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Mila [183]
3 years ago
13

Is the sequence geometric? if so, identify the common ratio 1/5,2/15,4/45,8/135,16/405,...

Mathematics
2 answers:
Romashka-Z-Leto [24]3 years ago
7 0
So have the sequence: \frac{1}{5} , \frac{2}{15} , \frac{4}{45} , \frac{8}{135} , \frac{16}{145} ,...
To check if the sequence is geometric, we are going to find its common ratio; to do it we are going to use the formula: r= \frac{a_{n} }{a_{n-1}}
where 
r is the common ratio 
a_{n} is the current term in the sequence 
a_{n-1} is the previous term in the sequence
In other words we are going to divide the current term by the previous term a few times, and we will to check if that ratio is the same:

For a_{n}= \frac{2}{15} and a_{n-1}= \frac{1}{5}:
r= \frac{ \frac{2}{15} }{ \frac{1}{5} }
r= \frac{2}{3}

For a_{n}= \frac{4}{45} and a_{n-1}= \frac{2}{15}:
r= \frac{ \frac{4}{45} }{ \frac{2}{15} }
r= \frac{2}{3}

For a_{n}= \frac{8}{135} and a_{n-1}= \frac{4}{45}:
r= \frac{ \frac{8}{135} }{ \frac{4}{45} }
r= \frac{2}{3}
As you can see, we have a common ratio!

We can conclude that our sequence is a geometric sequence and its common ratio is \frac{2}{3} 
Mariulka [41]3 years ago
7 0
<h3>The answer is :</h3>

yes; \frac{2}{3}

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Step-by-step explanation:

 1/9x+10/9

=1/9(x+0.1)

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Please! Solve f(x)-g(x) if f(x)=1/2x^4 - x^2 and g(x)= 3/4x^4 +3x^3 - x^2
igomit [66]

Answer:

f(x)-g(x)=\frac{-1}{4}x^{4}-3x^{3}

Step-by-step explanation:

This is a subtraction between polynomials, since both functions are polynomials, hence, to solve the problem with need to perform the subtraction, by coefficients.

f(x)= \frac{1}{2}x^{4}+0x^{3}-x^{2}\\\\g(x)=\frac{3}{4}x^{4}+3x^{3}-x^{2}

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f(x)-g(x)=\frac{-1}{4}x^{4}-3x^{3}

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3 years ago
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Wewaii [24]

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1)A

2)B

3)A

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Step-by-step explanation:

7 0
3 years ago
Which values for h and k are used to write the function f of x = x squared 12 x 6 in vertex form?
Nesterboy [21]

The values of h and k when f(x) = x^2 + 12x + 6 is in vertex form is -6 and -30

<h3>How to rewrite in vertex form?</h3>

The equation is given as:

f(x) = x^2 + 12x + 6

Rewrite as:

x^2 + 12x + 6 = 0

Subtract 6 from both sides

x^2 + 12x = -6

Take the coefficient of x

k = 12

Divide by 2

k/2 = 6

Square both sides

(k/2)^2 = 36

Add 36 to both sides of x^2 + 12x = -6

x^2 + 12x + 36= -6 + 36

Evaluate the sum

x^2 + 12x + 36= 30

Express as perfect square

(x + 6)^2 = 30

Subtract 30 from both sides

(x + 6)^2 -30 = 0

So, the equation f(x) = x^2 + 12x + 6 becomes

f(x) = (x + 6)^2 -30

A quadratic equation in vertex form is represented as:

f(x) = a(x - h)^2 + k

Where:

Vertex = (h,k)

By comparison, we have:

(h,k) = (-6,-30)

Hence, the values of h and k when f(x) = x^2 + 12x + 6 is in vertex form is -6 and -30

Read more about quadratic functions at:

brainly.com/question/1214333

#SPJ1

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1 year ago
Which of the following values when placed in the ten's place for the number 1_1 will make it a prime number?
Sloan [31]
The answer is 181.

Ans: 8
6 0
3 years ago
Read 2 more answers
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