An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z or blackboard bold \mathbb {Z}.
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 16 ≤ x ≤ 22.
x f(x)
4 10
10 19
16 28
22 37
28 46
Answer:
Step-by-step explanation:
Which functions show a positive rate of change? Select all that apply
The functions that show a positive rate of change include the following:
A. y = 2x/3 - 2.
B. y = 7 - (-3x).
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be represented or modeled by using this linear equation:
y = mx + c
Where:
m represents the slope or rate of change.c represents the y-intercept.x and y are the data points.Generally speaking, a function with a positive rate of change represents an increasing function because its numerical value is increasing over time such as in the following increasing function:
y = 2x/3 - 2.
Slope, m = 2/3 (positive slope).
y = 7 - (-3x)
y = 7 + 3x
Slope, m = 3 (positive slope).
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The functions that show a positive rate of change are y = 2/3x - 2 and y = 7 - (-3x).
What is a positive function?A positive function is a function that has the values of x that are greater or higher than zero on the graph. It means that they are always increasing on the positive y-axis i.e. f(x) > 0.
The function's outputs known as the y-values, however, must be larger than zero even though the domain values i.e. (x-values) might be negative. A positive function, then, has values that are positive for all of its domain's parameters.
To determine the positivity of the function on the graph, the slope must also be positive. Using the linear function form y = mx + b.
where;
m = slopeb = y-interceptFrom the given information, the functions that demonstrated a positive slope are:
y = 2/3x - 2 andy = 7 - (-3x)Therefore, we can conclude that the functions that show a positive rate of change are y = 2/3x - 2 and y = 7 - (-3x).
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I need help with my math homework
Answer:
6 = D
7 = F
8 = A
9 = B
10 = C
Have a nice day ;)
I can’t figure this out. Which math expression means "52 more than an unknown number"?
O A. x- 52
• B. x+ 52
O C. 52 - x
• D. x = 52
Answer: B. x + 52
Step-by-step explanation:
The unknown number is represented as x.
The phrase "52 more than" means adding 52 to something
From this we can say that the expression is B. x + 52
What fraction in simplest form is 28 hours out of a week
The surface area of a cylinder is 24π m². The distance around the base of the cylinder is 3π meters and the diameter of a base of the cylinder is 4 meters. What is the height of the cylinder? Enter your answer, as a simplified fraction, in the box.
The height of the cylinder will be 6 meters.
What is a cylinder?One of the most fundamental curvilinear geometric shapes, a cylinder has traditionally been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In some modern branches of geometry, a cylinder may also be defined as an infinite curvilinear surface.
Given that the surface area of a cylinder is 24π m². The distance around the base of the cylinder is 3π meters and the diameter of the base of the cylinder is 4 meters.
The height of the cylinder will be calculated as:-
Surface area = 2πrh
24π = 2πrh
r x h = 12
The diameter is 4 meters so the radius is 2 cm.
r x h =- 12
h = 12 / r
h = 12 / 2 = 6 meters
The height of the cylinder will be 6 meters.
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Solve the system of equations x+3y=5 and -3x-2y=20 by combining the equations
On solving the linear equations x + 3y = 5 and -3x - 2y = 20, the value for x is x = -10 and the value of y is y = 5. When solved independently the value is obtained as -2x + y = 25.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The first linear equation is - x + 3y = 5
The second linear equation is - -3x - 2y = 20
On evaluating individually the equation obtained is -
-3x - 2y + x + 3y = 20 + 5
-2x + y = 25
Multiply equation (1) with 3 -
3(x + 3y) = 5 × 3
3x + 9y = 15.....(3)
Adding equation (3) and (2) -
-3x - 2y + (3x + 9y) = 20 + 15
-3x - 2y + 3x + 9y = 35
-2y + 9y = 35
7y = 35
y = 35/7
y = 5
Substituting the value of y in equation (1) -
x + 3y = 5
x + 3(5) = 5
x + 15 = 5
x = 5 - 15
x = -10
Therefore, the value of x and y is -10 and 5 respectively.
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There are 150,000 households in Market City. A local phone repair shop takes a random sample of 50 households and finds that the average number of phones per household from the sample last year that needed to be repaired was 1.05 ± 0.23. Which of the following is an estimate of the total number of phones that needed repairing last year in Market City?
Between 82 and 128 phones
Between 123,000 and 192,000 phones
Between 105 and 23 phones
Between 157,500 and 34,500 phones
The correct answer is Between 157,500 and 968,187 phones.
Which of the following best describes the approximate number of phones in Market City ?The average number of phones per household from the sample from the previous year that required repair was 1.05 0.23. This suggests that the range for the genuine population mean () might be between 1.05 - 0.23 = 0.82 and 1.05 + 0.23 = 1.28 phones per home.Since the sample size was 50 households, the estimate of the total number of phones that needed repairing last year in Market City can be calculated as follows:Estimate = 50 * (1.05 + 1.05) / 2 = 52.5Estimate = 52.5 * 150,000 = 7,875,000Therefore, an estimate of the total number of phones in Market City that required repair last year ranges from 7,875,000 - 7,875,000 * 0.23 = 6,068,125 to 7,875,000 + 7,875,000 * 0.23 = 9,681,875 phones.Therefore, the correct answer is between 157,500 and 968,187 phones.To learn more about estimation refer:
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Hace 8 años, Maria tenía 10 años y Luis 11 años. Dentro de 7 años, Nico tendrá 27 años ¿cuanto es la suma de las edades actuales de Maria Luis y Nico?
Their ages are given below:
Maria 18, Luis 19 Nico 20The sum of their ages would be 57 years.
How to find their ages?The current age of Nico is 27 - 7 = 20 years.
Therefore, Maria and Luis's current ages would be 8 years older than when they were 10 and 11 respectively,
so Maria is currently 18 years old and Luis is currently 19 years old.
Therefore, the sum of their current ages is 18 + 19 + 20 = 57 years.
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8 years ago, Maria was 10 years old and Luis was 11 years old. In 7 years Nico will be 27 years old, what is the sum of the current ages of Maria, Luis and Nico?
Write 0.000001365 in scientific notation.
Answer: 1.365 × 10-6
Step-by-step explanation:
All the numbers in scientific notation written in the form a × 10b, where b is an integer and the coefficient a is a non-zero real number between 1 and 10 in absolute value.
To convert 0.000001361 into scientific notation also known as standard form, follow these steps:
Move the decimal 6 times to right in the number so that the resulting number, m = 1.361, is greater than or equal to 1 but less than 10
Since we moved the decimal to the right the exponent n is negative
n = -6
Write in the scientific notation form, m × 10n
= 1.361 × 10-6
Therefore, 0.000001361 in scientific notation is 1.361 × 10-6 and It has 4 significant figures. In scientific e-notation it is written as 1.361e-6.
Please answer. I've been stuck on this question for a while.
Question: A business purchased a new printer. The number of the pages, y, printed by the new printer in x minutes is represented by the equation y=37x. The number of the pages printed by the OLD printer is represented in the graph below.
Which statements about the printers are true?
Select the TWO correct statements.
Answer:
The new printer prints 100 pages about 4 minutes faster than the old printer
The new printer prints 22 move pages per minute than the old printer
Step-by-step explanation:
New printer's equation
y = 37x
Old printer's equation
y = 15x
Since the graph is proportional you can take any ordered pair (except (0,0) and put it the form y/x to find the slope. For example, The point (2,30) 30/2 = 15 or the point (4, 60) 60/4 = 15 and so on.
The difference between the rates is 22 pages a minute (37 - 15).
Substituted in 100 for y and solve for x (minutes)
New:
y = 37x
100 = 37x Divide both sides by 37
100/37 =37x/37
3 = x This is rounded
This means that it takes about 3 minutes to print 100 pages.
Old:
y = 15x
100 = 15x Divide both sides by 15
100/15 = 15x/15
7 = x This is rounded
This means that it takes about 7 minutes to print 100 pages.
The new printer can print the same amount of page (100) in 4 less minutes (7-3)
Consider the function f(x). Select all of the following that include a vertical stretch of f(x).
The vertical stretch of f(x) will be -2f(x), 5.5f(x) - 1, 7f(x)
As is well known, the vertical stretch of f(x) occurs when the value of the parameter is changed in the following general form:
When a constant c with a value larger than one is scaled across the board of a function, it results in a vertical stretch. It is written as the vertical stretch from the original function f(x) to the new, stretched function g(x)=cf(x) where c>1 g ( x ) = c f ( x ) where c > 1.
f(k(x-d)) = y = a+ c
when |a| exceeds 1 since The function is stretched vertically by a dilation factor of |a| when |a| > 1 (when a > 1).
Thus, we select F, D, and A.
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The full question:
Consider the function f(x). Select all of the following that includes a vertical stretch of f(x)
A. -2f(x)
B. 0.25f(x)
C. -f(x) + 6
D. 5.5f(x) - 1
E. f(x) + 9
F. 7f(x)
#7
DE is a midsegment of AABC. Find the value of x .
X =
B
A 6 E
D
X
C
Using the Midsegment Theorem, the value of x is: 6.
What is the Midsegment Theorem of a Triangle?The Midsegment Theorem states that in a triangle, the segment that connects the midpoints of two sides of the triangle is parallel to the third side and is half as long as the third side. In other words, the midsegment of a triangle is parallel to the third side and has half the length of the third side.
Therefore the ratio of DE to AB would be: 1/2
Ratio of EC to AC would be: x/(x + 6)
Thus:
x/(x + 6) = 1/2
Cross multiply
2x = x + 6
2x - x = 6
x = 6
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what is the value of k? k= …..
please help quick
180 - 115 = 65
4k + 5 + 6k + 10 + 65 = 180
10k + 80 = 180
10k = 100
k = 10
George says to subtract fractions with different denominators, you always have to multiply the denominators to find the common denominator; for example: 3/8 - 1/6 = 18/48 - 8/48
Is George correct? Why or why not?
George is not correct because we can find the least common multiple of 8 and 6 which is 24. This allows us to solve the problem with simple numbers and ease our calculations to get the answer in the simplest form.
The equation solved by George is 3/8 - 1/6 = 18/48 - 8/48
To solve the given fractions in the simplest form, we will find the common denominator which would be the least common multiple of both denominators.
we can see that the numbers in the denominator are 8 and 6.
Multiples of 8: 8, 16, 24, 32, 40,...
Multiples of 6: 6, 12, 18, 24, 30,...
Hence, LCM of 8 and 6 is 24.
thus we can solve the equation as follows -
3/8 - 1/6
= 3*3/8*3 - 1*4/6*4
= 9/24 - 4/24
= 5/24
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Please explain and answer!
The Pythagorean identity is proved to be 1 + cot2 = cosec2, which results in sin2 + cos2 = 1.
How to verify Pythagorean identity?With the value of sine and the quadrant in which the angle is placed, we can use the Pythagorean identity to get the angle of cosine.
If we are given the cosine value and the quadrant in which the angle is placed, we may similarly compute the angle of sine.
Cosec2 = 1 + cot2
Therefore,
cosec2 = 1/sin2
Tan2 = cos2 / sin2 = cot2 = 1
Hence,
1/sin2 = 1 + cos2 / sin2.
multiplied both sides by sin2 as a result.
1(sin2 ) + (cos2 / sin2 ) = (sin2 / sin2 )
cos2 + sin2 = 1.
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Rewrite the following without an exponent.
(2/3) ^-1
The expression of (²/₃)⁻¹ without an exponent is given as;
3/2
How to use Laws of exponents?The different laws of exponents are;
1) Power Law of Exponents which is expressed as; (x^m)ⁿ = x^(mn)
2) Quotient Law of Exponents is expressed as; x^m ÷ x^n = x^(m - n)
3) Product Law of Exponents is expressed as; x^(m) * x^(n) = x^(m + n)
4) Law of Reciprocal is expressed as; a⁻ⁿ = 1/aⁿ
Now, we want to rewrite the expression (²/₃)⁻¹ without using an exponent.
From the law of reciprocal of exponents we can say that;
(²/₃)⁻¹ = 1/(²/₃)
= 3/2
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One afternoon Mr. And Mrs. Baxter and their 3 children were busy working outside in their garden. Mrs. Baxter was feeling hungry, so she went inside to the kitchen where there was a plate full of cookies. She ate 1/6 of the cookies and then went back to work. Mr. Baxter was feeling hungry, so he went inside and ate 1/5 of the remaining cookies and then went back to work. Next, Anna was feeling hungry, so she went inside and ate 1/4 of the cookies that were left on the plate and then went back to work. Then Tyler was feeling hungry, so he went inside, ate 1/3 of the cookies left on the plate and then went back to work. Finally, little Adam was feeling hungry, and he went inside and ate 1/2 of the remaining cookies, leaving 4 cookies on the plate. How many cookies were on the plate before anyone started feeling hungry?
24 cookies were on the plate before anyone started feeling hungry.
Let X be the number of cookies on the plate before anyone started feeling hungry.
After Mrs. Baxter ate 1/6 of the cookies, there were,
X - (X * 1/6) = 5/6X cookies left.
After Mr. Baxter ate 1/5 of the remaining cookies, there were,
5/6X - (5/6X * 1/5) = 5/6X- 1/6X = 4/6X cookies left.
After Anna ate 1/4 of the remaining cookies, there were,
4/6X - (4/6X * 1/4) = 4/6X- 1/6X = 3/6X cookies left.
After Tyler ate 1/3 of the remaining cookies, there were
3/6X - (3/6X * 1/3) = 3/6X- 1/6X = 2/6X cookies left.
After Adam ate 1/2 of the remaining cookies, there were,
2/6X - (2/6X * 1/2) = 2/6X- 1/6X = 1/6 cookies left.
We know, after Adam eats, 4 cookies are left, therefore,
1/6X = 4
So X = 4 *6 = 24
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Wendy solved an equation and found x to be 5. Which equation could she have solved?
O 2x + 4 = 12
O13-4x = 20
O 3x-10= 5x + 20
O 14+2x = 54 - 6x
The equation Wendy must have solve is 14+2x = 54 - 6x Option D
What is a linear equation?A linear equation is an equation whose highest power of the variable is 1.
recall that equation is a mathematical statement showing that two opposite sides are equal
the equation can be solved as follows
14+2x = 54 - 6x
Collecting the like terms from the equation we have
2x+6x = 54 -14
This implies that
8x = 40
Making x the subject of the relation
Therefore x=40/8 = 5
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a 6 foot-tall farmer wants to determine the height of his barn. he notices that his shadow is 10 feet long and his barn casts a shadow 75 feet long. how high is the barn?
By applying the proportional relationship formula, the height of the barn is 45 ft.
In a proportional relationship, each pair of data points is related in the same way, typically by multiplying them together. A proportionate relationship can be seen in a set of numbers, an equation, or a graphical representation. In this case, we are given that :
The height of the farmer (X1) = 6 ft
The height of the farmer’s shadow (Y1) = 10 ft
The height of the barn with farmer’s shadow (Y2) = 75 ft
To calculate the actual height of the barn (X2), we can use this following formula:
X1 : Y1 = X2 : Y2
6 : 10 = X2 : 75
X2 = (6 : 10) x 75
X2 = 45
Thus, the height of the barn is 45 ft
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5 POINTS UP FOR GRABS !!!
The area of the shaded part of the rectangle is 152 cm².
What is the shaded area?The area of the shaded part is the difference between the area of the larger rectangle and the smaller square.
Area of the shaded part = area of the larger rectangle - area of the square
Area of the larger rectangle = length x width
12cm x 18cm = 216 cm²
Area of the square = length²
= 8² = 64 cm²
Area of the shaded part = 216 - 64 = 152 cm²
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A department store receives a shipment of
3 boxes of glass ornaments. There are
25 ornaments in each box. Lucas opens the
boxes and finds that 6 of the ornaments are
broken. Based on this shipment, what
prediction can Lucas make about the next
shipment of ornaments?
F A delivery of 4 boxes will contain 4 more
broken ornaments than a delivery of
3 boxes.
G A delivery of 5 boxes will contain 6 more
broken ornaments than a delivery of
3 boxes.
H A delivery of 6 boxes will contain 6 more
broken ornaments than a delivery of
3 boxes.
JA delivery of 7 boxes will contain 10 more
broken ornaments than a delivery of
3 boxes.
The prediction that Lucas can make about the next shipment of ornaments is that H. A delivery of 6 boxes will contain 6 more broken ornaments than a delivery of 3 boxes.
How to calculate the word problem?It should be noted that a word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this case, since the department store receives a shipment of 3 boxes of glass ornaments and there are 25 ornaments in each box.
Lucas then opens the boxes and finds that 6 of the ornaments are broken. This implies that there are 2 broken for each box.
In this case, a delivery of 6 boxes will contain 6 more broken ornaments than a delivery of 3 boxes.
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Lisa makes $30 for 4 hours of babysitting. Write an equation to represent her earnings, e, relative to the number of hours, h, that she works. Assume the relationship is proportional.
please help
The equation which represents Lisa's earnings, e, relative to the number of hours, h, that she works assume a proportional relationship is e = 7.5h
How to write equations?Amount Lisa makes for babysitting = $30
Number of hours Lisa babysit = 4 hours
Total earnings = e
Number of hours = h
If the relationship is proportional, then
k = constant of proportionality
e = k × h
30 = k × 4
30 = 4k
divide both sides by 4
k = 30/4
k = 7.5
So therefore,
e = k × h
e = 7.5 × h
e = 7.5h
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2/5 meter= how many centimeters
Answer: 40 cm
Step-by-step explanation: 2/5 x 100 =
200/5 = 40
since 2005 the amount of money spent on restaurants in a certain country has increased at a rate of 4% each year in 2005 about 670 billion was spent on restaurants if the trend continues about how much money will be spent on restaurants in 2013 
Answer: Since 2005 the amount of money spent on restaurants in a certain country has increased at a rate of 4% each year. In 2005, about 670 billion was spent on restaurants.
To find the amount spent on restaurants in 2013, we can use the formula:
A = P(1 + r)^t
Where:
A = the final amount
P = the initial amount (670 billion)
r = the rate of increase (0.04 or 4%)
t = the number of years since the initial amount (8 years)
Plugging in the values, we get:
A = 670 billion (1 + 0.04)^8
A = 670 billion (1.04)^8
A = 670 billion * 1.4304
A = 951.8 billion
So, if the trend continues, about 951.8 billion will be spent on restaurants in 2013.
Step-by-step explanation:
An initial population of 430 quail increases at an annual rate of 9%. Write an exponential function to model the
quail population.
Answer:
An exponential function has the form y = ab^x, where a is the initial value, b is the base of the exponential function (in this case, 1 + the growth rate as a decimal) and x is the number of years.
Given that the initial population is 430 and the annual rate of increase is 9%, we can write the exponential function as:
y = 430 (1 + 0.09)^x
Where y is the quail population after x years, and the base (1 + 0.09) represents the growth rate of 9%. This function gives the population of the quail for any number of years x.
It's worth noting that the function is in the form of y = a*(1+r)^x where a is the initial value, r is the annual growth rate, and x is the number of years
a player of a video game is confronted with a series of 4 opponents and a(n) 73% probability of defeating each opponent. assume that the results from opponents are independent (and that when the player is defeated by an opponent the game ends). round your answers to 4 decimal places. (a) what is the probability that a player defeats all 4 opponents in a game? enter your answer in accordance to the item a) of the question statement (b) what is the probability that a player defeats at least 2 opponents in a game? enter your answer in accordance to the item b) of the question statement (c) if the game is played 3 times, what is the probability that the player defeats all 4 opponents at least once? enter your answer in accordance to the item c) of the question statement
The Probability that the player will win against each of the four opponents at least once is 0.7942.
The player has a P(W) = 0.80 winning chance.
The likelihood that the player will lose is hence P(L)= 1 - P(W) = 0.20.
The player is up against 4 different opponents in the video game.
It is stipulated that the game finishes when a player is defeated by an opponent.
The player can win in any of the following ways: L, WL, WWL, WWWL, and WWWW.
The results from each of the four opponents are distinct, meaning that the outcome of a game played against one opponent has no bearing on the outcome of a game against another.
P (Player defeats all 4 opponents) = 0.4096 is the probability that a player will win a game against all four opponents.
Thus, the probability that the player defeats all four opponents in a game is 0.4096.
(b) The likelihood that a player will win a game against at least two opponents is,
P = 1 (Player defeats at least 2) P = 0.64 when the player loses the first and second games.
Therefore, there is a 0.64 percent chance that the player will win at least two games against opponents.
Let X equal the number of times the player triumphs over all four opponents.
The likelihood that a player will win a game against all four opponents is,
P(WWWW) = 0.4096
The probability that a player will triumph over each of the four opponents at least once is,
P (X ≥ 1) = 1 - P (X < 1)
= 1 - P (X = 0)\s = 0.7942
Therefore, there is a 0.7942 probability that the player will win against all four opponents at least once.
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if the slope of a line in the xy plane that passes through the points (1/2/, -1) and (2, b) is 8/3, what is the value of b?
The slope of a line in the xy plane b = 13/3
The slope of a line in the xy plane can be calculated by using the equation m = (y2-y1)/(x2-x1). In this equation, m is the slope, x1 and y1 are the coordinates of the first point, and x2 and y2 are the coordinates of the second point.
Using this formula, we can solve for b.
m = (y2 - y1) / (x2 - x1)
8/3 = (b - (-1)) / (2 - (1/2))
24/3 = (b + 1) / (5/2)
24/3 * (5/2) = (b + 1)
40/3 = b + 1
40/3 - 1 = b
b = 13/3
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Determine if the conditions stated would result in a unique quadrilateral.
Select Yes or No for each statement.
Four sides and one angle, three sides and two included angles, or two neighboring sides and three angles, to construct a unique quadrilateral.
What is meant by unique quadrilateral?
If the two diagonals and three sides of a quadrilateral are known, it is possible to create it in a singular way. If the two neighboring sides and three angles of a quadrilateral are known, it can be built in an original fashion.
A polygon called a quadrilateral has four sides, four angles, and four vertices. If the size of a quadrilateral's sides and diagonal are known, it is possible to create it in a singular way.
They must have the same number of sides as angles because they are polygons and have four angles. Every quadrilateral has inner angles that sum to 360 degrees.
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HELP ASAP!! GIVING 50 POINTS!!
PLEASE SHOW WORK!
for any value of n, the nth term of the equation will be:
Aₙ = -3* 2ⁿ⁻¹
What is the geometric sequence?A geometric sequence is a sequence of numbers that follows a pattern where the next term is found by multiplying by a constant called the common ratio, r.
From the general formula of the nth term of the geometric sequence:
Aₙ = A₁* rⁿ-1
Given a geometric sequence:
-3, -6, -12, 24,.....
From the general formula of the nth term of the geometric sequence:
Aₙ = A₁* rⁿ⁻¹
in our case
a₁ = -3
ratio(r) = -6/-3 = 2
Thus for any value of n, the nth term of the equation will be
Aₙ = -3* 2ⁿ⁻¹
For instance,
8th term of the given sequence:
A₈ = -3* 2⁸⁻¹
A₈ = -3* 2⁷
A₈ = -384
Therefore, for any value of n, the nth term of the equation will be
Aₙ = -3* 2ⁿ⁻¹
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