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Write the first four terms of a decreasing Arithmetic Sequence. Use this to describe, in your own words, how to write both the Recursive and the Explicit Formulas for the sequence. Show how to use the
Recursive Formula to find the next two terms
Answers
Answer:
Write the first five terms of the sequence defined by the recursive formula.
a1=9an=3an−1−20, for n≥2" role="presentation" style="font-family: proxima-nova, sans-serif; -webkit-font-smoothing: subpixel-antialiased; padding: 1px 0px; margin: 0px; font-size: 15.696px; vertical-align: baseline; background: transparent; border: 0px; outline: 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">a1=9an=3an−1−20, for n≥2
The first term is given in the formula. For each subsequent term, we replace \displaystyle {a}_{n - 1}an−1 with the value of the preceding term.
n=1a1=9n=2a2=3a1−20=3(9)−20=27−20=7n=3a3=3a2−20=3(7)−20=21−20=1n=4a4=3a3−20=3(1)−20=3−20=−17n=5a5=3a4−20=3(−17)−20=−51−20=−71" role="presentation" style="font-family: proxima-nova, sans-serif; -webkit-font-smoothing: subpixel-antialiased; padding: 1px 0px; margin: 0px; font-size: 15.696px; vertical-align: baseline; background: transparent; border: 0px; outline: 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">n=1a1=9n=2a2=3a1−20=3(9)−20=27−20=7n=3a3=3a2−20=3(7)−20=21−20=1n=4a4=3a3−20=3(1)−20=3−20=−17n=5a5=3a4−20=3(−17)−20=−51
The recursive formula gives values based on the preceding term, while
the explicit formula is a general formula.
Correct response:
Recursive formula; aₙ = a₍ₙ₋₁₎ - 5Explicit formula; aₙ = 35 - 5·(n - 1)a₅ = 15, a₆ = 10How to write recursive and explicit formulaAn example of the first four terms of a decreasing Arithmetic Sequence is presented as follows;
35, 30, 25, 20Recursive formula:
From the above Arithmetic Sequence, we have;
The difference between each successive term is constant and equal to -5, therefore;
The recursive formula is; \(\underline{a_n = a_{n -1} - 5}\)Explicit formula
The sequence of numbers can be taken as the output of a linear function where the input is the term of the number.
To find the equation of the linear function, we have;
\(The \ slope, \ m = \dfrac{30 - 35}{2 - 1} = -5 = d = The \ common \ difference\)
The equation of the function in point and slope form is therefore;
aₙ - 35 = -5·(n - 1)
Which gives;
aₙ = 35 - 5·(n - 1)
Where;
aₙ = The value of the nth term of the Arithmetic Sequence
n = The term of the Arithmetic Sequence
35 = The first term of the sequence = a₁
-5 = The common difference = d
The explicit formula for the (a) Arithmetic Sequence is; aₙ = a₁ + (n - 1)·d
Which gives;
aₙ = 35 + (n - 1) × (-5) = 35 + (n - 1)·d
The explicit formula is; \(\underline{a_n = 35 - 5 \times (n - 1)}\)The next two terms are found by using the recursive formulas as follows;
a₅ = a₄ - 5
a₆ = a₅ - 5
Which gives;
a₅ = 20 - 5 = 15
Fifth term, a₅ = 15a₆ = 15 - 5 = 10
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Related Questions
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 442 gram setting. It is believed that the machine is underfilling the bags. A 44 bag sample had a mean of 438 grams. Assume the population variance is known to be 576. A level of significance of 0.1 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.
Answers
Answer:
p value is 0.1343
Step-by-step explanation:
Null: u>= 442
Alternative: u < 442
Using the formula for z score:
(x - u)/sd/√n
Where x is 438, u = 442 sd can be determined from the variance = √variance =√576 = 24 and n = 44
z score = 438-442 / (24/√44)
z score = -4/(24/6.6332)
z = -4/3.6182
z =-1.1055
Now let's find the p value at 0.1 significance level using a z score of -1.1055, using a p value calculator, p value is 0.1343 which greatest than 0.1 meaning the day is not sufficient enough to conclude that the machine is underfilling the bags.
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
The length KL is 8 units
The value of x is undefined
The length KL is 12 units
Calculating the length KLFrom the question, we have the following parameters that can be used in our computation:
The rhombus
Also, we have
DK = 8
A rhombus is a quadrilateral with all sides equal.
So, we have
KL = 8
Calculating the value of xHere, we have
SKAL = 2x - 8
There is no point S on the rhombus
This means that
x = undefined
Calculating the length KLHere, we have
DM = 5y + 2 and DK = 3y + 6
A rhombus is a quadrilateral with all sides equal.
So, we have
5y + 2 = 3y + 6
Evaluate
2y = 4
Divide
y = 2
So, we have
KL = 5 * 2 + 2
KL = 12
Hence, the length KL is 12 units
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A father has four sons, with heights of 68, 71, 72, and 75 inches. Determine the sampling distribution of
the sample mean height and the sampling distribution of the sample range of height for samples of
size n= 2.
Answers
The sampling distribution of the sample mean height and the sampling distribution of the sample range of height are 71.5 inches and 7 inches.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
Heights: 68, 71, 72, and 75 inches
Now,
Mean height.
= (68 + 71 + 72 + 75) / 4
= 286/4
= 71.5 inches
Sample range.
= Highest height - Lowest height
= 75 - 68
= 7 inches
Thus,
The mean height is 71.5 inches.
The sample range of height is 7 inches.
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Country A has an exponential growth rate of 4.3% per year. The population is currently 4,079,000, and the land area of Country A is 19,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?
Answers
The number of years it would it take for there to be one person for every square yard is 108,325.68 years.
How many years would it take for there to be one person for every square yard?When there is one person for every square yard, it means that the population and land area are equal in value.
Number of years = (In FV / PV) / r
FV = future populationPV = present populationr = rate of growth(In 19 billion / 4,079,000) / 0.043 = 108,325.68 years
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Suppose Winston's annual salary as an accountant is $60,000 and his financial assets generate $4,000 per year in interest. One day, after deciding to be his own boss, he quits his job and uses his financial assets to establish a consulting business, which he runs out of his home. He outlays $8,000 in cash to cover all the costs involved with running the business and earns revenues of $150,000. What is Winston's economic profit?
$138,000
$150,000
$142,000
$78,000
Answers
Winston's economic profit based on the forgone salary of $60,000, and the revenue of $150,000 is $78,000. The correct option is therefore;
$78,000
What is an economic profit?An economic profit is a profit that accounts for both the explicit and implicit costs of a business. The economic profit is obtained from the difference between the total revenue and the costs including the opportunity costs.
The annual salary of Winston as an accountant = $60,000
The amount Winston's financial asset generates = $4,000 per year
The cost of running the business = $8,000
The amount Winston earns as revenue = $150,000
Therefore;
Winston's opportunity cost which is the forgone alternative, is the amount he earns as an accountant = $60,000
The interest of $4,000, earned from the financial asset = The cost of using the financial asset for the business
The cost of running the business = $8,000
The total cost = Opportunity cost + Cost of making use of the financial asset + The business running cost
The total cost = $60,000 + $4,000 + $8,000 = $72,000
The economic profit = The total revenue - The total cost
Therefore;
Winston's economic profit = $150,000 - $72,000 = $78,000Learn more on economic profits here: https://brainly.com/question/13991283
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51 decreased by twice Jose's height
use the variable j to represent Jose's height.
Answers
Step-by-step explanation:
51 - 2j
maybe something is missing here, but that is the representation of what you wrote.
How you write 2 5/3 using radical notation
Answers
Answer:
2^5/3 = (2^5)^1/3 = 32^1/3 = ∛32
Step-by-step explanation:
what is 9,375 rounded to the nearest hundredth
Answers
9.38
Answer:
9400
Step-by-step explanation:
Because it's closer to 9400 than 9300
6x^2=-3x+1 to the nearest hundredth
Answers
The solutions to the quadratic equation 6x² = -3x + 1 to the nearest hundredth are -0.73 and 0.23.
What are the solutions to the quadratic equation?Given the quadratic equation in the question:
6x² = -3x + 1
To solve the quadratic equation 6x² = -3x + 1, we can rearrange it into standard form, where one side is set to zero:
6x² + 3x - 1 = 0
Now we can solve the equation using the quadratic formula, which states that for an equation in the form ax² + bx + c = 0, the solutions for x are given by:
\(x = \frac{-b \±\sqrt{b^2-4ac} }{2a}\)
Here; a = 6, b = 3, and c = -1.
Let's substitute these values into the quadratic formula:
\(x = \frac{-b \±\sqrt{b^2-4ac} }{2a}\\\\ x= \frac{-3 \±\sqrt{3^2-4\ *\ 6\ *\ -1} }{2*6}\\\\x = \frac{-3 \±\sqrt{9+24} }{12}\\\\x = \frac{-3 \±\sqrt{33} }{12}\\\\x = -0.73, \ x=0.23\)
Therefore, the values of x are -0.73 and 0.23.
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Consider a triangle A BC lIke the one below. Suppose that B=31°, a =53, and c= 12. (The figure Is not drawn to scale.) Solve the triangle.Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.If there Is more than one solution, use the button labeled "or"
Answers
Given,
The measure of angle B is 31 degree.
The measure of side a is 53.
The measure of side c is 12.
By law of cosine,
\(\begin{gathered} b^2=a^2+c^2-2accosB \\ b^2=2809+144-1272cos31^{\circ} \\ b^2=1862.68319 \\ b=43.1588 \\ b=43.16 \end{gathered}\)By law of sine,
\(\frac{}{}A=140.77^{^{\circ}}\)The measure of angle C is 8.23 degree.
I need some help with these, I would appreciate it.
Answers
A farm has 15 rows of fruit trees with 7 trees in each row. The last 4 rows of trees are cherry trees. The remaining trees are orange trees. How many orange trees are on the farm?
Answers
Answer:
Total number of orange trees = 77 trees
Step-by-step explanation:
Given:
Total number of rows = 15
Total number of cherry rows = 4
Number of trees in each rows = 7
Find:
Total number of orange trees
Computation:
Total number of orange trees = [Total number of rows - Total number of cherry rows][Number of trees in each rows]
Total number of orange trees = [15 - 4]7
Total number of orange trees = [11]7
Total number of orange trees = 77 trees
What are the slopes to these ? Please answer
Answers
5. is slope of 0
6. is slope of -7
7. is slope of -2
8. is slope of -3/2
9. is slope of -1
10. is slope of 0 :)
The function f(x)= 2x +4x^-1 has one local minimum and one local maximum.
This function has a local maximum at x=?
with value ?
and a local minimum at x=?
with value ?
Answers
The requried, local minimum and maxium for the given function is √2 and -√2.
We need to find the local maximum and local minimum of the function \(f(x) = 2x + 4x^{(-1)}.\)
First, we find the derivative of f(x):
\(f'(x) = 2 - 4x^{(-2)} = 2 - 4/x^2\)
Setting f'(x) = 0 to find the critical points:
\(2 - 4/x^2 = 0\)
Solving for x, we get:
x = ±√2
To determine whether these critical points are local maxima or minima, we need to examine the sign of the second derivative:
\(f''(x) = 8x^{(-3)}\)
When x = √2, f''(√2) = 8/(√2)³ = 8√2 > 0, so x = √2 is a local minimum.
When x = -√2, f''(-√2) = 8/(-√2)³ = -8√2 < 0, so x = -√2 is a local maximum.
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solve this proof. help pls
Answers
Answer:
Step-by-step explanation:
Use SAS congruency; AD=DC, and they both share side BD. Also, BD is the perpendicular bisector to AC, so it also forms 2 right angles. Proof using SAS.
Or, if you don’t know SAS congruency, you may use SSS congruency;
Use the Pythagorean theorem. Side length AB^2 = AD^2 + BD^2
BC^2 = DC^2 + BD^2.
AD=DC, so therefore AB = BC. Use SSS congruency, and there you go.
The graph compares the weights in pounds of 100 dogs and cats that are brought in
to a veterinarian's office. Using the medians, how much more does a typical dog weigh than a typical cat?
Answers
Answer:20
Step-by-step explanation:this is wrong
Answer:
40
Step-by-step explanation:
subtract median of dogs and median of cats
The population of a certain inner-city area is estimated to be declining according to the model P(t)=184,000e^−0.012t, where t is the number of years from the present. What does this model predict the population will be in 6 years? Round to the nearest person.
__________ people
Answers
Answer:
EZ answer 9+10=21
Step-by-step explanation:
Graph the line
Y=-2x-5
Answers
Step-by-step explanation:
I hope this helps you answer your questions about graphing the line.
19. The product of two consecutive integers is 5 more than three times the larger
Answers
x-1 = smaller number
x*(x-1)=5+3x
x^2-4x-5=0 use the formula
x=5
x-1=4
the 2 numbers are 5&4 or -1,-2
A 100 foot long moving walkway moves at a constant rate of 6 feet per second. Al steps onto the start of the walkway and stands. Bob steps onto the start of the walkway two seconds later and strolls forward along the walkway at a constant rate of 4 feet per second. Two seconds after that, Cy reaches the start of the walkway and walks briskly forward beside the walkway at a constant rate of 8 feet per second. At a certain time, one of these three persons is exactly halfway between the other two. At that time, find the distance in feet between the start of the walkway and the middle person.
Answers
The distance between the start of the walkway and the middle person is 52 feet.
It is given that a 100 foot long moving walkway moves at a constant rate 6 feet per second.
AI steps into the start of the walkway and stands this means speed of AI is 6 feet per second.
Bob steps onto the start of he walkway two second later and stolls forward along walkway 4 feet per second that means 10 feet [per seconds.
And CY reaches the starts of the walkway and walks briskly forward beside the walkway at a rate of 8 feet per second.
At the time s we gave that,
\(\frac{8(s-4)+10(s-2)}{2}\) = 6s
\(\frac{8s -32 + 10s - 20}{2}\) = 6s
18s - 52 = 12s
6s = 52
s = \(\frac{26}{3}\)
At the time AI has travels,
6* \(\frac{26}{3}\) = 52 feet.
Therefore distance between the start of the walkway and the middle person is 52 feet.
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Solve the following system of equations by graphing. Then determine whether the system is consistent or inconsistent and whether theequations are dependent or independent. If the system is consistent, give the solution.- 6x + 6y = -24- 4x + 4y = -12
Answers
Given:
- 6x + 6y = -24
- 4x + 4y = -12
Simplest form of the above equation is,
- x +y = -4
y=x-4 .................. (1)
- x + y = -3
y=x-3 .................. (2)
Let us find some points for the (1) equation.y=x-4
When x=1, we get, y=-3
When x=2, we get, y=-2
When x=3, we get, y=-1
(1, -3), (2, -2), and (3, -1).
Let us find some points for the (2) equation.
When x=1, we get y=-2
When x=2, we get y=-1
When x=3, we get y=0
(1, -2), (2, -1), and (3, 0).
Hence, the graph is,
Sicne, line are parallel.
Hence, the system is inconsistent.
That is, the system has no solution.
The linear equations in the slope intercept form is,
y= x+ (-4)
y= x+ (-3)
write 0.4% in a fraction or mixed number in simplest form
Answers
simplified: 1/250
You need to use for 4/5 of a cup of strawberries for a single pie how many cups are needed for nine pies
Answers
Answer:
36/5 or 7.2 cups
Step-by-step explanation:
4/5 times 9/1 is equal to 36/5
you should probably simplify to decimal
if A=[ 1 2 3 4]and AB=[ 3 4 -1 ] the the order of matrix B is
Answers
The order of matrix B is 4 by 3
How to determine the order of matrix BOrder of matrix refers to the the number of rows and the number of column of a matrix
from the given question
matrix A is of the order 1 x 4matrix AB is of the order = 1 x 3The order of matrix B is determined from the Order of matrix A and the product
Matrix B must have same number of rows as the columns of matrix A hence matrix B has 4 columnsMatrix B must have same number columns as the column of matrix AB hence matrix B has 3 columnsThere matrix has order of 4 x 3 which is
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Abby is filling a 100 quart dog bath using a 2 gallon bucket. how many buckets will it take to fill the dog bath?
Answers
( or 12.5 buckets)
Step by step
We know the bath holds 100 quarts
We know 100 quarts is equal to 25 gallons
( 4qts to 1 gallon)
If Abby is using a 2 gallon bucket, divide 25 gallons by 2
25/2 = 12 1/2 buckets to fill the bath
plsss answer the questions
Answers
Answer:
1) (7x - 8) - (2x + 4)
= 7x - 8 - 2x - 4
= 5x - 12
2) (8x - 6y) - (2x - y)
= 8x - 2x -6y + y
= 6x - 5y
3) (12xy + 5y) - (23xy - 3y)
= 12xy - 23xy + 5y + 8y
= -11xy + 13y
= 13y - 11xy
the store bought a pair of shoes for 50.00 and sold it for 80.00 what percentage was the mark up?
Answers
Answer:
60%
Step-by-step explanation:
The required markup percentage is 60%. The store bought the shoes for 50 dollars and got 30 dollars out of it when they sold it. And that mark up percentage is 60%. 30 dollars is 60 percent of the cost of the shoe. I don't know if you will understand this but this is the answer.
A rectangular prism has a width of x2 inches and a length of xy2 inches and a height of xy inches.
Which expression represents the volume of the rectangular prism in cubic inches?
2x^2y^2
2xy^3 + 2x^2y
2x^4y^3
x^3y^2
Answers
In this case, the width is x^2 inches, the length is xy^2 inches, and the height is xy inches.
Substituting these values into the formula, we get:
V = (xy^2)(x^2)(xy)
Simplifying, we get:
V = x^4y^3
Therefore, the expression that represents the volume of the rectangular prism in cubic inches is x^4y^3.
What is the equation of the line in slope-intercept form? y = _ x + _
Answers
Decide whether the statement is possible or impossible.
sin^2θ+cos^2θ=8
Is the statement possible or impossible, and why? Show all work and reasoning for answer.
Answers
The statement sin²Ф + cos²Ф = 8 is impossible.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
sin²Ф + cos²Ф = 8 ____(1)
The standard formula is sin²Ф + cos²Ф = 1 _____(2)
Now,
Comparing (1) and (2).
sin²Ф + cos²Ф = 8 is never possible unless 8 is on both sides.
i.e
8 (sin²Ф + cos²Ф) = 8
Thus,
The statement is impossible.
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