The price of a train ticket consists of an initial fee plus a constant fee per stop.

Alik [6]

Answer:

32, 16, 8, 4, 2, 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:

$a_{n} = a_{1} • r^{n-1}$

Where $a_{n}$ is the nth term, $a_{1}$ is the first term in the sequence, n is the term number, and r is the common ratio.

Since we already know the first term, $a_{1}$ will simply be 32.

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.

There are 6 total terms, r is raised to the n – 1 so 6 – 1 = 5, and that will be the degree of this root.

$\sqrt[5]{\frac{a_{6}}{a_{1}}}$ =

$\sqrt[5]{\frac{1}{32}}$ =

$\frac{1}{2}$ .

Therefore: $r = \frac{1}{2}$ .

Using all the information we have, we can find the explicit rule:

$a_{n} = a_{1} • r^{n-1}$

$a_{1}$ = 32
$r = \frac{1}{2}$

$a_{n} = a_{1} • r^{n-1}$ →

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

________________________________

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

For instance:

$a_{1} = 32 • (\frac{1}{2})^{1-1}$

$a_{1} = 32 • (\frac{1}{2})^{0}$

$a_{1} = 32 • 1$

$a_{1} = 32$

$a_{6} = 32 • (\frac{1}{2})^{6-1}$

$a_{6} = 32 • (\frac{1}{2})^{5}$

$a_{6} = 32 • \frac{1}{32}$

$a_{6} = 1$

3 0

3 years ago

Read 2 more answers

A fishbowl has a capacity of 192 fluid ounces. How many quarts is that?

DENIUS [597]

Answer:

hope this helps

Step-by-step explanation:

192 fl oz. = 6 quarts

to get this you divide the fluid ounces by 32.

7 0

3 years ago

Ursula says the distance between -5.47 and 5.47 on a number line is equal to |-5.47|. explain her error

tresset_1 [31]

Your absolute value cannot be negative.

5 0

3 years ago

recall that two angles are supplementary if the sum of their measure is 180. find the measures of two supplementary angles if on

aleksklad [387]

Answer:

I don't know if it's correct

but I tried

Step-by-step explanation:

let the angle be x

20+4x+x=180

20+5x=180

5x=160

x=32

5 0

3 years ago

If a female is 5ft even has 8 oz of 80 proof liquor over hours, will it be out of her system and blood a 000 on a breathalyzer 1

den301095 [7]

Answer:No

Step-by-step explanation:

No

4 0

4 years ago