what is the common ratio of the geometric sequence below? –2, 4, –8, 16, –32, ...

Answers

Answer 1

Answer:

The common ratio of the geometric sequence is:

[tex]r=-2[/tex]

Step-by-step explanation:

A geometric sequence has a constant ratio 'r' and is defined by

[tex]a_n=a_1\cdot r^{n-1}[/tex]

where

aₙ is the nth terma₁ is the first termr is the common ratio

Given the sequence

[tex]-2,\:4,-8,\:16,\:-32,\:...[/tex]

Compute the ratios of all the adjacent terms:  [tex]r=\frac{a_n+1}{a_n}[/tex]

[tex]\frac{4}{-2}=-2,\:\quad \frac{-8}{4}=-2,\:\quad \frac{16}{-8}=-2,\:\quad \frac{-32}{16}=-2[/tex]

The ratio of all the adjacent terms is the same and equal to

[tex]r=-2[/tex]

Therefore, the common ratio of the geometric sequence is:

[tex]r=-2[/tex]

Related Questions

0.5(400 + d) =4.25 d=​

Answers

Answer:

d = 53.33333

Step-by-step explanation:

Solve for d on calculator

Answer:

pleas help me asap please!!!!!!

pleas help me asap please!!!!!!

Step-by-step explanation:

pleas help me asap please!!!!!!

Help i need to finish it today And can you explain the steps so i wont need help next time or if you don’t want to its okay :)

Answers

Answer:

110 feet

Step-by-step explanation:

The formula to find the area of a rectangular prism is A = 2 (wl + hl + hw)

Substitute the values:

A = 2 (5x5 + 3x5 + 3x5)

A = 2 (25 + 15 + 15)

A = 2 (25 + 15 + 15)

A = 2 (55)

A = 110


Two mechanics worked on a car. The first mechanic charged $115 per hour, and the second mechanic charged $65 per hour. The mechanics
combined total of 15 hours, and together they charged a total of $1475. How long did each mechanic work?

Answers

Answer:

Here is another case where we have two unknowns (the number of hours each mechanic worked) so we'll need two equations to solve.

Let A = number of hours first mechanic worked (the one who charged $45/hour)

Let B = number of hours second mechanic worked (the one who charged $105/hour)

From the problem statement, we know that the two mechanics worked a combined 35 hours so the first equation is:

Equation 1: A hours + B hours = 35 hours

We also know that in total, the charge was $2475.  So the second equation is:

Equation 2: (A hours x 45 dollars/hour) + (B hours x 105 dollars/hour) = 2475 dollars

So our two equations are:

1: A + B = 35

2: 45A + 105B = 2475

Multiply both sides of the first equation by -45 to get the following:

-45A - 45B = -1575

Now the two equations are:

1: -45A - 45B = -1575

2: 45A + 105B = 2475

Add them together and the "A" term drops out:

-45B + 105B = -1575 + 2475

or

60B = 900

Now divide both sides by 60:

B = 15

Now plug B = 15 into the first equation:

A + 15 = 35 thus A = 20

So Mechanic A (at $45/hour) worked 20 hours and Mechanic B (at $105/hour) worked 15 hours

Check: 20x45 + 15x105 = 900 + 1575 = 2475

Step-by-step explanation:

hope it helps you (:

Tina went out to eat and her bill was $24.75.
She wants to leave the waiter a 20% tip. How
much more money will be added to her bill
once she included the tip?

Answers

Answer:

your awnser should be. 24.75 + 20% = $29.70

so the amount added to her bill is $4.95

Answer:

the bill will be 4.95 more than the original cost without the 20% tip.

Step-by-step explanation:

cost before tip: 4.75

cost after 20% tip: 29.70 or 30.00 (rounded)

please help it’s due today !

Answers

Answer:

x = -7

Step-by-step explanation:

-7(?)=49

negative times a negative is a positive

7×7=49

-7×-7=49

Enter the value of (−8)(45)(18).

Answers

Answer
-6480
If you need to show work I have no problem with putting it in the comments :)
Answer would be -6480

What is the circumference of this circle?

Answers

Answer:

37.68

Step-by-step explanation:

[tex]c = 2 \times 6 \times 3.14 = 37.68[/tex]

The correct answer should be 18.84. To get to this answer you need to multiply 6 by pi (3.14).

1 Expand and simplify each expression
a) x(x+2)+x(x+5)

Answers

x^2 + 2x + x^2 + 5x

2x^2 + 7x

i need help with thisss

Answers

Answer:

width= 223.9 ft

Step-by-step explanation:

perimeter=2(l+w)

948.2=2(250.2+w)

948.2=500.4+2w

948.2-500.4=2w

447.8=2w

w=447.8/2

  =223.9 ft

hey! please help on this question i'll give brainliest <333 .

Answers

Answer:

C, the third choice

Step-by-step explanation:

The Large Counts Condition must be met so that the sampling distribution of a sample proportion is approximately normal. Using appropriate notation, write out the Large Counts Condition for Normality.

Answers

Answer:

np>10 and n(1-p)>10

Step-by-step explanation:

Appropriate notation the Large Counts Condition for Normality is The Large Counts Condition for Normality states that is the number of successes and failures  which should be above the 10 to be assume normality                                    that is here express as n(p)>10 and n(1-p)>10 This is the notation of the Large Counts Condition for Normality.

The Large Counts Condition for Normality: np ≥ 10 and nq ≥ 10.

The Large Counts Condition, also known as the Large Sample Size Condition, is a requirement that must be met to ensure that the sampling distribution of a sample proportion is approximately normal when sampling from a population. This condition is necessary to apply the normal distribution to the sample proportion for various statistical inferences.

Let's denote the following:

- n: The sample size, i.e., the number of observations in the sample.

- p: The population proportion of the characteristic of interest.

- q: The complementary probability to p, such that q = 1 - p.

The Large Counts Condition for Normality states:

np ≥ 10 and nq ≥ 10

In other words, the product of the sample size (n) and the population proportion (p) must be greater than or equal to 10, and the product of the sample size (n) and the complementary probability (q) must also be greater than or equal to 10.

When both of these conditions are satisfied, the sampling distribution of the sample proportion can be approximated by a normal distribution. This approximation is useful for constructing confidence intervals and performing hypothesis tests related to proportions.

To know more about Large Counts, refer here:

https://brainly.com/question/30984845

#SPJ6

(1/2x-3/8) ÷1/3+4/7(5-1/4x)

Answers

Answer:

[tex]\frac{19}{14}x + \frac{97}{56}[/tex]

Step-by-step explanation:

I've written my working in the picture. I hope it's clear. :,)

I've expanded the brackets, simplied the fractions before simplifying them again, having found the common denominators of the constants and x terms.

Question 3
Find the slope-intercept form of the equation of the line that passes through (-6, 2)and is parallel to y=2x+3

Answers

Answer:

How to use Algebra to find parallel and perpendicular lines. ... y = mx + b. Slope- Intercept Form ... Find the equation of the line that is: ... For y = 3x + 2: the slope is 3, and y- intercept is 2.

¿conjunto de fuerzas aplicado sobre un objeto de manera que la linea de accion de todas las fuerzas convergan en un mismo punto?, ¿ cual es el conjunto de esas fuerzas? ​. agradecería mucho si lo contestan porfis uwu

Answers

Answer:

Fuerzas Convergentes

Fuerza Resultante

I kinda need help with this

Answers

Answer:

7.

Step-by-step explanation:

What you can do to figure it out is divide 35 by all the answers. If it comes out even that's the answer. 35/7 = 35

hope this helps, good luck :)

21/5 as a whole number

Answers

4.2 is the answer of this question you are asking ✌️
4.2 is the answer. Hoped this helped a bit!

Nick opens a savings account with $50. Each week after, he deposits $15. In how many weeks will he have saved at least $500?

Answers

Answer:

30 weeks

Step-by-step explanation:

$450÷$5=30

He already had $50 in there

Answer:

30 Weeks

Step-by-step explanation:

Since we need to reach a total of 500, we have 50, so we need 450 to get 500, 15 a week, 30 times 15 equals 450. So (30 Weeks) times (15 Each Week) equals 450 plus that 50 he added in the savings account.

BRAINLIEST PLS HELP!!!

Answers

the answer is a......

Please I need help fast please help me

Answers

Answer:   0-o uhhhh 0-o

uhhhh0-o

Step-by-step explanation:

Jackson practices piano four times a week he practices for 40 minutes each time how many minutes does Jackson practice until weeks

Answers

Answer:

160 min or 2.66666667 hours per a week

Step-by-step explanation:

its very simple

40*4=160

hope I helped :)

Anthony's little brother gets on a carousel that is 8 meters in diameter. At the start of the ride, his brother is 3 meters from the fence to the ride. How far will his brother be from the fence after the carousel rotates 240°?

Answers

Answer:

9 m

Step-by-step explanation:

Given that:

Carousel diameter = 8m

Radius of carousel = 8m / 2 = 4m

From the attached picture :

xo = d ; from the diagram attached ;

Using Pythagoras :

Cosθ = Adjacent / hypotenus

Cos 60 = d / 4

0.5*4 = d

d = 2

d = 2m

d + length of Radius + initial distance from fence

2m + 4m + 3m = 9m

Find each value below.




Answers

Bbbgkwjejejejejehehehejejejejeje

Answer:

7.) x = 21

8.) y = 6

9.) angle F = 62 degrees

10.) TS = 10

Step-by-step explanation:

5y-2 = 28

5y = 30

y = 6

4x+6 = 90

4x = 84

x = 21

angle F = 90-28

angle F = 62 degrees

3z-8 = z+4

2z = 12

z = 6

TS = z+4 = 10

The ratio of boys to girls in a class is 2 to 3. There are 10 boys in the class. How many girls are there? Be sure to show your work.

Answers

Answer:

15 girls

Step-by-step explanation:

Well, the ratio of 2/3, boys to girls. So, you would then try to find an (almost) common denominator, so 2/3 is equivalent to 10/15. In this case, there would be 15 girls

Lol hope this helps

25: Find the value of 9v+9 given that -7v-4=3
Simplify

Answers

Answer:

9v + 9 = 0

Step-by-step explanation:

9 (-1) + 9 = 0

tan 2A + sin 2A=4 tan A/(1 - tan4 A)​

Answers

Answer:

[tex]when \: \\ \tan(2x) = \frac{2 \tan(x) }{1 - {( \tan(x)) }^{2} } \: \: and \\ \sin(2x) = \frac{2 \tan(x) }{1 + {( \tan(x)) }^{2} } \\ then \\ \sin(2x) + \tan(2x) = \frac{2 \tan(x) }{1 - {( \tan(x)) }^{2} } + \frac{2 \tan(x) }{1 + {( \tan(x)) }^{2} } \\ = \frac{2 \tan(x)(1 + {( \tan(x)) }^{2} + 2 \tan(x) (1 - {( \tan(x)) }^{2} }{(1 + {( \ \tan(x)) }^{2}(1 - {( \tan(x)) }^{2} } \\ = \frac{2 \tan(x) \times 2 }{1 - {( \tan(x) }^{4} } \\ = \frac{4 \tan(x) }{1 - {( \tan( \times ) )}^{4} } [/tex]

Step-by-step explanation:

If you need any explanation. I can do it, my friend. you can communicate with me to that or any thing do you need in math

3. Solve for x. Round to the nearest tenth *
25
16
22

Answers

Answer:

51.3 degrees

Step-by-step explanation:

How many times bigger is a group of 21 marbles than a group of 7 marbles?

Answers

Answer:

21/7=3

3 times bigger.

Step-by-step explanation:

M<6=(x+10), m<2=(x+15)
<6 and <2 are alternate interior angles

Answers

Answer:

ano ang pinag kaiba noon kaysa ngayon

Find C and a so that f(x) = CaX models the situation described. State what the variable x represents in your formula. In 2000 a house was worth $220,000, and its value decreases by 11% each year thereafter. please help im failing ​

Answers

Answer:

f(x) = Ca^x

x = years since 2000.

f(0) = 220000 = Ca^0 = C

f(x) = 220000a^x

f(1) = 220000(1-0.11) = 220000a^1

a = 0.89

f(x) = 220000(0.89)^x

So each year reduces by 89%

Ivan and Tanya share £150 in the ratio 4: 1
Work out how much more Ivan gets compared to Tanya.​

Answers

Answer:

Ivan got £90 more than Tanya.

Step-by-step explanation:

Ivan and Tanya share the amount £150 in the ratio of 4 : 1

Amount received by Ivan = [tex]150\times \frac{4}{(4+1)}[/tex]

                                          = [tex]150\times \frac{4}{5}[/tex]

                                          = £120

Similarly, amount received by Tanya = [tex]150\times \frac{1}{(4+1)}[/tex]

                                                             = £30

Difference in their amounts = 120 - 30

                                              = £90

Therefore, Ivan got £90 more than Tanya.                                                                                                        

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