Find the probability of rolling two dice and getting a sum of 11.

What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?

Trava [24]

Answer:

$\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}$

Step-by-step explanation:

The explicit formula for a geometric sequence:

$a_n=a_1r^{n-1}$

$a_n$ - n-th term

$a_1$ - first term

$r$ - common ratio

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}$

We have

$a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...$

The common ratio:

$r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}$

<h2>It's not a geometric sequence.</h2>

If $a_3=-\dfrac{1}{16}$ then the common ratio is $r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}$

Put to the explicit formula:

$a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}$

Put $a_n=\dfrac{1}{1024}$ and solve for <em>n </em>:

$-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1$

$\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6$

5 0

3 years ago

WILL GIVE BRAINLIEST

tiny-mole [99]

The expressions for each of the given statements are

a. 6 + z

b. 20 - x

c. x/6 - 8

d. x + 5/4

<h3>Writing an expression </h3>

From the question, we are to write an expression for each of the given statement

a. the sum of 6 and z

That is,

6 + z

b. the difference between 20 and x

That is,

20 - x

c. 8 less than the quotient of x divided by 6

That is,

x/6 - 8

d. x increased by 5 divided by 4

That is,

x + 5/4

Hence, the expressions for each of the given statements are

a. 6 + z

b. 20 - x

c. x/6 - 8

d. x + 5/4

Learn more on Writing an expression here: brainly.com/question/17651563

#SPJ1

4 0

2 years ago

Consider the following theorem and proof.Theorem: The number âš2 is not rational number.Proof: Let's suppose âš2 is a rational n

ololo11 [35]

Answer:

The statement "Both of the numbers a and b cannot be even." is justified by the fact that a/b is simplified lowest terms

Step-by-step explanation:

We need to show that the √2 is an irrational number.

And from the given steps of proof stated in the question, we need to find the assumption that justifies the fact : " Both of the number a and b cannot be even".

First take the given options :

Option a : √2 is a rational number

√2 being an rational or irrational has no relation of a and b to be even or odd. So, this option is rejected.

Option B : a/b is simplified lowest terms

This shows that a and b are not even because if a and b are even then a/b can be simplified in other lowest term.

Option c : √2 is a irrational number

Similarly, By using the inverse part of Option A, option c is also rejected.

Option d : The fact that b divides a evenly

This only shows that the a is even. This does not give any idea about b is even or not. So option D is also rejected.

Option E : The fact that a and b are whole numbers

This fact does not imply that the a and b are even or odd. So option E is also rejected.

Hence, The statement "Both of the numbers a and b cannot be even." is justified by the fact that a/b is simplified lowest terms

7 0

3 years ago

PLS ANSWER ASAP Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to

irina [24]

The correct answer is c. 16.6

Explain

The triangle left side
Opposite side= hypotheses x sin 0

Plugin

Opposite side = 39 x sin 43

39 x 0.68

26.60

The right side

Opposite side = adjective side x tan0

Opposite side = 26.60 x tan 32

26.60 x 0.62

X= 16.6

Hope this help you :D

6 0

4 years ago

For the basic function f(x)=x, what conclusions can you make about f(x) and f(x)-5? Select all that apply.

babunello [35]

Answer:The ansewers are c and d.

Step-by-step explanation:

The function f(x)=x is really y=x.

7 0

3 years ago