Write a recursive formula for the sequence 7, 4, 1, -2, -5, .... Then find the next term.


A. [tex]a_{n} = a_{n - 1} - 3[/tex], where [tex]a_{1} = -8[/tex]; 7

B. [tex]a_{n} = a_{n - 1} - 3[/tex], where [tex]a_{1} = 7[/tex]; -8

C. [tex]a_{n} = a_{n - 1} + 3[/tex], where [tex]a_{1} = -3[/tex]; 22

D. [tex]a_{n} = a_{n - 1} + 3[/tex], where [tex]a_{1} = 7[/tex]; -8

Answers

Answer 1

Answer:

option B

Explanation:

Recursive Formula: aₙ = aₙ₋₁ + d

Given Sequence: 7, 4, 1, -2, -5,....

Identify the common difference:

second term - first term

4 - 7 = -3  or 1 - 4 = -3 or -2 - 1 = -3

So formula:

[tex]\sf a_n = a_{n-1}-3[/tex], where [tex]\sf a_1 = 7[/tex]

Find next term:

[tex]\sf a_6 = a_{6-1}-3 = -5-3 = -8[/tex]


Related Questions

Figure A is a scale image of figure B

Answers

Answer:

x = 7.5 units

Step-by-step explanation:

10   *   .75    = 7.5

Grace collected data from twenty of her friends about the number of pets they have. The median number of pets is two.

What does the median say about Grace's data set?
Answer options with 4 options
A.
Everyone Grace surveyed has two pets.
B.
More of Grace's friends have two pets than any other number.
C.
Two is the middle number when the number of pets in the data set is ordered from least to greatest.
D.
Two is the difference between the greatest and least number of pets Grace's friends have.

Answers

The statement which median describe about Grace's data set is 2 is the middle number when the number of pets in the data set is arranged from least to greatest.

What is the median of a data set?

The median of the data is the middle value of the data set when it arrange in ascending or descending order.

Grace collected data from twenty of her friends about the number of pets they have.  The median number of pets is two.

Median=2

By the definition of median of data set, the median two tells that the middle value of the pet is 2 when arranged in high to low point.

Thus, the statement which median describe about Grace's data set is 2 is the middle number when the number of pets in data set is arranged from least to greatest.

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22. Which of the following is the equation of the circle shown below? .2 = a. x2 + (y + 3)2 = 3 b. x2 + (y - 3)2 = 3 c. x2 + (y + 3)2 = 9 d. x2 + (y - 3)2 = 9 = --13 2​

Answers

Answer:

23456789-123456789

Step-by-step explanation:

es la cuadricula

NEED ANSWER ASAP
Analyze the graph below to identify the key features of the logarithmic function. (6 points)

The x‐intercept is x = −5, and the graph approaches a vertical asymptote at x = −6.
The x‐intercept is y = −5, and the graph approaches a vertical asymptote at y = −6.
The x‐intercept is x = 5, and the graph approaches a vertical asymptote at x = 6.
The x‐intercept is y = 5, and the graph approaches a vertical asymptote at y = 6.

Answers

The x intercept is lies at the midpoint of (-6 and -4

so

x=-5 is the x intercept

And it's translation of logx

translated equation

y=log(x+6) as log x has x intercept at 1

Now the vertical asymptote is at

(x+6)=0x=-6

Option A

Answer:

The x‐intercept is x = −5, and the graph approaches a vertical asymptote at x = −6

Step-by-step explanation:

From inspection of the graph:

x-intercept is where the curve intercepts the x-axis → x = -5

y-intercept is where the curve intercepts the y-axis → y ≈ 0.75

An asymptote is a horizontal or vertical line which the curve gets infinitely close to, but never touches.

From the portion of the curve in the graph, it appears that the curve gets very close to but never touches:

the vertical line x = -6the horizontal line x = 1

(However, without seeing a large portion of the graph, we cannot be sure, particularly for the horizontal asymptote).

Therefore, from the given solution options:

The x‐intercept is x = −5, and the graph approaches a vertical asymptote at x = −6

A cube has a volume of 0.215ft³. What is te length of each side of the cube?

Answers

Answer:

length ≈ 0.599 feet

Step-by-step explanation:

volume = length³

0.215ft³ = length³

cube root both sides to isolate the length

∛(0.215ft³) = length

length ≈ 0.599 feet

<~~• ¥ Pls HELP me!! ¥ • ~~>

I can’t figure out the 3 box’s pls help

Answers

Answer:

the 4th box is divided by 2. sorry but don't know the others

Step-by-step explanation:

PLEASE HELP ME I NEED HELP

Answers

Step-by-step explanation:

here you go hope it helps

Answer:

a = 9

b = 9√3

Step-by-step explanation:

Please help.
fiona asked 150 students to select their favorite fruit and then recorded the results in the bar graph below. fiona will ask another 45 students to select their favorite fruit. based on the information in the bar graph, how many more students from the next 45 are likely to select oranges rather than bananas their favorite fruit?

Answers

The number of students that are more likely to select oranges rather than bananas their favorite fruit from the next 45 is; 3.

What no. of students from the next 45 are likely to select oranges rather than bananas their favorite fruit?

It follows from the task content that the number of students surveyed initially is 150 and only, 30 -20 = 10 students preferred orange to bananas.

On this note, it follows that the number of students who prefer oranges rather than bananas from the next 45 is; = (45 × 10)/150 = 3.

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3/5 x 2/3 [please help bme bronroer

Answers

Answer:

3/5 = 0.6

2/3 = 0.6 (recurring)

0.6 x 0.6

= 0.36

Answer:

[tex] \dfrac{2}{5} [/tex]

Step-by-step explanation:

[tex]\dfrac{3}{5} \times \dfrac{2}{3} = \dfrac{3 \times 2}{5 \times 3} = \dfrac{3 \times 2}{3 \times 5} = \dfrac{3}{3} \times \dfrac{2}{5} = 1 \times \dfrac{2}{5} = \dfrac{2}{5}[/tex]

PLEASE HELP WILL MARK BRAINLIEST 45 POINTS

Answers

Answer:

I got 58.5

I multiplied 3x9 to get 27

then 3x6 to get 18

then 3x9/2 to get 13.5 and added them all together.

Area of bottom triangle = 27/2= 13.5
Area of bottom rectangle = 9x3=27
Area of upper rectangle = 6x3=18

Hope I helped!

Help Please. Solve for x.​

Answers

Answer:

x = 16

Step-by-step explanation:

sec(60) = 32 /x

2 = 32/x

x2 =32

x = 16

What is |1 − 8i|?
A. 65
B. √13
C. √-65
D. √65

Answers

Hey There !

|1-8i| is in the form of |a+bi| = √a^2+b^2

So now ,

a = 1 b=-8

=> √1^2+(-8)^2

=> √1+64

=> √65

Hence option D is correct

Hope this helps you!:)

jackson bought 3 pounds of candy for 9.60. What was the price of this candy in cents per ounce? PLS HELP

Answers

Answer:

The price of candies in cents per ounce is 20 cents per ounce.

Step-by-step explanation:

960 cents/(48 oz) = 20 cents/oz

4x - 5y = 20 , what are the steps for solving for y?

Answers

Answer:

Check explanation below!

Step-by-step explanation:

» Solving

Step 1: Subtract 4x from both sides.

[tex]4x-5y-4x=20-4x[/tex] [tex]-5y=-4x+20[/tex]

Step 2: Divide both sides by -5.

[tex]\frac{-5y}{-5} = \frac{-4x+20}{-5}[/tex] [tex]y=\frac{4}{5}x-4[/tex]

please help me solve this solve the triangle round to nearest tenth​

Answers

Answer:

the measurement of the angle A is 39.17°

Simplify [tex]\frac{sin^2x+cos^2x}{sin x}[/tex]

Answers

Let's see

[tex]\\ \rm\Rrightarrow \dfrac{sin^2x+cos^x}{sinx}[/tex]

sin²x+cos²x=1

[tex]\\ \rm\Rrightarrow \dfrac{1}{sinx}[/tex]

[tex]\\ \rm\Rrightarrow cosecx[/tex]

Answer:

cosec x

(or csc x)

Step-by-step explanation:

Trig Identities

[tex]\sf \sin^2 x + \cos^2 x=1[/tex]

[tex]\sf \dfrac{1}{\sin x}=cosec\: x[/tex]

Therefore,

[tex]\begin{aligned}\implies \sf \dfrac{\sin^2x + \cos^2x}{\sin x} &= \sf\dfrac{1}{\sin x}\\\\ & = \sf cosec\:x \end{aligned}[/tex]

-
Which equation has the same solution as x2 - 6x - 12 = 0?
A (x + 3)2 = 21
B (x - 3)2 = 21
(x + 3)2 = 3
Dx-3) = 3

Answers

Answer:

[tex](x-3)^2 =21[/tex]

Step-by-step explanation:

[tex]~~~~~~~x^2-6x-12=0\\\\\implies x^2 -6x +9-21=0 \\\\\implies x^2 -2\cdot x \cdot 3 +3^2=21\\\\\implies (x-3)^2 =21[/tex]

FIND THE EXACT AREA PLEASE HELP ILL GIVE BRAINLIESTTTT

Answers

Check the picture below.

[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2-r^2)~~ \begin{cases} r=\stackrel{smaller}{radius}\\ R=\stackrel{larger}{radius}\\[-0.5em] \hrulefill\\ r=2\\ R=3 \end{cases}\implies \begin{array}{llll} A=\pi (3^2-2^2)\implies A=5\pi \\\\\\ A\approx 15.71 \end{array}[/tex]

Which graph correctly shows point A as the sum of the complex numbers z1 and z2?
Which graph correctly shows point A as the sum of the complex numbers z1 and z2?
A.

B.

C.

D.

Answers

The graph which correctly shows the point A as the sum of the complex numbers z₁ and z₂ is graph number 4.

What is complex number?

A complex number is the combination of real and imaginary number. In a complex number, real part and imaginary part of the number are written together. For example,

a+bi

Here, (a) is the real part while (b) is the imaginary part.

To add the two complex number on the graph, the addition as transition method is used.

In this one complex number is translated to the tip of the other graph. The resultant of addition is equal to the distance between them.

On the graph 4, the transition method of addition is applied.Thus, the graph which correctly shows the point A as the sum of the complex numbers z₁ and z₂ is graph number 4.

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The orbit of a planet around the sun is not circular; it is an ellipse with
the Sun at one focus. The aphelion of a planet is the greatest distance
from the sun and the perihelion is its shortest distance. The mean
distance of a planet from the sun is the length of the semimajor axis of
the elliptical orbit. The perihelion of Pluto is 4551 million miles, and the
distance from the center of its elliptical orbit to the sun is 897.5 million
miles. Find the aphelion of Pluto. What is the mean distance of Pluto
from the Sun? Write an equation to represent the orbit of Pluto around
the Sun.

Answers

The equation to represent the orbit of Pluto around the Sun will be x²/4659.42 + y²/4566.31 = 1.

How to compute the equation?

The distance from the center of the elliptical orbit to the sun is 897.5 million miles. The aphelion will be:

= 5448.5 + 897.5

= 6346 million miles

The equation of ellipse will be:

x²/a² + y²/b² = 1

x²/4659.42 + y²/4566.31 = 1

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What is the circumference of a circle with a diameter of 85 feet?
feet
(Use 3.14 for Pi.)

Answers

Answer:

266.9 feet

thats the answer

sana makatulong poww huhu

Answer: 266.9 ft

Step-by-Step Solution:

d = 85 ft
r = 85/2 = 42.5 ft

Circumference = 2πr

Therefore,
= 2πr
= 2 * π * r
= 2 * 3.14 * 42.5
= 6.28 * 42.5
= 266.9

=> Circumference = 266.9 ft

Design a poster
DESIGN A POSTER TO
SHOW HOW TO COMPARE
AND ORDER DECIMALS.

Answers

Answer:

but how do you want it done?

Step-by-step explanation:

HELP please need this now

Answers

Answer:

3000 square inches.

Step-by-step explanation:

First, scale this one up. Multiply each by 2. consider area of a trapezoid. A = 1/2 (b1 + b2) h. This will be 1/2 (20 + 30) * 20, so you'll get 500 square in. Then, multiply by 6 since Buffy is making 6 of them. 500 * 6 = 3000 square inches.

will mark brainlist if you answer ! :)

Answers

Answer:

Option 4

Step-by-step explanation:

What is the area of this right triangle?

30 mm²

39 mm²

60 mm²

78 mm²

Answers

Answer:

30

Step-by-step explanation:

since we are looking for the area of a right triangle you want to use the legs of the triangle. Basically 5x12 over 2= 30, I think I am correct if not I apologize/

Answer:

the answer is 78

Step-by-step explanation:

12x 5= 60

60x13=180

180+600=780

the answer equals up to 78

The product of the polynomials (3x 2) and (-x^3 – 3) is . when this product is multiplied by (3 x), the coefficient of x4 in the result is

Answers

Answer:

(3x + 2)(-x^3 - 3) =

3x(-x^3 - 3) + 2(-x^3 - 3) =

-3x^4 - 2x^3 - 9x - 6 <== result of multiplying (3x+2)(-x^3-3)

now multiply that by (3+x)...

(3+x)(-3x^4 - 2x^3 - 9x - 6) =

3(-3x^4 - 2x^3 - 9x - 6) + x(-3x^4 - 2x^3 - 9x - 6) =

-9x^4 -6x^3 - 27x - 18 - 3x^5 - 2x^4 - 9x^2 - 6x =

-3x^5 - 11x^4 - 6x^3 - 9x^2 - 33x - 18 <== result of multiplying by (3 + x)

the coefficient of x^4 = -11 <==

Step-by-step explanation:

Answer:

(3x + 2)(-x^3 - 3) =

3x(-x^3 - 3) + 2(-x^3 - 3) =

-3x^4 - 2x^3 - 9x - 6 <== result of multiplying (3x+2)(-x^3-3)

now multiply that by (3+x)...

(3+x)(-3x^4 - 2x^3 - 9x - 6) =

3(-3x^4 - 2x^3 - 9x - 6) + x(-3x^4 - 2x^3 - 9x - 6) =

-9x^4 -6x^3 - 27x - 18 - 3x^5 - 2x^4 - 9x^2 - 6x =

-3x^5 - 11x^4 - 6x^3 - 9x^2 - 33x - 18 <== result of multiplying by (3 + x)

the coefficient of x^4 = -11 <==

Step-by-step explanation:

What is the sum of the first five terms in this series?
6 - 6/3 + 6/9 - 6/27 + . . .?

Answers

Answer:

4 14/27

Step-by-step explanation:

The first five terms

6

-6/3

6/9

-6/27

+6/81

The first thing to do is change all the fractions denominators to 81.

Sum = 6*81/81 - 6(27)/81 + 6*9/81 - 6*3/81 + 6/81

Now add

Sum = 366/81

Sum = 4 14/27

Sum = 4.5185

Note the first term. It has been multiplied by 6*81/81. The 81 over 81 does not change the value of anything 6 * 81/81 is still 6. It just makes it easier to combine with the other members of the series.

$6300 at 5% annual rate, compounded semi- annually, for 2 years

Answers

Answer:

$6954.02.

Step-by-step explanation:

The formula is

A = P(1 + 0.05/n)^2n   where A is the amount compounded, P = initial investment and n is the number of years.

A = 6300(1 + (0.05)/2)"(2*2

=  6954.02

Find the value of X. Round to the
nearest tenth.
7.4in
2.4in
x

Answers

Answer:

4.4 inches

Step-by-step explanation:

Here, we are interested in calculating the value of x.

Mathematically, a line that comes from the center of the circle and extends to a chord, divides the chord into two equal parts.

This means what we have is a right angled triangle with the radius being the hypotenuse, the half of the length of the chord as the other side of the triangle.

3.7 is half the length of the chord i.e 7.4/2

Thus;

using Pythagoras’ theorem

x^2 = 2.4^2 + 3.7^2

Pythagoras’ posited that the square of the hypotenuse is equal to the sum of the squares of the other two sides of the triangle.

Thus;

x^2 =5.76 + 13.69

x^2 = 19.45

x = √(19.45)

x = 4.41 inches which is 4.4 inches to the nearest tenth

Answer:

Central angle = 31 / 4 radians

=

Length of the arc = (3 1 / 4) (radius) = 45 in

=

=> radius = 45 in * 4 / (31) = 45 * 4 / (3 * 3.14) in

=

radius = 19.1 in

=

Answer: 19.1 in

Step-by-step explanation:

Correct me if I'm wrong

Please help brainliest who answer's first and correct

Answers

Answer:

just start at like 220 i am pretty sure

Step-by-step explanation:

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