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Papessa [141]
3 years ago
9

Which of the following infinite series has a finite sum? Explain your reasoning.

Mathematics
1 answer:
ikadub [295]3 years ago
7 0

Answer:

d. 20+10+5+2.5+...

Step-by-step explanation:

No geometric series with a common ratio of magnitude greater than 1 will have a finite sum. Nor will any arithmetic series.

Those descriptions exclude answer choices a, b, c. Choice d is a geometric series with a common ratio of 1/2, so will have a finite sum. (It is 40.)

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If a₁ = 4 and an = 5an-1 then find the value of a5.
igor_vitrenko [27]

The value of a_{5} is 2500, when a_{1}=4 and 5a_{n-1}.

Given that, a_{1}=4 and 5a_{n-1}.

We need to find the value of a_{5}.

<h3>What is an arithmetic sequence?</h3>

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Now, to find the value of a_{5} :

a_{2} =5a_{2-1}=5a_{1}=5 \times4=20

a_{3} =5a_{3-1}=5a_{2}=5 \times20=100

a_{4} =5a_{4-1}=5a_{3}=5 \times100=500

a_{5} =5a_{5-1}=5a_{4}=5 \times500=2500

Therefore, the value of a_{5} is 2500.

To learn more about arithmetic sequence visit:

brainly.com/question/15412619.

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5 0
2 years ago
X^2+ 3 has a value of 28. What term in the sequence has a value of 28?
VikaD [51]

Answer:

5th term

Step-by-step explanation:

x^2 +3 = 28

Subtract 3 from each side

x^2+3-3 =28-3

x^2 = 25

Take the square root of each side

sqrt(x^2) = sqrt(25)

x = 5

(x could be -5, but there are not usually negative terms in a sequence)

5 0
2 years ago
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What is the midpoint of the segment shown below?
Aneli [31]

Answer:

(1, -3/2)

Step-by-step explanation:

The x coordinate is the same for both endpoints so the x coordinate for the midpoint is 1

The y coordinate for the midpoint is found by adding the two y coordinates and dividing by 2

(2+-5)/2 = -3/2

The midpoint is

(1, -3/2)

5 0
3 years ago
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What’s the volume of a cylinder with a radius of 6ft and height of 14ft? pls show work
Daniel [21]

Answer:

<em><u>Given </u></em><em><u>-</u></em>

  • <em><u>radius </u></em><em><u>of </u></em><em><u>cylinder </u></em><em><u>=</u></em><em><u> </u></em><em><u>6</u></em><em><u> </u></em><em><u>ft</u></em>
  • <em><u>height </u></em><em><u>of </u></em><em><u>cylinder </u></em><em><u>=</u></em><em><u> </u></em><em><u>1</u></em><em><u>4</u></em><em><u> </u></em><em><u>ft</u></em>

Now ,

volume = \pi \: r {}^{2} h \\  =  >  \frac{22}{\cancel{7}}  \times 6 \times\cancel{ 14} \\  \\  =  > 22 \times 6 \times 2 \\  =  > 264 \: ft {}^{3}

hope helpful~

5 0
2 years ago
I need help please and thank you
Debora [2.8K]
1. The variable A added to the sum of the variable D and 6
2. 10 added to b multiplied by 2
4 0
3 years ago
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