9514 1404 393
Answer:
solve for f(n) in terms of f(n-1)
Step-by-step explanation:
In general, you solve for f(n) in terms of f(n-k) for k = 1, 2, 3, ....
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Usually, such questions arise in the context of arithmetic or geometric sequences.
Arithmetic sequence
The explicit formula for an arithmetic sequence has the general form ...
a(n) = a(1) +d(n -1) . . . . . . . first term a(1); common difference d
The recursive formula for the same arithmetic sequence will look like ...
a(1) = a(1) . . . . . . . the first term is the first term
a(n) = a(n-1) +d . . . the successive terms are found by adding the common difference to the term before
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Note: The explicit formula may be given as the linear equation a(n) = dn +b. Then the first term is a(1) = d+b.
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Geometric sequence
The explicit formula of a geometric sequence has the general form ...
a(n) = a(1)·r^(n -1) . . . . . . first term a(1); common ratio r
The recursive formula for the same geometric sequence will be ...
a(1) = a(1) . . . . . . the first term is the first term
a(n) = a(n-1)·r . . . the successive terms are found by multiplying the term before by the common ratio
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Note: The explicit formula may be given as the exponential equation a(n) = k·r^n. Then the first term is a(1) = kr.
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Other sequences
Suppose you're given the quadratic sequence ...
a(n) = pn^2 +qn +r
Since the sequence is known to be quadratic (polynomial degree 2), we expect that we will only need the two previous terms a(n-1) and a(n-2). Effectively, we want to solve ...
a(n) = c·a(n-1) +d·a(n-2) +e
for the values c, d, and e. Doing that, we find ...
(c, d, e) = (2, -1, 2p)
So, the recursive relation is ...
a(1) = p +q +r
a(2) = 4p +2q +r
a(n) = 2a(n-1) -a(n-2) +2p
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Additional comment
The basic idea is to write the expression for a(n) in terms of terms a(n-1), a(n-2) and so on. That will be easier for polynomial sequences than for sequences of arbitrary form.
There are some known translations between explicit and recursive formulas for different kinds of sequences, as we have shown above. If you recognize the sequence you have as being of a form with a known translation, then you would make use of that known translation. (For example, Fibonacci-like sequences are originally defined as recursive, but have explicit formulas of a somewhat complicated nature. If you recognize the form, translation from the explicit formula may be easy. If you must derive the recursive relation from the explicit formula, you may be in for a lot of work.)
6x + 4y > 12
What’s the x and y intercepts
Answer:
x interprets: 2,0
y interprets: 0,3
Step-by-step explanation:
CAN YOU HELP ME WITH THIS EXERCISE: 3(x6) + 8 = 5(x-5)-1
X= -1. That’s the answer for this
Answer:
Step-by-step explanation:
3(x6) + 8 = 5(x-5) - 1
we move all the terms to the left:
3(x6) + 8 -(5(x-5) -1 ) = 0
We add all the numbers together, and all the variables:
3x^6 - ( 5 ( X-5) - 1) + 8 = 0
We calculate terms in parentheses: - ( 5 ( x-5) - 1 ) , so :
5(x-5)-1
we multiply:
5x - 25 -1
we add all the numbers together, and all the variables:
5x - 26
back to the equation:
- ( 5 x - 26)
2(x+7) = -4x + 14
What is the value of x, will give brainliest to first answer
Answer:
x = 0
Step-by-step explanation:
[tex]2(x+7)=-4x+14\\x+7=-2x+7\\x=-2x\\3x=0\\x=0[/tex]
Answer:
x=-0
Step-by-step explanation:
This is my 2 try can someone plz help me get the answer
Answer:
surface area is the answer
For an object to remain at rest, which of the following must be
true?
А
The forces on it are balanced.
B
There is no friction.
с
Gravity does not act on it.
D
The object has no mass.
Answer:
B
There is no friction
Step-by-step explanation:
if the object is stationary , it's not moving, no forces acting on it how can it produces friction ?
Which number would make this number sentence true? (3 + 2) x ? = 5 x 8
Answer:
8
Step-by-step explanation:
3+2=5
5 x 8 = 5 x 8
Answer:
8
Step-by-step explanation:
2 numbers are in perenticies so do them first 3+2 = 5 Then wait dont do nothing with that do 5x8 to get what to need to get 5 x? to witch is
40 so 8 would be the correct answer
A man has 1/5 of a kilogram of lentils. He shares it equally amongst 3 people. How many kilograms does each person get? Answer needs to be the fraction of a kilogram
Answer:
1/15
Step-by-step explanation:
1/5 divided by three is the same as 1/5*1/3. 1*1=1 and 5*3=15
Number 8 please I don’t know anything
Answer:
A. Domain: 1,2 Range: 0,1,4
B. Domain: 0,2,4, Range: 1,2,3,
Step-by-step explanation:
Domain is the x axis
Range is the y axis
find the slope of the line graph blow
Answer:
x-2y+2=0
Step-by-step explanation:
An airline company has a number of airplanes, n, that seat 250 customers each. Write an equation to represent, c, the total number of customers that can be seated by all of the airplanes.
if n = 12 use your equation to determine the total.
Answer:
n×250=c
3000 people
Step-by-step explanation:
Since each airplane seats 250 people and we need to see the total number of people able to be seated, we multiply the amount of airplanes by seats, and get the equation of n×250=c.
And then if we have 12 airplanes, n=12, the equation becomes 12×250=c.
c=3000 people
(hope this helps!)
the Jones family and Khan family go to the fayre. The Jones family pay £76.50 for 4 adults and 5 children. The Khan family pay £48 for 2 adults and 4 children.
Answer:
Is this an incomplete question or?
What is the area of this figure?
Enter your answer in the box.
mm²
Composite figure composed of a a right triangle with a base of 3 mm and a height of 4 mm, and two rectangles, one with side lengths of 3mm and 4mm, the other with side lengths of 1 mm and 6 mm.
12cm2 or 24 because if u do b and h and subtract half u will 12
Which angels are corresponding?
Answer:
8 and 16
Step-by-step explanation:
8 and 16 are corresponding angles
hope this helps....
A rectangle measures 6 inches by 15 inches. If each dimension of the rectangle is dilated by a scale factor of 1/3 to create a new rectangle
HELP ME PLEASEEEE I NEED IT ASAP
Answer:
3× + 3 = 10 + 2× find like terms 3× -2× = 10 -3 × = 7 final answer 7
help please?? hurry!! Find the values of the variables in the diagram above
Answer:
C = 95 degrees.
Step-by-step explanation:
The line is being intersected by parallel lines, so that means that those angles will add up to 180. 180-85=95.
A flying squirrel's nest is 6 meters high in a tree. From its nest, the flying squirrel glides 8 meters to reach an acorn that is on the ground. How far is the acorn from the base of the tree? If necessary, round to the nearest tenth.
Answer:
2 meters
Step-by-step explanation:
a pair of shoes originally priced at $120 are on sale for 89.99 what percent discount was applied ?round to the nearest whole percent.
Answer:
25%
Step-by-step explanation:
Divide 89.99 or 90 (since you are rounding) by 120, and you get .7499 or 75%. You have 25% ($30) as the discount because 90 is 75% of $120.
help please will give brainliest PLEASE
Answer:
I think the answer is b the answer is b
Answer:
The answer is really and surely B
Will mark brainliest. Please help! find the surface area of a cylinder whose radius is 1.2mm and whose height is 2mm.
Answer:
25.1mm²
Step-by-step explanation:
Total surface area of a cylinder = 2πr(r+h)
r is the radius = 1.2mm
h is the height = 2mm
Substitute
TSA = 2(3.14)(1.2)[1.2+2]
TSA = 7.536[3.2]
TSA = 24.1152
Hence the total surface area of the cylinder is 25.1mm²
Answer:
The
answer is actually ( in acellus that is )
24.1
Step-by-step explanation:
-7n=35
what does n equal and show your steps and ur solution plz thx
reply or answer asap
Answer:
n = - 5
Step-by-step explanation:
The expression is given as ;
-7n = 35
Divide both sides by -7
-7n/-7 = 35/-7
n= -5
The value of n is -5
plsss answer this will mark brainiest
a certain coin is a circle with a diameter of 18mm. What is the exact area of either face of the coin in terms of pi (3.14)
Answer:
254.34 mm².
Step-by-step explanation:
For this problem, we use the formula to find the area of a circle, which is[tex]A=\pi r^2[/tex] . [tex]r[/tex] is the radius, which we can find by dividing the diameter by 2 and [tex]\pi[/tex] in this case is 3.14.
[tex]A=\pi r^2\\A=3.14*(18/2)^2\\A=3.14*9^2\\A=3.14*81\\A=254.34[/tex]
Therefore, the area of either face of the coin is 254.34 mm².
I hope this helps!
A linear function is graphed in the coordinate plane below. What is the Y-intercept of the graph of the function
PLEASE PLEASE HOW MANY TIMES CAN I SAY PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer like
Answer 1.___________
Answer 2.___________
Answer 3.___________
Answer 4.___________
Answer 5.___________
The highest scorer of the women's basketball championship was Jessica Bradley. She scored 118 more points than Tina Harner, her teammate. Together, Bradley and Harner scored 1552 points. How many points did each player score during the championship?
Answer:
Jessica scored 835 points,
and Tina scored 717 points.
Step-by-step explanation:
Let $j$ stand for Jessica Bradley, and let $t$ stand for Tina Harner. By turning the words of this problem into equations, we get:
j - 118 = t
and, j + t = 1552.
Now that we have a system of equations, all we have to do now is to solve it.
By substituting the value of t (first equation) into the second equation, we get:
j + (j - 118) = 1552.
Get rid of the parentheses:
j + j - 118 = 1552
Simplifing:
2j - 118 = 1552
2j = 1670
j = 835.
Now that we know how many points Jessica scored, we can easily find out how many points Tina scored. By sticking in the value of Jessica's score into the first equation.
835 - 118 = t
t = 717.
So, the answer to this problem is (j, t) = (835, 717).
Find the geometric mean of sqrt 77 and sqrt 343.
Answer:
12.75
Step-by-step explanation:
The computation of the geometric mean of sqrt 77 and sqrt 343 is given below:
As we know that
Geometric mean = [tex]\sqrt{ab}[/tex]
where
a is the first number = [tex]\sqrt{77}[/tex]
And, the b is the second number = [tex]\sqrt{343}[/tex]
Now first we have to convert into a number
For a it, is = 8.78
And, for b, it is = 18.52
Now the geometric mean is
[tex]= \sqrt{8.78 \times 18.52}[/tex]
= 12.75
please help I've been having a bad day can you help with this math question
Answer:
id say a or b but....... maybe not
Step-by-step explanation:
Answer:
C) 918,450 cm^3
Step-by-step explanation:
Consider the graph shown. Which function could this graph represent
Answer:
x
Step-by-step explanation:
Which expressions are equal to 4y + 8 + 4y + 8?
Answer:
8y + 16
Step-by-step explanation:
Put the like variables together