Find an explicit formula for the geometric sequence below.

Find An Explicit Formula For The Geometric Sequence Below.

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

The nth term ( explicit formula) of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = - 2 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{\frac{4}{3} }{-2}[/tex] = - [tex]\frac{2}{3}[/tex] , then

[tex]a_{n}[/tex] = - 2 [tex](-\frac{2}{3}) ^{n-1}[/tex] ← explicit formula

Answer 2

Answer:

Step-by-step explanation:

The formula for an explicit geometric formula (as opposed to a recursive one) is

[tex]a_n=a_1(r)^{n-1}[/tex] where a(n) is representative of the position of a number in the sequence, a(1) is the first number in the sequence, and r is the common ratio. The common ratio is the same number that must be either multiplied in or divided out to get to the next number in the term. Notice that the top numbers in our sequence are doubling which implies we are multiplying the top numbers by -2, and the bottom numbers are going up by multiples of 3. So our common ratio is -2/3. Try it and see:

[tex]-2(-\frac{2}{3})=\frac{4}{3}[/tex]  and

[tex]\frac{4}{3}(-\frac{2}{3})=-\frac{8}{9}[/tex] etc.

Therefore, the explicit geometric formula for this sequence is

[tex]a_n=-2(-\frac{2}{3})^{n-1[/tex]

You can use this formula to find any number in the sequence; for example, if you wanted to know the 100th number in this sequence, simply replace n with 100 and do the math. That's what an explicit formula is used for.


Related Questions

big ideas integrated 1 chapter 8 test? anyone ?

Answers

Answer:

Uh, sure! :)

Step-by-step explanation:

Please help :) will mark brainliest

Answers

Answer:

1) C: 113 m

2) C: 572.3 m²

3) B: 61.2 cm²

4) A: $2.2

6) C: 756 yd³

8) D: 3402 mm²

9) A: 25x + 125 < 500

Step-by-step explanation:

1) Formula for circumference of circle is;

C = 2πr

radius; r = 18 m

C = 2π × 18

C ≈ 113 m

2) Formula for area of a circle is;

A = πr²

Here we have diameter; d = 27

Thus, radius; r = 27/2 = 13.5 m

A = π × 13.5²

A = 3.14 × 13.5²

A ≈ 572.3 m²

3) The diameter of the semicircle is parallel to the base of the rhombus. Thus, diameter; d = 7 cm

Thus, r = 7/2 = 3.5 cm

Area of semi circle = ½πr² = ½ × π × 3.5² = 19.2 cm²

Area of rhombus = base x height = 7 × 6 = 42 cm²

Total area of object = 42 + 19.2 = 61.2 cm²

4) Cost of banana per pound = $0.4 per pound

Amount of banana bought = 5.5 pound

Amount spent = 0.4 × 5.5 = $2.2

6) Volume of triangular prism is;

V = ½bhl

b = 12 yd

h = 7 yd

L = 18 yd

Thus;

V = ½ × 12 × 7 × 18

V = 756 yd³

8) Volume of cuboid at the base;

V1 = lbh = 25 × 9 × 9 = 2025 mm²

Volume of cuboid at top;

V2 = 9 × 9 × 9 = 729 mm²

Volume of triangular prism;

V3 = ½bhl = ½ × 9 × 9 × (25 - 9) = ½ × 81 × 16 = 648 mm²

Total volume = 2025 + 729 + 648 = 3402 mm²

9) Cost per class; $25 per class

Charge for the supplies = $125

He doesn't want to spend more than $500.

Thus;

25x + 125 < 500

Decide whether the ordered pair (-2,-8) is a solution of the equation.
y = 4x
Is (-2,-8) a solution to y = 4x?
Yes or no

Answers

Answer:

Yes it is

Step-by-step explanation:

Because 4 ×-2=-8

The area of the parallelogram below is___square meters

Answers

Answer:

48 m^2

Step-by-step explanation:

Since this is a parallelogram, you can think of it as taking the triangle off of the left side and reattaching it on the right side to make a rectangle. After you visualize it as a rectangle, you just have to multiply 8 by 6 to get 48 meters squared.

What is the surface area?
Find the surface Area?

Answers

Answer:

[tex]150 km^{2}[/tex]

Step-by-step explanation:

Use the surface area equation of cylinder: [tex]A = 2\pi rh + 2\pi r^{2}[/tex]

The diameter is 6 km but you need the radius for the formula, so you divide the diameter by 2.

6÷2 = 3 --> r = 3

You already know h, aka the height.

Plug everything into the equation.

Answer:

150.72

Step-by-step explanation:

im usin 3.14 as pi btw

the term net means like imagine you unfold the shape like the walls of the shape are paper. its now a 2d net, which includes a rectangle and two circles.

so, surface area of a circle is pi r^2 so 3.14 * 3 * 3 = 28.26

times two cause theres two circles; top and bottom :3

56.52 = 28.26 * 2

rentangle surface area = h*l

the height of the rectangle is 5 and the length is the circumference of the circle

circumference is 2*3.14*r, which in this problem, is 3

2*3.14*3 = 18.84

now, h*l is 18.84*5 = 94.2

94.2 + 56.52 = 150.72

i just need a little help on this one sorry for the bother

Answers

Answer:

they look like their curved at about  70? 65? and they would be the same

Step-by-step explanation:

Answer: Both C and D are 76

Step-by-step explanation:

Because this is a isosceles triangle both C and D are the same. Subtract 28 from 180 and you get 152. So D and C combined equals to 152 so divide that by 2 an you get 76.

here is a graph of y=x^2-7x+10 for values of x from 0 to 7.

write down the roots of x^2 -7x +10=0.
ASAP please

Answers

Answer:

Roots of the function are x = 2, 5.

Step-by-step explanation:

Roots of a function are defined by the x-intercepts of the graph.

From the given graph in the question,

x-intercepts → x = 2, 5

Now confirm it by solving the equation algebraically,

x² - 7x + 10 = 0

x² - 5x - 2x + 10 = 0

x(x - 5) - 2(x - 5) = 0

(x - 5)(x - 2) = 0

x = 2, 5

Therefore, roots of the function are x = 2, 5.

< 3 Plz help 10th grad maths < 3 i don't understand
b. Calculate the equivalent resistance of the circuit.
c. Calculate the current through the battery.
d. How much current is passing through each resistor?
e. Calculate the voltage drop across each resistor.
f. How does the voltage drop across each resistor compare to the voltage of the battery?

Answers

Answer:

Step-by-step explanation:

this is math or physics

Answer:

brainliest please, sorry for the inconveniences

8. The sum of three consecutive multiples of 11 is 759. Find the multiples.

Answers

Answer:

252, 253, 254

Step-by-step explanation:

[tex] \frac{759}{3} \\ = 253[/tex]

253 is the median. so the multiples will be 252, 253, 254

use circle C

classify arc MNO in circle C

Answers

Answer:

Semicircle

Step-by-step explanation:

As we can see, the arc is bounded by the chord MO

since the chord passes through the center of the circle, we have it that the chord is a diameter

Mathematically, an arc bounded by a diameter represents half of a circle

So we can conclude that the arc MNO in circle C is a semicircle

The conjugate of complex number z = 3 + 2i is

Answers

_

z = a-bi

i think this is the answer

Pls helppp!!! Find the ninth term of the sequence
5,4,1,-4,-11...
The ninth term is??

Answers

Answer:

-20 because it's 5-1=4-3=1-5=-4-7=-11-9=-20

Answer:

-59

Step-by-step explanation:

It's subtracting each number by the next ODD number

subtract 1

subtract 3

then 5, 7, 9 and so on

how to measure latitudes​

Answers

Answer:

Lines of latitude run in horizontal parallels and represent distance north or south from the equator, measured in an angle from the centre of the Earth. The equator represents 0° and each pole represents 90°

Step-by-step explanation:

Answer: Hope This Helps!

Step-by-step explanation:

Use the sight line on the top of the aiming beam to align the beam with the North Star. Use the protractor to measure the angle between the beam and the horizon (which is 90º to the plumb line). This angle is your latitude.

Find the value of x so that x – 4 = -2

Answers

Answer:

x=2

Step-by-step explanation:

[tex] - 2 + 4 = 2[/tex]

Andre has a summer job selling magazine subscriptions. He earns $25 per week plus $3 for every subscription he sells. Andre hopes to make at least enough money this week to buy a new pair of soccer cleats. Let `n` represent the number of magazine subscriptions Andre sells this week. Write an algebraic expression for the amount of money he makes this week.

Answers

Answer:

C = 25 + 3n

Step-by-step explanation:

Andre has a summer job selling magazine subscriptions.

We are told that:

Andy earns $25 per week plus $3 for every subscription he sells.

Let us represent

C = Total amount of money he makes this week

n = the number of magazine subscriptions Andre sells this week.

Hence, Our Algebraic expression =

C = $25 + $3 × n

C = 25 + 3n

Please help me with this question. The answer is $745,000 but I need working out.

Answers

Answer:

745,000

Step-by-step explanation:

200,000x.03= 6000

150,000x.025=3,750

Commission.    2,350

total.                12,100

total fees.            20,000

less above.           12,100

=.remaining fees    7,900

divide by .02(2% commission)

=remaining sales price 395,000

tier 1 200000

tier 2 150000

tier 3 395,000 (calculated above)

=.       745,000 sales price

Find the solution set of the quadratic equation over the set of complex numbers.
5x2 + 8x + 4 = 0
1+1
A)
x=-1- or -1
-
B)
X
4 2i
or
5
4
5
+
2i
5
2
5
C)
6i
5
or
2
5
+
61
5
1
3i
1
4
D)
31 or
+
4.

Answers

Answer:

c

Step-by-step explanation:

Answer:

D confirm bro............

Is this inequality true or false?
5v > 25, v = 3

Answers

Answer:

False

Step-by-step explanation: 5x3 is 15 and 25 is greater than 15 so the inequality is false.

Select all of the equations where x = 5 is the solution:

2 = 7 - x

1 + x = 6


x - 4 = 9


10 ÷ x = 2

10x = 2

Answers

number 1 2 and 4 are the ones with 5
2 = 7 - x
substitute x
2 = 7 - 5
true bc 7-5=2
this is an answer

1+x=6
substitute x
1+5=6
this is also an answer

x - 4 = 9
substitute x
5-4=9
not true
not an answer

10/x = 2
substitute x
10/5 = 2
true
is an answer (remember the / is divided by)

10x= 2
substitute x
10(5) = 5
false 10•5= 50
not an answer

can someone please answer this? i will mark brainly

Answers

The answer is 14 Tickets

Factor as the product of two binomials
x² – 4 =

Answers

Answer:

(x-2) (x+2)

Step-by-step explanation:

------------------

(x-2) x (x+2) is the answer

solve for x. round your answer to the nearest tenth if necassary.​

Answers

Answer:

32.9 degrees

Step-by-step explanation:

cos (x) = 21/25

cos^1 (21/25)

= 32.856 --> round to 32.9

Answer:

32.9°

Step-by-step explanation:

You can see that relative to the angle that is x, we are given the side lengths that are adjacent and the hypotenuse. The trig function associated with this is cosine, and we get:

cos(x) = adj / hyp --> 21 / 25

To find x as the angle, we use the function arccosine,

x = arccosine(21/25)

x = 32.85988038°

And this rounds up to 32.9°

What is her average from Macy scores

Answers

Answer: 85.2

Step-by-step explanation:

The answer is correct because, to find your grades your bassicaly just looking for the mean. To find the mean you have to take all the numbers and add them after you do that you have to divide how ever much numbers you added. So in this case we do 90 plus 76 plus 88 plus 80 plus 92. That equals 426, and since we added five numbers we divide the answer by 5 and that equals 85.2.

Hope This Helps!

7.

Choose the linear inequality that describes the graph. The gray area represents the shaded region.


A. y ≥ 2x – 2

B. y ≥ 2x + 2

C. y ≥ –2x + 2

D. y ≤ 2x – 2

Answers

Answer:

A. y ≥ 2x – 2

Step-by-step explanation:

if x<-2 then x can be​

Answers

Answer:

x ={-3, -4, -5 , -6, -7, ...}


Transform pentagon ABCDE according to (x, y) + (x - 2, y - 3). Which new coordinates are correct for pentagon A'B'C'D'E
A) A'(-1,3)
B) B'(3, 4)
C) C'(6,-1)
D) D'(2,-4)
E) E'(-6, -5)

Answers

The correct coordinates are A'(-1,3) and C'(6,-1)

Transformation of coordinates

From the given figure, we have the coordinates ABCDE under the translation (x, y) + (x - 2, y - 3)

Given the following coordinate points (1, 6), B(6, 6), C(8, 2), D(4, -2) and E(-2, -5). The resulting coordinate after transformation will be:

A = (1-2, 6-3) = (-1, 3)B = (6-2, 6-3) = B'(4, 3) C = (8-2, 2-3) = C'(6,-1) D =  (4-2, -2-3) D'(2,-5) E =  (-2-2, -5-3) = E'(-4, -8)

Hence the correct coordinates are A'(-1,3) and C'(6,-1)

Learn more on translation here: https://brainly.com/question/12861087

LEAN CADA CONDICIÓN Y COLOQUEN UNA X A LOS NÚMEROS QUE LA CUMPLEN:



UN NÚMERO ES DIVISIBLE POR 3 CUANDO LA SUMA DE SUS CIFRAS ES MÚLTIPLO DE 3.


352 405 625 813 1.011 2.546 5.104





UN NÚMERO ES DIVISIBLE POR 4 CUANDO SUS DOS ÚLTIMAS CIFRAS SON CEROS O MÚLTIPLOS DE 4.


170 512 700 914 1.302 3.164 7.480





UN NÚMERO ES DIVISIBLE POR 6 CUANDO ES DIVISIBLE POR 2 Y POR 3.


213 460 522 720 2.310 4.503 5.316 AYUDA PLS

Answers

Answer:

I speak english srry

Step-by-step explanation:

Please help quicky!!!!!!!!!!​

Answers

Answer:

≈ 2,826 cm^3

Step-by-step explanation:

V = πr^2h

V = 3.14 · 10^2 · 9

V = 3.14 · 100 · 9

V = 314 · 9

V = 2,826

Can someone please help me? i’ve asked twice but people didn’t comment to help! If you’re not gonna help please don’t comment!! I’m not able to open any files, so its best if you tell me or explain the answers..

Answers

Answer:

lenth = x= 12cm

Breadth = y = 8cm

Step-by-step explanation:

Given :

The length of a rectangle is 4 cm more than its width

The area of the rectangle is 96 cm²

To Find :

Width of the rectangle.

Solution :

Let the length of the rectangle be x cm.

Let the breadth of the rectangle be y cm.

Case 1:

➣  _____(1)

Case 2 :

We have the formula for area of the rectangle as follows :

Where,

l = length → x cm

b = breadth → y cm.

Substitute, x = 96/y in equation 1,

Divide by minus sign,

As per assumption, y = breadth of the rectangle.

•°• y = -12 is not acceptable.

Substitute, y = 8 in equation 1,

How do you work out the area of a triangle? ​

Answers

(Base x Height) / 2 is the formula
Area= 1/2 •base•height
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