.Prove a+ar+ar2+………+arn-1=a(rn -1 ) r-1

Answers

Answer 1

Answer:

See below.

Step-by-step explanation:

Call the sum of the first n terms S.

S = a + ar + ar^2 + ar^3 + ... + ar^(n -1)

Multiply both sides by r.

Sr = ar + ar^2 + ar^3 + ar^4 + ... + ar^n

No subtract S - Sr.

      S =  a + ar + ar^2 + ar^3 + ar^4 + ... + ar^(n -1)

(-)    Sr =       ar + ar^2 + ar^3 + ar^4 + ... + ar^(n - 1) + ar^n

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

  S - Sr = a - ar^n

S(1 - r) = a(1 - r^n)

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

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

a + ar + ar^2 + ar^3 + ... + ar^(n -1) = a(r^n - 1)/(r - 1)


Related Questions

Find the value of x and found to the nearest degree help ASAP

Answers

Answer:

22

Step-by-step explanation:

sin(X) = perpendicular/base

sin(X) = 7/19

X=arcsin(7/19)=22

cho f(t)=(t-4)u(t-2)phep bien doi laplace la
F(s)=e^-2s/s^2-2e^-2s/s62

Answers

Step-by-step explanation:

cho f(t)=(t-4)u(t-2)phep bien doi laplace la

F(s)=e^-2s/s^2-2e^-2s/s62

SEE QUESTION IN IMAGE

Answers

Answer:

See below

Step-by-step explanation:

(b)

The table is attached

(i)

The graph is attached

(ii)

(a) Cumulative frequency is 500, median is at 249, 250, the horizontal line from point 250 on y-axis intersecting the graph at approximately 52%, this is the median

(b)  Vertical line from the 45% mark intersects the graph at approximately 177th point. The number of candidates passed the test:

500 - 177 = 323

(iii) P(pass) = 323/500 = 0.626 or 62.6%

a, 0,03m3=............ dm3=...........cm3

Answers

Answer:

0.03 m³ = 30 dm³ = 30000 cm³

O.03m3=30dm
0.03m3=30000000cm3

Find the area of given figure: 6cm 2cm 3cm 1cm​

Answers

Answer:

12cm²

Step-by-step explanation:

separate it to two parts, rect and square

rect- 3cm×1cm =3cm²

square- 3cm×3cm =9cm²

then, 3cm²+9cm²=12cm²

The answer to the question is 12.

The polygons in each pair are similar. find the missing side length​

Answers

If both are similar ratio of sides will be same

[tex]\\ \sf\longmapsto \frac{x}{25} = \frac{7}{5} \\ \\ \sf\longmapsto 5x = 7 \times 25 \\ \\ \sf\longmapsto 5x = 175 \\ \\ \sf\longmapsto x = \frac{175}{5} \\ \\ \sf\longmapsto x = 35[/tex]

tìm tất cả giá trị thực của tham số m để đồ thị hàm số y=x³-mx²+4 cắt trục hoành tại ba điểm phân biệt

Answers

Answer:

실례합니다?

Step-by-step explanation:

질문이 뭔가요??? 이해가 안가요? 어느 언어?

what is percent of a number

Answers

Step-by-step explanation:

a fraction of a number out of 100%

Answer and step-by-step explanation:

Percent (%) means per 100

A percentage is a number or ratio expressed as a fraction of 100

Example 50% of 8 = 8*50/100 = 4

find the third proportional of 3 5 7

Answers

Answer: Third proportion is 21/5.

Step-by-step explanation:

Let the proportion be x

so,

3:5:x:7

so

3:5 = x:7

or, 3/5 = x/7

or, 21 = 5x

or, x = 21/5

A water butt contains 512.6
liters of water when full. It is
80% full. Daniel is using a
small bucket to empty the
butt. The bucket holds
525ml of water. How many
small buckets can be
completely filled by the water in the butt?

Answers

Answer:

u can solve ur self but let me help you

Step-by-step explanation:

simply:subtract 525ml from 512.6 liters

Find the exact value of the indicated trigonometric function for the acute angle a:
Given: sin a=5/13, Find: cos a and tan a

Answers

Answer:

cos a = 12/13

tan a = 5/12

You use these properties to solve the question,

sin²a+cos²a=1

tana=sina/cosa

Can someone please help?

Answers

Answer:

1.

C. 6561 is the answer that the table represents

Answer:

B

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a, b ] = [ 8, 9 ] , then

Continuing the table from x = 6 , multiplying values of y by 3

x     y

6   729

7  2187  

8  6561

9  19683

f(b) = f(9) = 19683

f(a) = f(8) = 6561

average rate of change = [tex]\frac{19683-6561}{9-8}[/tex] = [tex]\frac{13122}{1}[/tex] = 13122 → B

What is the answer if 202^2 base3 - 112^2 base3?

Answers

Answer:

Hello,

answer is 204 in base 10 or 21120 in base 3

Step-by-step explanation:

[tex]((202)_3)^2=(202*202)_3=(112211)_3\\\\((112)_3)^2=(112*112)_3=(21021)_3\\\\(112211-21021)_3=(211120)_3=(204)_{10}\\\\\\\\\\Other\ way\\\\((202)_3)^2=((20)_{10})^2=(400)_{10}\\\\((112)_3)^2=((14)_{10})^2=(196)_{10}\\\\(400-196)_{10}=(204)_{10}=(21120)_3[/tex]

repost , can someone help asap!

Answers

Answer:

y = -3/4x + 3

Step-by-step explanation:

Solve the quadratic equation by factoring

Answers

Answer:

6(5m-2)(7m+8)=0

1). 210m^2+156m-96=0

2). 35m^2+26x-16

3). 35m^2+40m-14m-16

4). (35m^2+40m)+(-14m-16)

5). 5m(7m+8)-2(7m+8)

6). (5m-2)(7m+8)

7.) m= 2/5, -8/7

On the 2nd step I divided 6 on both sides.

three consecutive even numbers add up to 105 determine the product of the three numbers​

Answers

Answer:

34 + 35 + 36 = 105

Step-by-step explanation:

there are 160 girls and 240 boys in a school
i. find the percent of girls in the school
ii. find the percent of boys in the school.​

Answers

Answer:

girls = 40%

boys = 60%

Step-by-step explanation:

Girls = 160

boys = 240

total students = 160+240

= 400

so,

percent of girls = (160/400)×100%

= (2/5)×100%

= 2×20%

= 40%

so,

percent of boys = 100% - 40%

= 60%

What is the equation of the line that passes through (-12,6) and (-6,1)?

Answers

To find the equation, find the slope. To find the slope find the change in y/ change in x.

(1-6)/(-6+12)= -5/6

Then use the equation, y=mx+b, to solve for y int. First, substitute the slope in for m, and then choose a coordinate to substitute for y and x.

1=-5/6(-6)+b
1=5+b
-4=b

y=-5/6x-4 is the equation of the line.


Tìm nghiệm của đa thức sau:2x mũ 2-5x-3

Answers

bạn tham khảo cách này nha

Find the area of the shaded regions:

Answers

Answer:

18[tex]\pi[/tex]

[tex]\frac{80}{360} * 81 \pi[/tex]

Step-by-step explanation:

PLEASE HELP DUE IN 15 MNUTES MARKING BRAINLIEST AND 15 POINTS YOU DONT HAVE TO EXPLAIN MUCH

Answers

Answer:

see below

Step-by-step explanation:

11a   -2(x^2 -3)

Distribute

-2*x^2 -2(-3)

-2x^2 +6

11b  2x(x+4)

 Distribute

2x*x +2x*4

2x^2 +8x

12 The perimeter is the sum of all sides

The top is equal to the bottom and the left side is equal to the right

x-10 + x+20+x-10+x+20

Combine like terms

4x +20

Find the missing side. Round to the nearest tenth

Answers

We know

[tex]\boxed{\sf cos\theta=\dfrac{Base}{Hypotenuse}}[/tex]

[tex]\\ \sf\longmapsto cos59=\dfrac{x}{28}[/tex]

[tex]\\ \sf\longmapsto 0.5=\dfrac{x}{28}[/tex]

[tex]\\ \sf\longmapsto x=28\times 0.5[/tex]

[tex]\\ \sf\longmapsto x\approx 14[/tex]

Answer:

[tex]x = 14[/tex]

Step-by-step explanation:

[tex] \cos( \theta) = \frac{a}{h} \\ \cos(59) = \frac{x}{28} \\ 0.5 \times 28 = x \\ 14 = x[/tex]

What is the domain of the given function? {x | x = -6, -1,0,3}, { y | y = -7,-2,1,9}, {x | x = -7, -6, -2, -1, 0, 1, 3 , 9}, { y | y = -7, -6 , -2 , -1 , 0 , 1 , 3 , 9}

Answers

Answer:

domain = {-6,-7,-7,-7}

Answer is Indians onyl answer kindergarten level super simple questions

Can someone please explain how to do this? You don't have to answer the questions but If you can give me an explanation/formula to solve. it would help me a lot thank you. marking brainliest when I can.

Answers

Answer:

a. The 1's are heavier than the x's. There isn't a whole number on top of the x's.

b. The equation would be 2x<9 because the 9 is greater(heavier) than the 2x. To continue to solve you would divide 2 by both sides. That would turn into x<9/2.

Step-by-step explanation:

Which of the following is the inverse of F(x) = -2x + 3?

Answers

Answer:

D

Step-by-step explanation:

y=-2x+3

y-3=-2x, x=(3-y)/2. f^(-1) (x) = (3-x)/2. The equation is (3/2)-x/2.

Answer:

c

Step-by-step explanation:

SEE QUESTION IN IMAGE

Answers

Answer:

1.54

Step-by-step explanation:

First, we can take into account that mean = sum / number of students. Therefore, we can find the sum of each group of students, as

1.67 = sum / 20

1.50 = sum / 16

1.40 = sum / 14

Multiplying each equation by the number of students in the group to isolate the sum, we get

1.67 * 20 = 33.4

1.50 * 16 = 24

1.40 * 14 = 19.6

We can sum these up to get the total sum of all three groups of students, resulting in

33.4 + 24 + 19.6 = 77

As mean = sum / number of students, we can say that

total mean = total sum / total number of students

total mean = 77 / (20+16+14)

= 77/50

= 1.54

more geometry help :)

Answers

Answer:

Step-by-step explanation:

Multiply both the co-ordinates of each vertex by the scale factor and then simplify it.

A(-3 , 2)    A'(-3*8 , 2 * 8) = A' (-24 , 16)

B(2,1)         B'(2*8 , 1*8)  = B'(16,8)

C(-1,-3)       C'(-1*8,-3*8)= C'(-8,-24)

Answer:

see explanation

Step-by-step explanation:

Assuming the dilatation is centred at the origin, then multiply each ot the coordinates by the scale factor 8

A (- 3, 2 ) → A' (8(- 3), 8(2) ) → A' (- 24, 16 )

B (2, 1 ) → B' (8(2), 8(1) ) → B' (16, 8 )

C (- 1, - 3 ) → C; (8(- 1), 8(- 3) ) → C' (- 8, - 24 )

Select all the points that are on the graph of the line y = −1/4 x + 3.
a. (0, -1/4)
b. (0, 3)
c. (1, 11/4)
d. (1, 3)
e. (1, 13/4)
f. (3, 0)

Answers

The points on the graph ( b , c )

I hope I helped you ^_^

SOMEONE HELP ME PLEASE

Answers

here's the answer to your question

your answer is 51.7%

I have two identical dice with the numbers
-1, 2, -3, 4, -5 and 6
I roll my dice and work out my total.
Which of the following totals cannot be achieved?
a) 3
b) 7
c) 8

Answers

Answer:

7 cannot be achieved

-1 + 6 = 5

-3 + 4 = 1

-5 + 2 = -3

as you can see, no combinations can form seven

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