers

1. x = 28

2. x = 13

3. x = 11

4. x = 50

5. x = 53

6. x = 77

7. x = 5

8. x = 70

Write the equation of the line in slope-intercept form given:

m = 3/7 through (-7, 7)

Answers

Answer:

y=3/7x+10

Step-by-step explanation:

y-y1=m(x-x1)

y-7=3/7(x-(-7))

y-7=3/7(x+7)

y=3/7x+21/7+7

y=3/7x+3+7

y=3/7x+10

Farias car is worth 22000. Of the value of the car decreases by 8% what will her car be worth next year?

Answers

Answer:

$17600

Step-by-step explanation:

Which equation is the result of adding theses two equations -2x+4y=17 3x-10y=-3

Answers

Answer:

x=-79/4, y=-45/8. (-79/4, -45/8).

Step-by-step explanation:

-2x+4y=17

3x-10y=-3

---------------

3(-2x+4y)=3(17)

2(3x-10y)=2(-3)

----------------------

-6x+12y=51

6x-20y=-6

------------------

-8y=45

y=45/-8=-45/8

3x-10(-45/8)=-3

3x+450/8=-3

3x+225/4=-3

3x=-3-225/4

3x=-12/4-225/4

3x=-237/4

x=(-237/4)/3

x=(-237/4)(1/3)

x=-237/12=-79/4

Solve for x
x^2 - 7x + 10 = 0​

Answers

Answer:

Step-by-step explanation:

x²-7x+10=0

(x-2)(x-5)=0

x=2 or x=5

Answer:

Step-by-step explanation:

x2−7x+10=0

Step 1: Factor left side of equation.

(x−2)(x−5)=0

Step 2: Set factors equal to 0.

x−2=0 or x−5=0

x=2 or x=5

(You can confirm this by plugging in the numbers yourself)

3x-4y=-14 6x+3y=27 don’t understand how to solve

Answers

tama Ang kanyang sagot

​Triangles ABC​ and DFG are similar.

Which proportion can be used to find the value of DG¯¯¯¯¯¯?


a 15/7=5/DG

b DG/15=5/7

c 5/7=15/DG

d 5/DG=15/6
Two triangles A B C and D F G. A B is 5 inches. B C is 6 inches. A C is 7 inches. D F is 15 inches. F G is 18 inches. Angle B is congruent to angle F.

Answers

Answer:

C

Step-by-step explanation:

Since every side of ΔABC is dilated by 3, or triple the size

We multiply every length of ΔABC by 3

But the length of DF and FG are already done for us but DG is not, which is essential to finding the answer

7 x 3 = 21

DG = 21

5/7 = 15/21

5 ÷ 7 = 0.71

15/21 = 0.71

5/7 = 15/21

Value of [tex]\boldsymbol{DG}[/tex] in a triangle [tex]DFG[/tex] is equal to [tex]\boldsymbol{21}[/tex] inches. To understand the calculations, check below.

Define similar triangles.

Two triangles are said to be similar if their sides are proportional and their angles are equal.

Triangles [tex]ABC,DFG[/tex] are similar

[tex]\frac{AB}{DF}=\frac{BC}{FG}=\frac{AC}{DG}[/tex]

[tex]\frac{5}{15}=\frac{7}{DG}[/tex]

[tex]DG=21[/tex] inches

So, value of [tex]DG[/tex] is equal to [tex]\boldsymbol{21}[/tex] inches

Find out more information about triangle here:

https://brainly.com/question/2773823?referrer=searchResults

Lorenzo's lovely lamp land buys a lava lamp for $24. They sell the lamp to the end customer for $50.40. What is the markup percent?

Answers

Answer:

110%

Step-by-step explanation:

100%->24

1%-> 0.24

50.40 -24 = 26.40

26.40÷0.24=110%

Please help quick will give brainliest!

Answers

Answer:

The statement that correctly uses limits to determine the end behavior of f(x) is;

[tex]\lim\limits_{x \to \pm \infty} \dfrac{7 \cdot x^2+ x + 1}{x^4 + 1}= \lim\limits_{x \to \pm \infty} \dfrac{7 }{x^2 }[/tex] so the end behavior of the function is that as x → ±∞, f(x) → 0

Step-by-step explanation:

The given function is presented here as follows;

[tex]f(x) = \dfrac{7 \cdot x^2+ x + 1}{x^4 + 1}[/tex]

The limit of the function is presented as follows;

[tex]\lim\limits_{x \to \pm \infty} \dfrac{7 \cdot x^2+ x + 1}{x^4 + 1}[/tex]

Dividing the terms by x², we have;

[tex]\lim\limits_{x \to \pm \infty} \dfrac{\dfrac{7 \cdot x^2}{x^2} + \dfrac{x}{x^2} + \dfrac{1}{x^2} }{\dfrac{x^4}{x^2} +\dfrac{1}{x^2} }= \lim\limits_{x \to \pm \infty} \dfrac{7 + \dfrac{1}{x} + \dfrac{1}{x^2} }{x^2 +\dfrac{1}{x^2} }[/tex]

As 'x' tends to ±∞, we have;

[tex]\lim\limits_{x \to \pm \infty} \dfrac{7 + \dfrac{1}{x} + \dfrac{1}{x^2} }{x^2 +\dfrac{1}{x^2} } = \lim\limits_{x \to \pm \infty} \dfrac{7 + 0 + 0 }{x^2 +0 } = \lim\limits_{x \to \pm \infty} \dfrac{7 }{x^2 }[/tex]

However, we have that the end behavior of 7/x² as 'x' tends to ±∞ is 7/x² tends to 0;

Therefore, we have;

[tex]f(x) \rightarrow 0 \ as \lim\limits_{x \to \pm \infty} \dfrac{7 }{x^2 }[/tex]

The statement that correctly uses limits to determine the end behavior of f(x) is therefor given as follows;

[tex]\lim\limits_{x \to \pm \infty} \dfrac{7 \cdot x^2+ x + 1}{x^4 + 1}= \lim\limits_{x \to \pm \infty} \dfrac{7 }{x^2 }[/tex] so the end behavior of the function is that as x → ±∞, f(x) → 0.

Find the area of the regular octagon.

Answers

Answer:

3*4

=12 sq. cm

= 12 cm²

Answer:

48cm^{2}

Step-by-step explanation:

[tex]A=4ah=4*4*3=48 cm^{2}[/tex]

An observer (O) spots a plane flying at a 42° angle to his horizontal line of sight. If the plane is flying at an altitude of 15,000 feet, what is the distance (x) from the plane (P) to the observer (O)?

A right triangle is shown with angle O marked 42 degrees, hypotenuse marked x, and height marked 15,000 feet.

10,035 feet
16,648 feet
20,188 feet
22,417 feet

Answers

Answer:

22,417

Step-by-step explanation:

Just took the test.

Pythagoras theorem states that for a right angle triangle the square of the hypotenuse is equal to the sum of the other two sides of the plane. The distance (x) from the plane (P) to the observer (O) is 22417.75 feet.

Given information-

The observer angle to the plane is 42 degrees.

The height of the plane is 15000 feet.

As angle O is 42 degree and the height is 15000. Let suppose the base is y feet long. Thus angle O can be given as,

[tex]\begin{aligned} \tan42^o&=\dfrac{15000}{y} \\ y&=\dfrac{15000}{\tan42^o} \\ y&=16660\\ \end[/tex]

Thus the base of the right triangle is 16660 feet.

Pythagoras theorem

Pythagoras theorem states that for a right angle triangle the square of the hypotenuse is equal to the sum of the other two sides of the plane.

For the given problem the  the hypotenuse side is x feet.

[tex]\begin{aligned}\\ x^2&=15000^2+16660^2\\ x&=22417.75\\ \end[/tex]

Thus the distance (x) from the plane (P) to the observer (O) is 22417.75 feet.

Learn more about the Pythagoras theorem here;

https://brainly.com/question/343682

(2a^(3)-a^(2)b)/(36b^(2))-:(2a-b)/(9b^(2))


Domain?

Answers

-3a3b - 40a2b2 + 8a2 - 30ab3 - 28ab - 36b2

                     4    

i looked it up

find the sum −10t−7−10t−7

Answers

Answer:

-20t-14

Step-by-step explanation:

-10t-10t= -20t

-7-7= -14

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