Answers
Answer:
2, 3, 4, 9, 32, 279, 8896, 2481705, 22077238784 2,490,930 neither 121,800Step-by-step explanation:
1. Recursively-defined sequenceYou want the first 9 terms of the recursive sequence defined by ...
[tex]\begin{cases}s_1=2\\s_2=3\\s_n=s_{n-2}(s_{n-1}-1)\end{cases}[/tex]
The attached spreadsheet uses the given formula for the next term. It shows the terms to be ...
2, 3, 4, 9, 32, 279, 8896, 2481705, 22077238784
2. Sequence sumThe attached spreadsheet sum function has been used to find the sum of the first 8 terms. That sum is ...
2490930
3. Sequence typeThe sequence of problem 1 has neither a common difference nor a common ratio between successive terms. It is neither arithmetic nor geometric.
4. Sum of arithmetic sequenceThe sum of the first n terms of an arithmetic sequence with first term a1 and common difference d is given by ...
Sn = (2a1 +d(n -1))(n/2)
You have a sequence with a1 = 12 and d = (18-12) = 6. You want the sum of the first 200 terms.
S200 = (2·12 +6(200 -1))(200/2) = 121,800
The sum is 121,800.
__
Additional comment
A spreadsheet is a nice tool for finding terms of a recursively-defined sequence. The formula can include as many terms as necessary, and it can be replicated thousands of times, if necessary. The limitation is that arithmetic is generally limited to 16 significant figures, or so.
Answer:
1.
s₁ = 2
s₂ = 3
s₃ = 4
s₄ = 9
s₅ = 32
s₆ = 279
s₇ = 8,896
s₈ = 2,481,705
s₉ = 22,077,238,784
2. 2,490,930
3. Neither.
4. 121,800
Step-by-step explanation:
Question 1A recursive rule for a sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.
Given recursive rule:
[tex]\begin{cases}s_n=s_{n-2} \cdot (s_{n-1}-1)\\s_1=2\\s_2=3\end{cases}[/tex]
Therefore, the first 9 terms of the sequence are:
[tex]s_1=2[/tex]
[tex]s_2=3[/tex]
[tex]\begin{aligned}s_3&=s_{3-2} \cdot (s_{3-1}-1)\\&=s_{1} \cdot (s_{2}-1)\\&=2 \cdot (3-1)\\&=2 \cdot 2\\&=4 \end{aligned}[/tex]
[tex]\begin{aligned}s_4&=s_{4-2} \cdot (s_{4-1}-1)\\&=s_{2} \cdot (s_{3}-1)\\&=3 \cdot (4-1)\\&=3 \cdot 3\\&=9 \end{aligned}[/tex]
[tex]\begin{aligned}s_5&=s_{5-2} \cdot (s_{5-1}-1)\\&=s_{3} \cdot (s_{4}-1)\\&=4 \cdot (9-1)\\&=4 \cdot 8\\&=32 \end{aligned}[/tex]
[tex]\begin{aligned}s_6&=s_{6-2} \cdot (s_{6-1}-1)\\&=s_{4} \cdot (s_{5}-1)\\&=9 \cdot (32-1)\\&=9 \cdot 31\\&=279\end{aligned}[/tex]
[tex]\begin{aligned}s_7&=s_{7-2} \cdot (s_{7-1}-1)\\&=s_{5} \cdot (s_{6}-1)\\&=32 \cdot (279-1)\\&=32 \cdot 278\\&=8896\end{aligned}[/tex]
[tex]\begin{aligned}s_8&=s_{8-2} \cdot (s_{8-1}-1)\\&=s_{6} \cdot (s_{5}-1)\\&=279 \cdot (8896-1)\\&=279\cdot 8895\\&=2481705\end{aligned}[/tex]
[tex]\begin{aligned}s_9&=s_{9-2} \cdot (s_{9-1}-1)\\&=s_{7} \cdot (s_{8}-1)\\&=8896\cdot (2481705-1)\\&=8896\cdot 2481704\\&=22077238784\end{aligned}[/tex]
Question 2Given series:
[tex]\displaystyle \sum^8_{k=1} s_k[/tex]
The sum notation asks to find the sum of the first 8 terms of the sequence from question 1.
Therefore:
[tex]\begin{aligned}\displaystyle \sum^8_{k=1} s_k&=s_1+s_2+s_3+s_4+s_5+s_6+s_7+s_8\\&=2+3+4+9+32+279+8896+2481705\\&=2490930\end{aligned}[/tex]
Question 3If a sequence is arithmetic, the difference between consecutive terms is the same (this is called the common difference).
If a sequence is geometric, the ratio between consecutive terms is the same (this is called the common ratio).
As the difference between consecutive terms it not the same, the sequence is not arithmetic.
As the ratio between consecutive terms is not the same, the sequence is not geometric.
Therefore, the sequence is neither arithmetic nor geometric.
Question 4[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given arithmetic sequence:
12, 18, 24, ...Therefore:
a = 12d = 18 - 12 = 6To find the sum of the first 200 terms, substitute the found values of a and d into the formula along with n = 200:
[tex]\begin{aligned}S_{200}&=\dfrac{1}{2}(200)[2(12)+(200-1)(6)]\\&=100[24+(199)(6)]\\&=100[24+1194]\\&=100[1218]\\&=121800\end{aligned}[/tex]
Related Questions
it is given that the rainfall in 2017 of 420mm was 25% more than in 2016. Find the annual rainfall in 2016
Answers
The annual rainfall in 2016 is 336 mm.
Let the annual rainfall in 2016 be 100x mm.
Now it is given that rainfall in 2017 is 25% more than rainfall in 2016.
So. rainfall in 2017 is = 100x + 100x*(25/100) = 100x+25x = 125x mm
Also given that the amount of rainfall in 2017 = 420 mm.
According to question the suitable equation is,
125x = 420
x = 420/125
x = 3.36
Hence the rainfall in 2016 is = 100x = 100*3.36 = 336 mm.
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Hillary ate 2/3 of a bag of Hot Cheetos in 3/4 of an hours. How much
of the bag of Hot Cheetos will Hillary eat in 5 hours.
Answers
Answer:
40/9
Step-by-step explanation:
4.8 is what percent of 12
Answers
Answer:40%
Step-by-step explanation:
Violet was comparing the price of chicken breast at two stores. The equation
y = 11.38x represents the total cost, in dollars and cents, y, that it costs for
pounds of chicken breast at SuperGrocery B. At SuperGrocery A, 3 pounds of chicken
breast costs $19.11.
How much more expensive is it, per pound, to buy chicken
breast at Store B than at Store A?
Answers
The chicken breast being brought at store B is more expensive than store A as it costs $5.01 more per pound.
Given,
Violet was comparing the price of chicken breast at two stores.
The equation which represents the total cost, in dollars and cents, y, that it costs for x pounds of the chicken breast at Super grocery B is:
y = 11.38x
whereas at store A the chicken breast of 3 pounds costs $19.11.
we are asked to determine how expensive is it per pound to buy chicken breast at store B than store A.
⇒ at store B the total cost is:
y = 11.38x
check the total cost of 3 pounds of chicken breast at store B:
⇒ y = 11.38(3)
since x represents the number of pounds.
⇒ y = $34.14
at store the chicken breast of 3 pounds costs $19.11
⇒ cost difference at both stores for simillar quantity:
⇒ 34.14 - 19.11
= 15.03
The cost of chicken per pound = 15.03/3
= $5.01
Hence the chicken breast at store B is $5.01 more expensive per pound than the chicken breast at store A.
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find the value of f(4) for the function f(a)=7(a+2) "-7"
Answers
Answer: 35
Step-by-step explanation:
[tex]f(4)=7(4+2)-7\\\\f(4)=7(6)-7\\\\f(4)=7(5)\\\\f(4)=35[/tex]
I need the answer and work please.
Answers
Answer: you prob fininshed 5,3
Step-by-step explanation:
also this is easy im srry for doing this
SUPER EASY!!!!
Given the inequality 3x ≤ 24, determine the value of x.
S:{11}
S:{8}
S:{15}
S:{34}
Answers
Answer:
The answer to the question is B or 8
Step-by-step explanation:
this is because ther is 3x meaning three time what ever the answer is and because 8x3=24 it is equal to 24 so 24 is less than or equal to 24 hence the corr6 answer is 8.
Answer:
the answer is 8
in a fruit punch drink, the 3 ingredients are apple juice, orange juice and cranberry juice. If 1/3 of the drink in apple juice and 1/2 is orange juice then write the ratio of cranberry juice to apple juice to orange juice in its simplest form
URGENT
Answers
The ratio of cranberry juice to apple juice to orange juice in the fruit punch is = 1 : 2 : 3
Let the total quantity of juice is 60 ml .
Now the apple juice is 1/3 of 60 = 20 ml
The orange juice is 1/2 of 60 = 30 ml
Therefore cranberry juice = 60 -(20+30) ml = 10 ml
Now the ratio of cranberry juice to apple juice to orange juice
= 10 : 20 : 30
= 1 : 2 : 3
We can exactly find out how much of one simple quantity is included in the other by simply comparing two amounts of the same units. Ratios can be divided into two smaller groups.
One is the part to the whole ratio; the other is the part to the part ratio. The exact relationship that is between the two distinct entities or groupings is only exactly depicted by the part-to-part ratio.
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How many ways are there to split the integers 1 through 14 into 7 pairs so that in each pair the
greater number is at least 2 times the lesser number?
Answers
The number of ways to split the integers, given the condition and using the Fundamental Counting Theorem, is of:
144.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes considering all trials is calculated by the multiplication of the factorials as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Given the condition that the greater number is at least 2 times the lesser number we have that the pairs are composed by one number between 1 and 7 and another number between 8 and 14.
Hence the pairs of each number are built as follows:
For the pair of the number 7, there are only one possible outcome, which is of 14.For the pair of the number 6, there are two possible outcomes, which are of either 12 or 13.For the pair of the number 5, there are three possible outcomes, which are of either 10, 11, and whichever of 12 or 13 is not paired with 6.For the pair of the number 4, there are four possible outcomes, which are of either 8, 9, and the two remaining numbers that are not paired with 5 or 6.For the pair of the number 3, there are three possible outcomes, which are the remaining numbers that are not paired with 4, 5 or 6.For the pair of the number 2, there are two possible outcomes, which are the remaining numbers that are not paired with 3, 4, 5 or 6.For the pair of the number 1, there is one possible outcome, which is the remaining numbers that is not paired with 2,3, 4, 5 or 6.Hence the number of ways to split the numbers is:
2 x 3 x 4 x 3 x 2 = 144.
(the numbers were multiplied because of the Fundamental Counting Theorem).
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Which inequality is equivalent to -x<8
Answers
Answer:(-7, infinite down)
Step-by-step explanation: -7,-8,-9...
Solving an Equation Involving Inverse Trigonometric Functions
sec^-1 x = csc^-1 2
Answers
The solution of the trigonometry function is 2√3/3.
What is the trigonometric function?
Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given trigonometric function is
sec^(-1) x = csc^(-1) 2
Assume that,
csc^(-1) 2 = z
→ 2 = csc z
→ 1/2 =1/ (csc z)
→ 1/2 =sin z
The trigonometry identity is [tex]\cos x =\sqrt{1-\sin^2x}[/tex].
[tex]\sqrt{1-(\frac{1}{2})^2 } =\cos z[/tex]
→ cos z = √3/2
→ sec z = 2/√3
→ sec z = 2√3/(√3×√3)
→ sec z = 2√3/3
→ z =sec^(-1) ( 2√3/3) = csc^(-1) 2
Putting csc^(-1) 2 = sec^(-1) ( 2√3/3):
sec^(-1) x = sec^(-1) ( 2√3/3)
→ x = 2√3/3
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if a=5, b=-2 and c=3 find the value of abc
Answers
Answer:
-30
Step-by-step explanation:
the order of multiplication doesn't matter
a*b*c = 5*-2*3 = -30
Which of the following are characteristics of the graph of the absolute value
parent function?
Check all that apply.
A. It goes through the origin.
B. It is in quadrants I and II.
C. The left half has a slope of 1.
D. It is V-shaped.
Answers
Answer: All Are correct
Step-by-step explanation:
Look at graph, the vertex hits the origin, the parent function is on the top half of the graph (quads 1 and 2), both the left and right side have a slope of 1, and it is v shaped!
Write a real world situation that could be modeled by the expression, 300+7x.
Answers
A real world situation that could be modeled by the expression, 300+7x is that Bob bought goods for $300 and then bought 6 pens that cost x dollar each.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both
In this case, Bob bought goods for $300 and then bought 6 pens that cost x dollar each. The total cost will be:
= 300 + (7 × x)
= 300 + 7x
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Please help
A waste bin is in the shape of a cylinder . The diameter of the base is 20cm and the height is 25cm . what is the volume of the waste bin.
Answers
Answer:
[tex]250\pi[/tex] cm³
Step-by-step explanation:
If the radius is 20 cm, the diameter is 10 cm.
Thus, the volume is [tex]\pi(10^2)(25)=250\pi[/tex] cm³.
The ratio of boys to girls in a class is 5:4. There are 36 students in the class. How many
students are girls?
Answers
Answer:
Let the girls be x
then, 5:4 = 5x and 4x
,
total stud.=36 so,
5x+4x=36
9x=36
x=36÷9
hence
x=4
now, boys = 5x=5×4=20
girls= 4x=4×4=16
so there are 16 girls
Help please i dont know how to do this.
Answers
A 270° counterclockwise rotation about the origin is the different one
How to determine which one is different?Rotation simply means turning
In order to answer this question, you need to know some rules about rotation. They are as follows:
1. If a point P, whose position vector is (x,y), is rotated 90° counterclockwise rotation about the origin, the position of the image P' is (-y, x)
2. If a point P, whose position vector is (x,y), is rotated 270° clockwise rotation about the origin, the position of the image P' is (-y, x). This is the same number 1
3. A 90° leftward rotation about the origin is the same as a 90° counterclockwise rotation about the origin. This is the same with number 1
4. If a point P, whose position vector is (x,y), is rotated 270° counterclockwise rotation about the origin, the position of the image P' is (y, -x). This is different from the other three.
From the graph: A(1, 2), B(2, 4), C(4, 2)
Answer for the different question: A'(2, -1), B'(4, -2), C'(2, -4)
Answer for the same three question: A'(-2, 1), B'(-4, 2), C'(-2, 4)
Therefore, a 270° counterclockwise rotation about the origin is the different one. The 4th option is the answer
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The function y=f(x) is graphed below. What is the average rate of change of the function f(x) on the interval −9≤x≤1?
Answers
The average rate of change of the function f(x) on the interval −9≤x≤1 is of:
r = -0.2.
How to obtain the average rate of change of a function?The average rate of change of a function is obtained by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given by the equation presented as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
Over the interval −9≤x≤1, the bounds of the interval are given as follows:
a = -9, b = 1.
From the graph shown by the image presented at the end of the answer, the numeric value of the function at each of these bounds is given as follows:
f(-9) = 3.f(1) = 1.Hence the average rate of change of the function on the interval is calculated as follows:
r = (1 - 3)/(1 - (-9)) = -2/10 = -0.2.
Missing InformationThe graph is shown by the image at the end of the answer.
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A 30-sided regular polygon has an angle measure represented as 6g°. Determine the value of g.
g = 30
g = 28
g = 180
g = 168
Answers
The value of g, for a 30-sided regular polygon has an angle measure represented as 6g° is calculated to be 28
How to find the value of gThe problem is solved using the formula for number of angles for n sided polygon
The formula is (n - 2)180
where n = number of sides
for 30-sided polygon the angles is solved as below
= (n - 2)180
= ( 30 - 2 ) * 180
= 28 * 180
= 5040
this is represented as 6g
each angle is measured 5040 / 30 = 168
6g = 168
g = 28
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Answer: 28
Step-by-step explanation: 168 is the whole polygon, so 6 times 28 is 168 therefore its correct, btw i also did the test
The number of men and women receiving bachelor's degrees each year has been steadily increasing. For the years 1970 through the projection of 2014, the number of men receiving degrees (in thousands) is given by the equation y= 3.9x+446, and for women, the equation is y= 14.2x+316, where x is the number of years after 1970.
Answers
Answer:
if what I think you want is the number of bachelor degrees from from 1970 to 2014 for both men and women is then:
men: 617.6
women: 940.8
Step-by-step explanation:
from 1970 to 2014 it is 44 years so we plug 44 into x for both equations
Men:
y = 3.9(44) + 446
y = 171.6 + 446
y = 617.6
Women:
y = 14.2(44) + 316
y = 624.8 + 316
y = 940.8
The height of a plant grew linearly over the course of a month. Initially the plant was 2 inches tall and it grew at an average rate of change of 0.125 inches per day.
a. Find an equation that models the height of the plant H in terms of the number of days d.
b. Determine the height of the plant after 15 days.
Answers
The equation that models the height of the plant H in terms of number of days is H = 1.875+0.125d and the height of the plant after 15 days is 3.75 inches.
According to the question,
We have the following information:
Initially the plant was 2 inches tall and it grew at an average rate of change of 0.125 inches per day.
2, 2.125, ...
Now, this series will become an arithmetic progression.
Formula to find the nth term:
an = a+(n-1)d
H = 2+(d-1)0.125
H = 1.875+0.125d
Now, the height after 15 days will be:
H = 1.875+0.125*15
H = 1.875+1.875
H = 3.75 inches
Hence, the equation that models the height of the plant H in terms of number of days is H = 1.875+0.125d and the height of the plant after 15 days is 3.75 inches.
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A container ship left port last week carrying some goods that weighed a total of 130,980 tons. Today, it stopped in another port to unload. The weight of the goods on the ship is now 91,686 tons. By what percent has the weight of the goods on the ship decreased?
help please annnd thaannks
Answers
Answer:
30%
Step-by-step explanation:
130980-91686=39294
39294/130908=0.3
Answer: 168,609 ton
Hi, to answer this question, first we have to calculate the amount of the weight decrease by multiplying the original weight of the goods (240,870) by the percentage decrease in decimal form ( divided by 100)
Mathematically speaking:
240,870 (30/100) =72,261 ton
Finally we have to subtract that value to the original weight:
240,870-72,261 = 168,609 ton
Feel free to ask for more if needed or if you did not understand something.
Step-by-step explanation:
D degrees warmer than 50 degrees is 78 degrees
Answers
Answer:
28
Step-by-step explanation:
Translate words into math -- "warmer" means +, "is" means =
So D + 50 = 78
D = 78 - 50
D = 28
Is it possible for a number to be a product of 2, a product of 5,
and a product of 10? Explain.
Answers
Answer: Yes
Step-by-step explanation:
Yes, it is because if you multiply 2 and 5, you get 10. 2 and 5 LCM is also 10. If you check 2 and five multiples you see this is also proved true.
2 - 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 ...
5 - 5, 10, 15, 20 ...
How long will it take to double your money if you invest in an account that pays 8% interest, compounded continuously
Answers
The time that would be taken for the money to double is 9 years.
How long would it take to double the money?Given that a compound interest has to do with the type of interest that is charged both on the principal and on the interest. We know that the principal is the money that was invested.
Let the principal be P and let the time taken be t. Let us now apply the formula;
A = P(1 + r)^n
Where A = 2P and r = 0.08
2P = P(1 + 0.08)^n
2P/P = (1.08)^n
2 = (1.08)^n
ln2 = nln1.08
n = ln2/ln1.08
n = 0.693/0.077
n = 9
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A teacher is four times as old as a student in 20 years the student age will be half of the teacher age how old are they now
Answers
Let the present age of student be x
Present of teacher will be 4x
After 20 years,
Age of student = x + 20
Age of teacher = 4x + 20
According to the given condition after 20 years,
x + 20 = (4x + 20)/2
x + 20 = 2x + 10
2x - x = 20 - 10
x = 10
So student's present age is 10 years while teacher's is 4 x 10 i.e 40 years.
Hope This Helps You!
Write the equation in slope-intercept form. Then choose the line's slope and y-intercept from the choices. So, choose two total answers. 6x+8y=-32
Answers
Answer:
Slope = -3/4, y-intercept = -4
Step-by-step explanation:
[tex]6x+8y=-32 \\ \\ 3x+4y=-16 \\ \\ 4y=-3x-16 \\ \\ y=-\frac{3}{4}x-4[/tex]
So, the slope is -3/4 and the y-intercept is -4.
describe how to map line p onto line q
Answers
Answer:r
Step-by-step explanation:r
What does s equal in 3s=24
Answers
Answer is 8
If 10 pants cost 240u.m, how much will 8 pants cost?
Answers
8 pants wil cost 192 u.m.
Step-by-step explanation:1. Establish a rule of 3.10 pants ----> 240u.m
8 pants ----> x
2. Solve for x.In a rule of 3, whenever the x is located at the bottom right corner, you always have to multiply upwards and to the right, and then divide the resulting number by the number on the top left. This is the operation you need to make:
x= (8 x 240) / 10
x= 192
Check the attached image to get a better understanding of this process.
3. Conclude.
8 pants wil cost 192 u.m.
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Proportional quantities are divided into directly and inversely proportional.
Two magnitudes are said to be directly proportional
when we multiply one of them by a number, the other is multiplied by the same number, and when we divide one of them by a number, the other is divided by the same number.
Problem :
If 10 pants cost 240u.m, how much will 8 pants cost?
We have:
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \\ \bold{ Assumption \: { \rightarrow} 10 \: pants \: \rightarrow 240 \: u.m\\\sf \: \: \: \: \: \: \: \: \: Question \rightarrow8 \: pants \rightarrow \: x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]
As can be seen, the number of pants and the cost are magnitudes directly proportional, and therefore, we put the + sign below the pants and the - sign above.
Therefore we will have:
[tex]\boxed{ \bold{ \: x = \dfrac{240 * 8}{10} = 192 \: u.m} }[/tex]
So the 8 pants cost 192.