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
2(4x – 3) ≥ –3(3x) + 5x?Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?
nika2105 [10]

Answer:

x<=-1/2

Step-by-step explanation:

An inequality is a mathematical relationship that compares two unequal numbers using the number line

To solve the inequality 2x – 6 ≥ 6(x – 2) + 8

We first simplify both sides of the inequality

2x-6≥6x-12+8

2x-6≥6x-4

Add 6 to both sides

2x≥6x+2

-4x≥2

x≥2/-4

Sign changes when we divide both sides of equation by a negative sign

x<=-1/2

Therefore x is less than or equal to -1/2 on the number line

5 0
3 years ago
Samantha puts an initial $500 into a savings account. The account has a 4% annual compound interest rate. What is the function t
konstantin123 [22]
Hello! I can help you with this!

a. The function that would best represent Samantha's account is f(5) = 500(1 + 0.04)^5. This is because $500 is the principal, the interest rate is 4%, and we're looking for the amount in the savings account 5 years later.

b. Okay. 1 = 0.04 is 1.04. 1.04^5 is 1.216652902. It's a long decimal, but don't delete it. Multiply that decimal by 500 and you get 608.32645 and other numbers behind it or 608 when rounded to the nearest dollar. Samantha will have about $608 in her savings account in 5 years.

Note: The formula goes like this: f(x) = P(1 + r)^x. This means, you add 1 and the simple interest rate in decimal form together and raise that up by the exponent. There is no shortcuts for this, so you'll have to use the calculator. There will be a very long decimal, but don't clear it. Instead, multiply it by the principal to get the answer. It seems very complicating, but if you do this right, it gets easier overtime and you'll make less errors. There are more complex problems out there, so this formula is very important, but it was kept simple for this question.
7 0
3 years ago
How do you write 35 over 20 As a percentage
lara31 [8.8K]
In order to write \frac{35}{20} as a percentage, we must first convert the fraction into a decimal. We can do that simply by dividing.

35 / 20 = 1.75

In order to convert a fraction to a decimal, we must multiply it by 100

1.75 * 100 = 175%

\frac{35}{20} as a percentage is 175%.
Hope that helped =)
4 0
3 years ago
Read 2 more answers
Can somebody please help me bc im so lost its ridiculous
kodGreya [7K]

Answer:

1. A = 120

2. B = 98

3. C = 86

4. D = 176

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
I hope you can understand that picture:/
Shtirlitz [24]
The is a I think or it could be c I really don’t know sorry I try’s
7 0
3 years ago
Other questions:
  • How many factor pairs dose 24 have
    13·2 answers
  • What’s the value of 5 of 467.3985
    6·2 answers
  • Y=-2x+6<br> 3y-x+3=0 <br> Solving systems using substitution
    8·1 answer
  • F(x) = x + 2 g(x) = x – 4 (f g)(x) =
    13·2 answers
  • Find the coordinates of the focus and equation of the directrix for the parabola given by
    10·2 answers
  • Simplify.
    5·1 answer
  • 50 points! Can someone help me with the first one? I will mark brainliest.
    15·2 answers
  • Please help I need the answer to this
    14·2 answers
  • Which statement about this figure is true?
    14·2 answers
  • Pls tell the answer for 50 points!
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!