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lara [203]
3 years ago
9

What is the difference between an arithmetic sequence and a geometric sequence?

Mathematics
1 answer:
earnstyle [38]3 years ago
3 0

Answers

Part 1

Arithmetic sequence is a sequence by which the next term is found by adding a constant number. It can be a positive number or a negative number. This number is called the common difference. On the other hand, a geometric sequence is one whose next term is found by multiplying the previous term with a constant (common ratio).


Part 2

Sequences are useful in our daily lives as well as in higher mathematics. For example, the interest portion of monthly payments made to pay off an automobile or home loan, and  the list of maximum daily temperatures in one area for a month are sequences.

<u>Example: arithmetic sequence</u>

A child building a tower with blocks uses 15 for the bottom row. Each row has  2 fewer blocks than the previous row. Suppose that there are 8 rows in the tower. Find an for n = 8.

The number of blocks in each row forms an arithmetic sequence with a₁ = 15 and d= −2. The formula to be used is  an = a₁ + (n − 1)d.

<u>Example: geometric sequence </u>

An insect population is growing in such a way that each new generation is 1.5  times as large as the previous generation. Suppose there are 100 insects in the first  generation.  How many will there be in the fifth generation?

The population can be written as a geometric sequence with a₁ as the first generation  population, a₂ as the second-generation population, and so on. Then the fifth generation  population will be a₅. The formula to be used is an = a₁×r⁽ⁿ⁻¹⁾

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Step-by-step explanation:

The whole triangle ABD is a 30-60-90 right triangle. In 30-60-90 triangles, the smallest side is x, the middle side is x\sqrt{3}, and the largest side/hypotenuse is 2x.

Side AB is the smallest side and therefore x=300. Side BD is the middle side and so we can use x\sqrt{3} and we get BD=300\sqrt{3}=519.615

The question is asking for CD, and we know that CD can be equal to BD minus BC since that would isolate CD

Triangle ABC is also a 30-60-90 triangle but the 300 feet is the middle side in this triangle. So we can do 300=x\sqrt{3} and divide 300 by radical 3 and get that x=173.205

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Now that we have the whole side BD and the part of it BC. We can subtract BD by BC (519.615-173.205) and we get that CD=346.4

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3 years ago
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Akimi4 [234]
You didn’t give answer choices, so I would say it would probably be;


50/x Or some other variable.

If you aren’t clear on what a variable is, it’s a letter that represents an unknown factor or numerical value in an expression.
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So your answer should be 50/*variable*
In my example I used x, but your answer might use another letter.

I hope this helps, and I’m sorry if I’m wrong.
Good luck. :))
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