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3 years ago

Find the common ratio and an explicit form in each of the following geometric sequences.

Mathematics

1 answer:

Margaret [11]3 years ago

7 0

Answer:

The explicit form is $a_{n}=162(2/3)^{n-1}$

Step-by-step explanation:

The explicit form of a geometric sequence is given by:

$a_{n}=ar^{n-1}$

where an is the nth term, a is the first term of the sequence and r is the common ratio.

In this case:

a=162

The value of the common ratio is obtained by dividing one term by the previous term.

For the first and second terms:

108/162=2/3

For the second and third terms (In order to prove that 2/3 is the common ratio)

72/108=2/3

Therefore:

r=2/3

Replacing a and r in the formula:

$a_{n}=162(2/3)^{n-1}$

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Zielflug [23.3K]

Answer:

$(4a)^{-3}*^{-4}$

$x^m*x^n=x^{m+n}$

$(4a)^{-3}*a^{-4}$

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$\cfrac{1}{4^3} \:a^{-7}$

$\boxed{\frac{1}{64a^{7}} }$

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3 years ago

Find the equation of the line that passes through (-2,8) and has a slope of -3/2

vfiekz [6]

Answer:

y = 0x -3/2

you can write it as -3/2

slope = 0

Step-by-step explanation:

4 0

3 years ago

Find ST and TR <br> Will mark brainest

vlada-n [284]

Hello there! :D

Firstly, I want you to understand an important concept. This has something to do with absolute value. So, although distance is a number, it is neither positive nor negative. It does not necessarily involve value. So, what we are looking for today will not have a negative sign in front of it. We are simply looking for distance!

Let's start with ST, because the distance between those is smaller and therefore I can better explain this to you. T is at the point 19.1, and S is at the point 14. We need to find the amount of distance between the two. How do we do that?

Subtraction! In order to find this value we can subtract the smaller number from the larger number.

19.1-14= 5.1

ST is 5.1

Now we can look at the distance between TR. We are actually going to add numbers together! We know that T is 19.1. If we were to put a dot at zzero and measure that distance, it would be 19.1. What is the distance from R to zero? That's right! The same principle is there. If we had a dot at zero and we're measuring from 4, the distance would be 7.5 (even though it is negative on the number line).

So, we can add these numbers together!

19.1+7.5= 26.6

TR is 26.6

I hope this helped you and you have a wonderful day,

Kai xx

3 0

3 years ago

A regular hexagon is shown below. Find the value of x.

Cloud [144]

The measure of each interior angle of the hexagon is 120°. Then the value of x will be 20°.

<h3>What is a polygon?</h3>

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

A regular hexagon is shown below.

Then the internal angle of the hexagon is (5x + 20)°.

Then the value of x will be

We know that each interior angle of the hexagon is 120°.

Then we have

5x + 20 = 120

5x = 100

x = 20

More about the polygon link is given below.

brainly.com/question/17756657

#SPJ1

8 0

2 years ago

The hypotenuse of a right triangle measures 15 cm and one of its legs

Kay [80]

Answer:

[see below]

Step-by-step explanation:

Use the Pythagorean Theorem.

$a^2+b^2=c^2$

'c' will be the hypotenuse.

The hypotenuse is 15 cm. One of the legs is 5 cm.

$5^2+b^2=15^2\\\\25 + b^2 = 225\\\\25-25+b^2=225-25\\\\b^2=200\\\\\sqrt{b^2}=\sqrt{200}\\\\ b=14.1421356237..., -14.1421356237$

14.1421356237 ≈ 14.1

The other leg should be about 14.1 cm.

Hope this helps.

4 0

3 years ago

Read 2 more answers