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
kkurt [141]
2 years ago
13

What is the value of the sum of all the terms of the geometric series 300, 60, 12, …?

Mathematics
1 answer:
ruslelena [56]2 years ago
3 0
<h3>Answer:   375</h3>

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

Work Shown:

a = 300 = first term

r = 60/300 = 0.2 = common ratio

We multiply each term by 0.2, aka 1/5, to get the next term.

Since -1 < r < 1 is true, we can use the infinite geometric sum formula below

S = a/(1-r)

S = 300/(1-0.2)

S = 300/0.8

S = 375

----------

As a sort of "check", we can add up partial sums like so

  • 300+60 = 360
  • 300+60+12 = 360+12 = 372
  • 300+60+12+2.4 = 372+2.4 = 374.4
  • 300+60+12+2.4+0.48 = 374.4+0.48 = 374.88

and so on. The idea is that each time we add on a new term, we should be getting closer and closer to 375. I put "check" in quotation marks because it's probably not the rigorous of checks possible. But it may give a good idea of what's going on.

----------

Side note: If the common ratio r was either r < -1 or r > 1, then the terms we add on would get larger and larger. This would mean we don't approach a single finite value with the infinite sum.

You might be interested in
Someone please help me with this question !!
yarga [219]
The answer is 12^8/9
6 0
3 years ago
Solve the equation?
stiks02 [169]

Answer:

A

Step-by-step explanation:

Given

p² + 2p - 8 = 0 ← in standard form

with a = 1, b = 2, c = - 8

Using the quadratic formula to solve for p

p = ( - 2 ± \sqrt{2^2-(4(1)(-8))} / 2

  = ( - 2 ± \sqrt{4+32} / 2

  = ( - 2 ± \sqrt{36} ) / 2

p = \frac{-2-6}{2} = \frac{-8}{2} = - 4

p = \frac{-2+6}{2} = \frac{4}{2} = 2

5 0
3 years ago
Read 2 more answers
HELP
vaieri [72.5K]
4/8 simplified is 2/4 i think
3 0
3 years ago
Express the fact that X differs from 2 by more than 3 as an inequality involving an absolute value. Solve for x
defon
An inequality is also an algebraic equation. However, instead of '=' sign, it uses either of these: <, >, ≤, ≥. To translate: <span>X differs from 2 by more than 3, that would be:

2 - x > 3 
We use the '>' equation because the open area should face the larger value. Solving the equation:
-x > 3 - 2
-x > 1
x > -1</span>
5 0
2 years ago
Solve the equation in the image
Margaret [11]

Answer: 55

Step-by-step explanation:

\sqrt[3]{4x-4}=6

Begin by cubing each side of the equation to get rid of the cubic root.

(\sqrt[3]{4x-4})^3=(6)^3\\ 4x-4=216

add 4

4x-4+4=216+4\\4x=220

Divide by 4

\frac{4x}{4}=\frac{220}{4}

x=55

7 0
3 years ago
Read 2 more answers
Other questions:
  • in 2010, there were 40 fish in a pond. one year later, the number of fish decreased by 30%. how many fish we're in the pond in 2
    5·1 answer
  • Terry can run 15 miles in the same amount of time it takes mark to run 21 miles. If mark runs 2mph faster than terry, how fast d
    10·1 answer
  • Help with this algebra question
    10·2 answers
  • Y= (x + 3/2) ^2 - 1/4<br> Convert to standard form
    14·1 answer
  • Hi! May I please have some help?
    7·2 answers
  • Solve the equation<br> 5x=-7x+6
    15·2 answers
  • Destiny can run one-eighth of a mile in three-quarters of a minute, and she can walk one-quarter of a mile in 4 minutes. How man
    6·1 answer
  • PLS HELP
    15·1 answer
  • Thank you will mark brainliest
    6·1 answer
  • Given the table, write and equation for the function, and describe what it does.<br><br> ASAP!!!
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!