Consider the first 2 terms of the sequence -6, 18,...
1. Determine the next 5 terms in the sequence if the sequence is arithmetic. Then write a function to
represent the arithmetic sequence.
2. Determine the next 5 terms in the sequence if the sequence is geometric. Then write a function to
represent the geometric sequence.

Answers

Answer 1

Answer:

arithmetic sequence: 24, 42, 66, 90, 114; y = 24x - 30

geometric sequence: -54, 162, -486, 1458, -4374; y = -6(-3)^(x - 1)

Step-by-step explanation:

Arithmetic sequence:

-6, 18, ...

18 - (-6) = 24

18 + 24 = 42

42 + 24 = 66

66 + 24 = 90

90 + 24 = 114

y = -6 + 24(x - 1)

y = -6 + 24x - 24

y = 24x - 30

Geometric sequence:

-6, 18, ...

18/(-6) = -3

18 * (-3) = -54

-54 * (-3) = 162

162 * (-3) = -486

-486 * (-3) = 1458

1458 * (-3) = -4374

y = -6(-3)^(x - 1)

Answer 2

The next 5 terms in the arithmetic sequence are 42, 66, 90, 114, 138.

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

Given that, the first 2 terms of the sequence -6, 18,....

Here, a=-6 and common difference = 18-(-6) =24

So, the next 5 terms in the arithmetic sequence are

18+24=42, 42+24=66, 66+24=90, 90+24=114, 114+24=138

42, 66, 90, 114, 138

The function is aₙ= -6+(n-1)24

= -6+24n-24

= 24n-30

The next 5 terms in the geometric sequence are

Here, a=-6 and common ratio = 18/(-6) =-3

Now, 18×(-3)=-54, -54×(-3)=162, 162×(-3)=-486, -486×(-3)=1458, 1458×(-3)=-4374

The function is [tex]a_n=-6(-3)^{n-1}[/tex]

Therefore, the next 5 terms in the arithmetic sequence are 42, 66, 90, 114, 138.

To learn more about an arithmetic sequence visit:

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Related Questions

A carpenter is making a wooden window frame that has a width of 1 inch. How much wood does the carpenter need to build the frame? 5.5 + 106 square inches 5.5 + 116 square inches 5.5 + 153 square inches 5.5 + 162 square inches

Answers

Diagram attached

Answer:

5.5+106 square inches

Step-by-step explanation:

The wooden frame has different shapes- semi circle, rectangles  and we would have to calculate area of all the shapes to get the wood required.

To get area of the circle, we use the formula π(R²-r²)/2. Subtract the inner radius from the outer radius =

π(6²-5²)/2= 11π/2

=5.5π square inches

We add area of the semi circle to area of the 3 rectangles from the diagram:

2×1×48×10×1=106 square inches

The rectangle with 10 inches is because we subtracted one inch from both sides of the 12 inches rectangle to avoid repetition and overvaluing the area

Total area =5.5π +106 square inches

Options must have ommitted the "π"

Answer:

5.5 + 106 square inches

Step-by-step explanation:

Correct on edge

Ehich of thr following expressions has a Simplified value of 3A -2?

Answers

the answer is B. -a+4+5a-a-6

illustrate. Then solve the
1.) A car is able to travel 210 km in 3 hours. How far can it
travel in 5 hours?​

Answers

Answer:

350 km

Step-by-step explanation:

210/x=3/5

x=350

tadaaa

350 km
Coras multiply and divide

someone HELP pls
what the value of -1/4[12x-0.2(12x + 8x]

Answers

Answer:

-2x

Step-by-step explanation:

What is the value of x?
799
A. 36°
B. 14°
C. 1440
D. 56

Answers

Option A because the whole triangle equals 180 degrees so as long as your option plus the numbers in the triangle equal 180° you will get it right

Write an equation for the line in slope-intercept
form
(Use integers or fractions for any numbers in the
equation.)

HELP I DONT UNDERSTAND !!

Answers

Answer:

I got m=(-2)

Step-by-step explanation:

y2-y1/x2-x1

4-0/0-2

4/-2

4/-2

-2

the slope is -2

can someone please help me with number 12? there’s only two options and you can see them in the picture.

Answers

Answer:

B)

Step-by-step explanation:

Because it can't be a because if you wanna get P it is 20/16 not 1 /12

Please answer correctly !!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!

Answers

Answer: 4). 35,56,89

Step-by-step explanation: for a triangle to be acute all three angles have to measure below 90 degrees

Answer:

your answer would be 4 or D

Step-by-step explanation:

a acute angle is and angle from 30-89

a 90 degree angle is just 90 degrees

and an obtuse angle is 91-130

so therefore you have your answer

D or 4

mark me brainiest

thanks for the points too

anddddd

sparkled and love

☆*: .。. o(≧▽≦)o .。.:*☆

Please Help

(x+50)/2 = 13x

Answers

Answer:

X=2

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

PLEAS HELP ASAP!!! What is the equation for the line in slope-intercept form? ​

Answers

Answer:

[tex]y = 8x[/tex]

Step-by-step explanation:

Find slope by using Rise/Run.

Use two coordinate points that are part of the graph.

(0,0) and (2,16)

[tex]m = \frac{16 - 0}{2 - 0} \\ m = \frac{16}{2} \\ m = 8[/tex]

We have the slope. We need to find the y-intercept.

From the graph, the graph passes y-axis (0,0). Therefore the y-intercept is at (0,0)

[tex]y = mx + b[/tex]

[tex]m = 8 \\ b = 0[/tex]

Substitute m = 8 and b = 0 in the equation.

[tex]y = 8x + 0 \\ y = 8x[/tex]

how many heavier is 9 pounds 20 ounces than 160 ounces (1 pound = 16 ounces)

Answers

1 pound = 16 ounces.

9 pounds 20 ounces =

9 x 16 = 144

144 + 20 = 164

164-160 = 4

9 pounds 20 ounces is 4 ounces heavier than 160 ounces.

Answer:

1 pound = 16 ounces

9 pounds 20 ounces =(9×16)+20= 144+20 =164 ounces

(164-160) ounces

9 pound 20 ounces is 4 ounces heavier than 160 ounces

4 ounce is the right answer.

how to factor 4x + 3 - 6x + 7

Answers

Answer:

im sorry if this is wrong if its what I was doing you have to switch 4x and 3 places Minusing 4x from 6x giving negative 2x or -2x then adding 3 to get 10 getting -2x + 10 or you could get -2x - 10

A chess club with 80 members is electing a new president. Hans received 32 votes. What percentage of the members voted for Hans?

Answers

Answer: 40%

Step-by-step explanation: To find what percentage of members voted for Hans simply multiply 32 by 100.

32 x 100 = 3200.

Then, divide that number, or 3200 by 80.

3200/80 = 40.

So, 40, or 40% of members voted for Hans.:)

PLEASE HELP THIS IS MY FINAL EXAM FOR ALGEBRA
The population of a town is decreasing at a rate of 1% per year. In 2000 there were 1300 people. Find the population of the town in 2008. *

Answers

Answer:

The answer is 1,300 people

f(x) = x2. What is g(x)?

A. g(x) = (3x)2
B. g(x) = 3x2
C. g(x) = 9x2
D. g(x)=1/3 X2

Answers

D lmk if that worked bud

Please answer correctly !!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!

Answers

Answer:

e

Step-by-step explanation:

E I just did this in edgunity

Which set of ordered pairs does not represent a function?
{(7,8),(−4,4),(3,8),(−7,−1)}
{(−5,−3),(−1,−8),(−7,0),(−5,−9)}
{(8,4),(6,−1),(−4,5),(9,4)}
{(8,−3),(4,0),(−4,9),(3,2)}

Answers

Answer:

The second one [(-5,-5),(-1,-8),(-7,0),(-5,-9)]

Step-by-step explanation:

This is because there is more than 1 point with the same X-Value

cos sec² a - cot²a=1​

Answers

Answer:

The relation is:

cosec^2(a) - cot^2(a) = 1.

Where:

cosec(x) = 1/sin(x)

cot(x) = 1/tan(x) = cos(x)/sin(x)

Let's prove this.

Ok, we know by the Pythagorean theorem, that:

r^2 = x^2 + y^2

And we have the trigonometric relations, for an angle "a" measured from the x-axis

cos(a) = x/r

sin(a) = y/r

tan(a) = y/x

Where r is the hypotenuse, x and y are the catheti.

Now, let's divide the  Pythagorean theorem by y^2 in both sides to get:

(r^2/y^2) = (x^2 + y^2)/y^2

r^2/x^2 = x^2/y^2 + y^2/y^2

r^2/y^2 = 1 + x^2/y^2

(r/y)^2 = 1 + (x/y)^2

and remember that:

y/r = sin(a)

then:

r/y = 1/sin(a) = cosec(a)

(r/y)^2 = cosec^2(a)

and:

y/x = tan(a)

then:

x/y = 1/tan(a) = cot(a)

and:

(x/y)^2 = cot^2(a)

replacing these in the equation (r/y)^2 = 1 + (x/y)^2 we get:

cosec^2(a) = 1 + cot^2(a)

cosec^2(a) -  cot^2(a) = 1

help pls..............

Answers

the answer is between D or C

Write the numerical expression as a power

giving brainlest if u do!!​

Answers

Answer: See explanation

Step-by-step explanation:

2. [tex]6^{5}[/tex]

4. [tex]3^{9}[/tex]

6. [tex]9^{3}[/tex]

8.[tex]\frac{2}{5} ^{2}[/tex]

Answer:

[tex]6^{5} \\3^{9} \\9^{3} \\\frac{2}{5} ^{2}[/tex]

Step-by-step explanation:

Describe the lines below as parallel,
perpendicular, or neither.

2x - 5y = 25 and y= 5x+3

Answers

Answer:

Neither.

Step-by-step explanation:

First, we write 2x - 5y = 25 in slope-intercept form. That gets us y = 2/5x - 5. Now, we graph both the lines (check the image attached). Parallel means extending in the same direction, everywhere equidistant. Perpendicular means the relationship between two lines that meet at a right angle (90 degrees). As we can see in the screenshot, these lines don't fit any of these categories, so we put "neither."

The lines 2x - 5y = 25 and y = 5x + 3 are neither parallel nor perpendicular

What are lines and their slopes?

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Equations of two lines are given, They are 2x - 5y = 25 and y = 5x + 3.

Now, Writing them in slope-intercept form,

2x - 5y = 25.

- 5y = - 2x + 25.

y = (2/5)x - 5.

And,

y = 5x + 3.

Now, We know lines parallel to each other have the same slope, and lines perpendicular to each other have a slope that is negative reciprocal of each other.

Therefore the lines y = (2/5)x - 5 and y = 5x + 3 are neither parallel nor perpendicular.

learn more about lines and slopes here :

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Can someone help me with this

Answers

Answer:

Expanded form - 90,000+400+3

Number names - Ninety thousand four hundred and three

1/2 (3x – 7) = 2(x - 3)

Answers

3/2x–7/2=2x–6
3/2x-2x=7-6
-1/2x=1
x=1:1/2
x=2

Jeffrey is making cookies to sell at the school fair. For one dozen cookies, he needs 2 ¼ cups of flour. if he has 33 ¾ cups of flour, how many dozen cookies can he make? How many total cookies can he make?

Please help me with this math problem‍​

Answers

Answer

Pretty sure he can make 15 dozens. Which means he can make 180 cookies.

Step-by-step explanation:

First, you would need to find how many times 2 1/4 cups can go into 33 3/4 cups. This would let you know how many dozens he can make. You would get an answer of 15 dozens. Then, you would multiply 15 times 12. You would multiply by 12 because a dozen is 12. You would then get an answer of 180. This means that he can make 180 cookies.

Hope I helped! :) Sorry if it's wrong :(

How many total pounds did the art club donate?

Answers

Answer:

see explanation

Step-by-step explanation:

the total pound did the art club donate is 468 pound

The surface area of the pyramid is

square inches.
fill in the blank

Answers

20736 squared inches
Find area of triangle first
(9*6)/2
27
Since there are four triangles
27*4
108
Area of a square
6*6
36
Add them
108+36
144
To get it to square inches multiply by 144
144*144
20736

solve the equation f(x)=2x+7 ​

Answers

Answer:

2

Step-by-step explanation:

How to do the problem below, and can you show the work as well, thanks.

Answers

Answer:

it should be B. welcome!!

Step-by-step explanation:

Which decimal is equivalent to the fraction 1/15?

Answers

Answer: 0.06 with 6 repeating

Step-by-step explanation:

You have to divide 1 by 15. You get 0.066666666666 which is the game as 0.06 with the 6 repeating.

Select ALL the true statements
a. Two squares with the same side lengths are always congruent.
b. Two rectangles with the same side lengths are always congruent.
c. Two rhombuses with the same side lengths are always congruent.
d. Two parallelograms with the same side lengths are always congruent.

Answers

Answer:

a

b

c

d

Step-by-step explanation:

balshdhsbwwqzhwhw

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