1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alex_Xolod [135]
3 years ago
8

A geometric series has second term 375 and fifth term 81 . find the sum to infinity of series .

Mathematics
1 answer:
Eduardwww [97]3 years ago
7 0

Answer:  \bold{S_{\infty}=\dfrac{3125}{2}=1562.5}

<u>Step-by-step explanation:</u>

  a₁,  375,  a₃,   a₄,  81

First, let's find the ratio (r). There are three multiple from 375 to 81.

375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}

Next, let's find a₁

a_1\bigg(\dfrac{3}{5}\bigg)=375\\\\\\a_1=375\bigg(\dfrac{5}{3}\bigg)\\\\\\a_1=125(5)\\\\\\a_1=625

Lastly, Use the Infinite Geometric Sum Formula to find the sum:

S_{\infty}=\dfrac{a_1}{1-r}\\\\\\.\quad =\dfrac{625}{1-\frac{3}{5}}\\\\\\.\quad =\dfrac{625}{\frac{2}{5}}\\\\\\.\quad = \dfrac{625(5)}{2}\\\\\\.\quad = \large\boxed{\dfrac{3125}{2}}

You might be interested in
A student solved this problem by working backwards. Joani has some stuffed animals. She has 2 times as many as Lily. Lily has 6
kramer
3x4=12 gives him 12 baseballs. he has 5 fewer tennis balls than base balls so you subtract 5 from 12 and you get 7 tennis balls.
5 0
3 years ago
What is the equation of the line with the same slope as the equation x-4y=3 and the y-intercept(0,-8)?
katen-ka-za [31]

Answer:

y = 1/4x -8

Step-by-step explanation:

First find the slope of the line

x-4y =3

Subtract x from each side

x-4y -x = -x+3

-4y = -x+3

Divide each side by -4

-4y/-4 = -x/-4 +3/-4

y = 1/4 x -3/4

This is in the form y= mx+b where the slope is m and the y intercept is b

The slope is 1/4

We want the same slope

y = 1/4x +b

we know the y intercept is -8

y = 1/4x -8

8 0
4 years ago
Read 2 more answers
You have decided to wallpaper your rectangular bedroom. the dimensions are 12 feet 6 inches by 10 feet 6 inches by 8 feet 0 inch
Papessa [141]
The wall area is the product of the room perimeter and the room height:
   A₁ = (2*(12.5 ft + 10.5 ft))*(8.0 ft) = 368 ft²

The window and door area together is
   A₂ = 2*((4 ft)*(3 ft)) + (7 ft)*(3 ft) = 45 ft²

The area of one roll of wallpaper is
   A₃ = (2.5 ft)*(30 ft) = 75 ft²

Then the number of rolls of wallpaper required will be
   1.1*(A₁ - A₂)/A₃ ≈ 4.74

5 rolls of wallpaper should be purchased.

_____
As a practical matter, not much of the window and door area can be saved. The rolls are 30 inches wide, but the openings are 36 inches wide. Some will likely have to be cut from two strips. The strips will have to be the full length of the wall, and the amount cut likely cannot be used elsewhere. If the window and door area cannot be salvaged, then likely ceiling(5.4) = 6 rolls will be needed (still allowing 10% for matching and waste).
8 0
3 years ago
Which of the following is true for the interval from 3-5 seconds
kondaur [170]

Answer:

Option C

Step-by-step explanation:

The given function is: h(t)=-16t^2+80t+108.

h(5)=-16(5)^2+80(5)+108=108.

h(3)=-16(3)^2+80(3)+108=204.

The average rate of change of this function on the interval t=3 to t=5 is given by:

\frac{h(5)-h(3)}{5-3}

\frac{204-108}{2}=-48

Since the average rate of change is negative on the interval 3-5 seconds, it means the ball is moving downwards at an average rate of 48 feet per second.

The correct choice is C.

6 0
3 years ago
Solve for x. X/5-7=4​
hjlf

Answer:

x = 55

Step-by-step explanation:

\frac{x}{5}  - 7 = 4 \\  =  > \frac{x}{5}  = 4 + 7 \\  =  >  \frac{x}{5}  = 11 \\  =  >  x = 11 \times 5 \\  =  > x = 55

Hope it helps.

Don't forget to click the Brainliest button if you like my answer.

7 0
2 years ago
Other questions:
  • The length of a rectangle is 12 inches. The width of the rectangle is 5 inches. Mia says the perimeter is 60 in2 and the area is
    7·1 answer
  • I have $3.35 in quarters and dimes. if i have 23 coins in all, find the number of quarters and dimes
    11·1 answer
  • the sum of three decimal numbers is 6 exactly one of the numbers is less than 1 what could the numbers be​
    6·1 answer
  • Write 33/72 in simplest form​
    7·2 answers
  • Help fast I’m giving 20 points’ The number of bacteria in a petri dish is 42 and is tripling every month
    13·2 answers
  • Can someone please help me:)
    13·1 answer
  • Pls help I’ll brain-lest ASAP
    9·1 answer
  • https://lists.office.com/Images/2fce1dfb-919f-4938-aab8-c47f0fc9182d/759a6d77-ea1a-4b50-a9bc-86157c96a662/T14LEZ48DGIIWGRBN9LPBU
    10·1 answer
  • The formula for the perimeter, P, of a rectangle is P = 2(1 + w),
    8·2 answers
  • Area of Parallelograms, Quadrilaterals, and Polygons - Quiz - Level F What is the area of this triangle? in. in2 Ich h = 5 in. b
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!