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3 years ago

6

A plane has a crusing speed of 300 miles per hour when there is no wind. At this speed, the plane flew 600 miles with the wind i

n the same amount of time it flew 400 mikes against the wind. Find the speed

1 answer:

Archy [21]3 years ago

4 0

300t=600
t=2
2y=400
y=400/2
Wind=200

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32, <u>16</u>, <u>8</u>, <u>4</u>, <u>2</u>, 1

Explanation:

The geometric mean can be represented by $\sqrt[n]{x_{1} • x_{2} • x_{3} • .. x_{n}}$ .

Which is the mean of the product of n numbers, used to find the average of a geometric progression.

Don't get confused by geometric mean, it is only asking you about the next numbers in the geometric sequence given the first and sixth term.

The explicit rule for a geometric sequence can be modeled by:

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Since we know it's geometric, there will be an exponential relationship, which means that we will use the geometric mean to find the common ratio.

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$a_{n} = a_{1} • r^{n-1}$

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$a_{n} = a_{1} • r^{n-1}$ →

$\boxed{a_{n} = 32 • (\frac{1}{2})^{n-1}}$

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We can test that this works by substituting the number location of the term you want to find.

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$a_{1} = 32 • (\frac{1}{2})^{1-1}$

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