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Oxana [17]
2 years ago
5

Determine whether the geometric series 27 + 18 + 12 + 8 + ... converges or diverges, and identify the sum if it exists.

Mathematics
1 answer:
Ne4ueva [31]2 years ago
6 0

The given geometric series as shown in the question is seen to; Be converging with its' sum as 81

<h3>How to identify a converging or diverging series?</h3>

We are given the geometric series;

27 + 18 + 12 + 8 + ...

Now, we see that;

First term; a₀ = 27

Second Term; a₁ = 2(27/3)

Third term; a₂ = 2²(27/3²)

Fourth term; a₃ = 2³(27/3³)

Thus, the formula is;

2ⁿ(27/3ⁿ)

Applying limits at infinity gives;

2^(∞) * (27/3^(∞)) = 0

Since the  terms of the series tend to zero, we can affirm that the series converges.

The sum of an infinite converging series is:

S_n = a/(1 - r)

S_n = 27/(1 - (2/3)

S_n = 81

Read more about converging or diverging series at; brainly.com/question/15415793

#SPJ1

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Answer:

  21.  y = 75000·0.935^t

  22.  after 74.6 days

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Step-by-step explanation:

22. It is convenient to use the graphing calculator to solve this problem. The number of days is where the exponential curve has the value 500. It is about 74.55 days. (see the first attachment)

__

23. y = 27.8112·1.18832^t (see the second attachment)

__

24. The rate of change is the difference between the base of the exponential and 1, often expressed as a percentage. The time period is the units of t.

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25. Evaluating the function for t=24 gives y ≈ 1748.30425259 ≈ 1748.

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<em>Comment on graphing calculator</em>

A graphing calculator can make very short work of problems like these. It is worthwhile to get to know how to use one well.

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Answer:

see below!!

Step-by-step explanation:

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Substitute the point into each equation and verify that it is true

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