For the geometric series 2 + 6 + 18 + 54 + ... , find S8

Answers

Answer 1

Answer:

[tex]\displaystyle S_{8}=6560[/tex]

Step-by-step explanation:

We have the geometric sequence:

2, 6, 18, 54 ...

And we want to find S8, or the sum of the first eight terms.

The sum of a geometric series is given by:

[tex]\displaystyle S=\frac{a(r^n-1)}{r-1}[/tex]

Where n is the number of terms, a is the first term, and r is the common ratio.

From our sequence, we can see that the first term a is 2.

The common ratio is 3 as each subsequent term is thrice the previous term.

And the number of terms n is 8.

Substitute:

[tex]\displaystyle S_8=\frac{2((3)^{8}-1)}{(3)-1}[/tex]

And evaluate. Hence:

[tex]\displaystyle S_8=6560[/tex]

The sum of the first eight terms is 6560.

Answer 2

Answer:

S₈ = 6560

Step-by-step explanation:

The sum to n terms of a geometric sequence is

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

where a is the first term and r the common ratio

Here a = 2 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{6}{2}[/tex] = 3 , then

S₈ = [tex]\frac{2(3^{8}-1) }{3-1}[/tex]

    = [tex]\frac{2(6561-1)}{2}[/tex]

    = 6561 - 1

    = 6560


Related Questions

Simplify (3 1/2+7)divided by (4 1/3-3)

Answers

Answer:

63/8

Step-by-step explanation:

3 1/2 = 7/2

4 1/3 = 13/3

[tex] \frac{ \frac{7}{2} + 7 }{ \frac{13}{3} - 3} [/tex]

[tex] = \frac{ \frac{21}{7} }{ \frac{4}{3} } [/tex]

[tex] = \frac{63}{8} [/tex]

31. Which inequality is represented by
this graph?


Answers

Answer:

A. x/5 - 6 > -4

Step-by-step explanation:

The graph shows that x > 10. We need to solve each of the inequalities. After we do, we see that A is the answer.

A. x/5 - 6 > -4

x/5 > 2

x > 10

Phương trình (m + 2)x2 – 2mx + 1 = 0 là phương trình bậc hai khi:
A. m ≠ 1. B. m ≠ -2. C. m ≠ 0. D. mọi giá trị của m.

Answers

B::: m ≠ -2.............

there are 32 students in a class and 20 of them own at least one pet what fraction of the class own pets

Answers

HOPE IT HELPS

PLEASE MARK BRAINLIEST

The fraction of the class that owns pets is 20/32, which can be simplified to 5/8.

To find the fraction of the class that owns pets, we divide the number of students who own pets by the total number of students in the class.

A fraction is a mathematical representation of a part-to-whole relationship. It is expressed as a numerical quantity written in the form of one number (the numerator) divided by another number (the denominator), separated by a horizontal line or slash (/).

The numerator represents the number of parts being considered or counted, while the denominator represents the total number of equal parts that make up the whole. Fractions can be used to describe a portion or share of something, as well as to compare quantities or perform mathematical operations.

Number of students who own pets: 20

Total number of students in the class: 32

Therefore, the fraction of the class that owns pets is 20/32, which can be simplified to 5/8.

To know more about  fraction , here

https://brainly.com/question/30154928

#SPJ2

Suppose a study finds that the correlation coefficient relating job satisfaction to salary is r=1. Which of the following are the proper conclusions?
I. High salary causes high job satisfaction.
II. Low salary causes low job satisfaction.
III. There is a very strong association between salary and job satisfaction.


I and II only

I, II and III

III only

I only

Answers

Answer:

its I, II and III.

Step-by-step explanation:

r values are from -1 to 1, if the value is 0 means there's no connection between values of variables, if its lower than 0, if the value of variable goes up the other goes down, if its higher than 0, than if one value of variable increases than the value of other variable increases too. the closer to 1 the stronger the association.

ever since Anthony started going to the gym 4 days per week he has been taking protein he wants to take every day to help build muscle. How many grams of protein does Anthony take for the entire day (100%)

Answers

Answer:

how much protein did he take per day tho?

What is the surface area ,in square meters of the toy box

Answers

Answer:426m^2

Step-by-step explanation:

I need help by 9:30!!! Please help! I would GREATLY appreciate it!!!!!
I have two questions:
1. Which is larger: a or -a
if a > 0 = a___-a
if a = 0. = a___-a
if a < 0 = a___-a

2. Which is larger: 1/a or 1/2a
if a > 0 = 1/a___1/2a
if a < 0 = 1/a___1/2a

Answers

Answer:

1. a>-a

EXAMPLE: 5>-5

2. a=-a

3. a<-a

EXAMPLE: -3<--3 = -3<3

Step-by-step explanation:

A line passes through the point (-3,6) and is parallel to the line with the equation y=
- 4x + 5. What's the equation of the line?

Answers

Answer:

y=-4x-6

Step-by-step explanation:

y=-4x+5  m1=-4

m1=m2=-4 (the number near x is equal for the line and the searched line)

y=m2x+b

6=-4(-3)+b

b=-6

y=-4x-6

Help me!!! Please to solve this problem of o. Math

a) Given a function f(x) = 2x + 3. Find (a) f(1), (b) f(-5), (c) f(a), (d) f(a + 2) (e) f(b)?

b) let f(x) = x + 4 define a function in the closed interval of -55x55, find f(-2), f(3) and f(7). ​

Answers

a:-

f(x)=2x+3

[tex]\\ \rm\Rrightarrow f(1)=2(1)+3=2+3=5[/tex]

[tex]\\ \rm\Rrightarrow f(-5)=2(-5)+3=-10+3=-7[/tex]

[tex]\\ \rm\Rrightarrow f(a)=2a+3[/tex]

[tex]\\ \rm\Rrightarrow f(a+2)=2(a+2)+3=2a+4+3=2a+7[/tex]

[tex]\\ \rm\Rrightarrow f(b)=2b+3[/tex]

b:-

f(x)=x+4

[tex]\\ \rm\Rrightarrow f(-2)=(-2)+4=2[/tex]

[tex]\\ \rm\Rrightarrow f(3)=3+4=7[/tex]

[tex]\\ \rm\Rrightarrow f(7)=7+4=11[/tex]

Step-by-step explanation:

[tex]thank \: you[/tex]

please help me
I need help

Answers

What would you like me to help you with?

What is the value of x in the equation
3x - y = 30, when y = 15?

Answers

Answer:

x = 15

Step-by-step explanation:

3x - y = 30

Given;

y = 15

To find;

value of 'x'

Putting the value of y in the given equation;

3x - 15 = 30

3x = 30 + 15

3x = 45

x = 45/3

x = 15

Answer:

x = 15

Step-by-step explanation:

3x - y = 30let y = 153x - 15 = 303x = 30 + 153x = 45x = 45/3x = 15Let's check:3x - y = 303(15) - 15 = 3045 - 15 = 3030 = 30

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Will Mark Brainlest Help Please Please ​

Answers

[tex]\\ \sf\longmapsto \left[{3a+b\atop a-b}\:\:\:{3c-d\atop a+b+d}\right]=\left[{3\atop 5}\:\:\;{6\atop 2d-1}\right][/tex]

Now constructing equations

[tex]\\ \sf\longmapsto 3a+b=3\dots(1)[/tex]

[tex]\\ \sf\longmapsto a-b=5\dots(2)[/tex]

[tex]\\ \sf\longmapsto 3c-d=6\dots(3)[/tex]

[tex]\\ \sf\longmapsto a+b+d=2d-1\dots(4)[/tex]

Adding eq(1) and (2)

[tex]\\ \sf\longmapsto 4a=8[/tex]

[tex]\\ \sf\longmapsto a=\dfrac{8}{4}[/tex]

[tex]\\ \bf\longmapsto a=2[/tex]

Put the value in eq(2)

[tex]\\ \sf\longmapsto a-b=5[/tex]

[tex]\\ \sf\longmapsto b=a-5[/tex]

[tex]\\ \sf\longmapsto b=2-5[/tex]

[tex]\\ \bf\longmapsto b=-3[/tex]

put the values in eq(4)

[tex]\\ \sf\longmapsto a+b+d=2d-1[/tex]

[tex]\\ \sf\longmapsto 2+(-3)+d=2d-1[/tex]

[tex]\\ \sf\longmapsto d-1=2d-1[/tex]

[tex]\\ \sf\longmapsto d-2d=-1+1[/tex]

[tex]\\ \sf\longmapsto -d=0[/tex]

[tex]\\ \bf\longmapsto d=0[/tex]

Put the value in eq(3)

[tex]\\ \sf\longmapsto 3c-d=6[/tex]

[tex]\\ \sf\longmapsto 3c-0=6[/tex]

[tex]\\ \sf\longmapsto 3c=6+0[/tex]

[tex]\\ \sf\longmapsto 3c=6[/tex]

[tex]\\ \sf\longmapsto c=\dfrac{6}{3}[/tex]

[tex]\\ \sf\longmapsto c=2[/tex]

En un cine que hay 550 personas, el 30% va a ver una película de terror, el 25% va a ver una novela, el restante va a ver una pelicula de ciencia ficcion ¿ cuantas personas van a ver cada pelicula?

POR FAVOR AYUDENMEN!!!!

Answers

Answer:

165 ver una pelicula de terror, 137.5 (138) ver una novela, y 247 ver una pelicula de ciencia ficcion.

Step-by-step explanation:

0.3 x 550 = 165

0.25 x 550 = 137.5 --> 138

165 + 138 = 303

550 - 303 = 247

Help please !!!!!!!!!!

Answers

Answer:

D

Step-by-step explanation:

A function means that each input value (in this case, x) has only one output value (y). The vertical line test states that if a vertical line intersects with the relation more than once, it is not a function. Therefore, as a vertical line at x=0 intersects with the graph twice, the graph fails the vertical line test

On a recent math test, Samantha scored 3 points for each of the 18 multiple choice questions she
answered correctly and 5 points for each of the 6 short response questions she answered
correctly.
She scored an additional 4 points for the bonus question. Write an expression for her total score on
the test and then find her score.

Answers

The required expression will therefore be:

(3×18) + (5×6) + 4

Her total score is 88points :

From the question given, we are told that Samantha scored 3 points for each of 18 multiple choice questions, this means that the total points made here is expressed as:

(3 × 18) ...1

If she got 5 points for each of the 6 short response questions she answered

correctly, the total point made will be expressed as;

(5×6) ... 2

Total score for an additional 4 points for the bonus question will be "4"

Expression for her total score will be the sum of all the expression above as thus:

(3×18) + (5×6) + 4

Taking the sum, her score will be:

= (3×18) + (5×6) + 4

= 54 + 30 + 4

= 84 + 4

= 88 points

The required expression will therefore be:

(3×18) + (5×6) + 4

Her total score is 88points

Learn more about sum here: https://brainly.com/question/16397188

Assume f(x) = 2x – 3 and g(x) = 5 - 2x. Find
оооо
A.5 - 2x
2х - 3
B.-8
5
C.3
5
D.2x – 3
5 - 2x

Answers

Answer: The chosen topic is not meant for use with this type of problem. Try the examples below.

x

=

2

,

y

=

1

x

=

9

,

y

=

10

x

=

9

,

y

=

4

m=8+n
PLZ HELP ASAP, WILL MARK BRAINLIEST!!!

Answers

[tex]\\ \qquad\quad\sf\longmapsto m=8+n[/tex]

Take n to left

[tex]\\ \qquad\quad\sf\longmapsto m-n=8[/tex]

Hence

if m=1

[tex]\\ \qquad\quad\sf\longmapsto n=m-8=1-8=-7[/tex]

if n=1

[tex]\\ \qquad\quad\sf\longmapsto m=8+1[/tex]

[tex]\\ \qquad\quad\sf\longmapsto m=9[/tex]


Can someone help me pleasee

Answers

Multiply both the powers.
2*3=6

So it’s 3x^6

Answer:

it's 9x^6.

hope it may help you

Help please anyone please

Answers

Welp....there's your answer

Rearrange each of the following in slope/y-intercept form, y = mx + b.
a. 3x - 6y + 8 = 0 b. -2x - 5y - 2 = 0

Answers

Answer:

a.

[tex]{ \tt{3x - 6y + 8 = 0}} \\ { \tt{ 6y = 3x - 8}} \\ { \boxed{ \bf{y = \frac{1}{2} x - \frac{4}{3} }}}[/tex]

b.

[tex]{ \tt{ - 2x - 5y - 2 = 0}} \\ { \tt{5y = - 2x + 2}} \\ { \boxed{ \bf{y = - \frac{ 2}{5} x + \frac{2}{5} }}}[/tex]

ndicate whether each of the following relationships is usually a direct relationship or an inverse relationship. a. A sports team's winning percentage and attendance at its home games: (Click to select) . b. Higher temperatures and sweater sales: (Click to select) . c. A person's income and how often he or she shops at discount stores: (Click to select) . d. Higher gasoline prices and miles driven in automobiles: (Click to select) .

Answers

Answer:

Following are the responses to the given question:

Step-by-step explanation:

The following relationships usually have a direct or inverse relationship, please indicate.

Win percentage and attendance during home games of a sports franchise are directly related.There is an inverse relationship between higher temperatures with sweater sales.An inverse link exists between a family's salary and how often he or she spends in bargain shops.There was an inverse relationship between higher gas prices and more miles traveled.

What is the expression for “the difference between four times a number and three times that number”???

Answers

Answer:

B

Step-by-step explanation:

The correct equation will be 4N-3N

express 5√72 in simplest radical form.

Answers

Answer:

30*sqrt(2)

Step-by-step explanation:

5*sqrt(72)=5*sqrt(36*2)=5*6*sqrt(2)=30*sqrt(2)

Pls help ASAP! Have to be done with school before I leave for work

Answers

Answer:

M = (-4, -5)

Step-by-step explanation:

M = (-2-6)/2 , (-10+0)/2

M = -8/2 , -10/2

M = (-4, -5)

Answer:

(-4, -5)

Step-by-step explanation:

x1 = -2 ,x2 =-6, y1= -10, y2=0

(-2-6/2 ,-10+0/2)

(-8/2, -10/2)

(-4,-5)

The mason will build a wall that uses 36 bricks in each row. The wall will be 140 rows high. Each brick weighs 4 pounds. What is the total weight of all the bricks?

Answers

Answer:

20,160 pounds

Step-by-step explanation:

bricks in each row * number of rows * pound of each brick

Answer:

20160 lbs

Step-by-step explanation:

To find the amount of bricks, multiply 36 by 140 which equals 5040. Then, multiply 5040 by the weight: 4. 5040×4=20160

what is answer guys
[tex]2x(x + 1) + 1(x + 1)[/tex]

Answers

Step-by-step explanation:

ᵉᵃˢʸ ᵖᵉᵃˢʸ

2x²+2x+x+1

2x²+3x+1

2x^2 + 3x + 1 (by simplification method)

Need an explanation

Answers

Answer: Choice B

[tex](6\sqrt{5}+5)i[/tex]

==========================================================

Work Shown:

[tex]\sqrt{-5}+\sqrt{-25}+\sqrt{-125}\\\\\sqrt{-1*5}+\sqrt{-1*25}+\sqrt{-1*25*5}\\\\\sqrt{-1}*\sqrt{5}+\sqrt{-1}*\sqrt{25}+\sqrt{-1}*\sqrt{25}*\sqrt{5}\\\\i*\sqrt{5}+i*5+i*5*\sqrt{5}\\\\i*\sqrt{5}+5i+5i*\sqrt{5}\\\\(i\sqrt{5}+5i*\sqrt{5})+5i\\\\(\sqrt{5}+5\sqrt{5})i+5i\\\\(6\sqrt{5})i+5i\\\\(6\sqrt{5}+5)i\\\\[/tex]

This points us to answer choice B

could someone explain how to figure this out (marking brainliest to the most helpful answer) I will report fakes.

Answers

I believe the answer is A.

Remember that in order to find the slope, we use the slope formula.

The slope formula is: rise/run

Triangle A: 3/4
Triangle B: 4/3
Triangle C: 9/16
Triangle D: 8/12
A because triangle a= 3/4

Which of the following questions are true? Select two that apply.

Answers

Answer: A and C

Step-by-step explanation:

The other choices aren't correct because

B. [tex]x^{\frac{4}{5} } =\sqrt[5 ]{x^{4}}[/tex]D. [tex](\sqrt{x^{3} } )^{8}=(x^{\frac{3}{2} } )^{8}=x^{\frac{24}{2} } =x^{12}[/tex]
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