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.)
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:
please HELP MEEEEEE .A store owner wants to make a candy that sells for $1 per pound.he has 50 lb of sugar candies that cost $1.20 per pound.how many pounds of gummy candies that cost 80 cents per pound should he add.
Answer:
50 pounds
Step-by-step explanation:
we can use the equation 60+80/100x=1(x+50)
we get 80/100 x because the gummy candies are 80 cents or 80/100x
we get 60 from multiplying 1.20$ x 50 = 60
solve:
60+80/100x = x+50
60 = x-80/100x+50
60-50 = 20/100x
10 = 20/100x
x= 10 x 100/20 = 10x5= 50 pounds
Using proportions, it is found that he should add 50 pounds of gummy candies that cost 80 cents per pound.
What is a proportion?A proportion is a fraction of a total amount.
This problem is organized as follows:
There is a total of 50 + x pounds.Of those, 50 cost $1.2 per pound.x cost $0.8 per pound.The selling price is of $1.Hence:
[tex]\frac{50}{50 + x}1.2 + \frac{x}{50+x}0.8 = 1[/tex]
[tex]\frac{60 + 0.8x}{50 + x} = 1[/tex]
[tex]50 + x = 60 + 0.8x[/tex]
[tex]0.2x = 10[/tex]
[tex]x = \frac{10}{0.2}[/tex]
[tex]x = 50[/tex]
He should add 50 pounds of gummy candies that cost 80 cents per pound.
More can be learned about proportions at https://brainly.com/question/24372153
(-5, -3); slope = -3/5
turn into y intercept equation please
plss helppp mee! The corporate team-building event will cost $18 if it has 3 attendees. How many attendees can there be, at most, if the budget for the corporate team-building event is $42? Assume the relationship is directly proportional.
Answer:
16 attendees at most. sorry if its wrong
Step-by-step explanation:
33 divided by 11 = 3.
3 for each attendee.
48 - 33 = 15.
15 divided by 3 = 5.
Find sin(0)
A. DE/EF
Answer: D. DE/DF
Step-by-step explanation: I got it right on edg...
help pls 6th grade math
Answer:
All of them are correct except for the last one which is incorrect
Step-by-step explanation:
All you need to substitute the answers given for "r" and see if its less than or equal to 2
- 3.5 [tex]\leq[/tex] 2 Correct (negative numbers are always smaller than a positive number)
- 2 [tex]\leq[/tex] 2 Correct (negative numbers are always smaller than a positive number)
-1 [tex]\leq[/tex] 2 Correct ( negative numbers are always smaller than a positive number)
0 [tex]\leq[/tex] 2 Correct ( 0 has a value much more less than the value of 2)
2 [tex]\leq[/tex] 2 Correct (they both have the same value as "2")
4 [tex]\frac{1}{4}[/tex] [tex]\leq[/tex] 2 Incorrect ( 4 [tex]\frac{1}{4}[/tex] has a much more greater value than 2, therefore this is incorrect)
how can i teach an entire year of alg 2 before next school year? i learned nothing this year and i want to take an advanced physics class next year but i’m scared it will affect me if i don’t learn it on my own ://
Answer:
use khan academy, its a website or an app which a lot of kids which are homeschooled learn education on.
Plssss I need help this question is really hard to find and I need this back quickly pls help me :(
Answer:
A) $402,500
Step-by-step explanation:
69100-57600= 11,500
11,500 x 35= 402,500
Need help with this one
Answer: Line 3
Step-by-step explanation:
71/3 - 21/4 (2 1/5 × 3/4) with working
What is the solution to 3.25k + 1 - 4.25k = -2
Answer: K=3
Step-by-step explanation: Have a nice day!-Lily ^_^
state if polygons are similar
Which is equivalent to 42x +49.
A. 2 (21 + 24)
B. 8x + 13
C. 4 (2x + 9)
D. 7 (6x + 7
Answer:
D. 7 (6x+7)
Step-by-step explanation:
Factor 7 out of 42x + 49
An object is moving east, and it’s velocity changes from 65 m/s to 25 m/s in 10 seconds.which describes acceleration
Answer:
The acceleration of object is -4 ms⁻²
Step-by-step explanation:
We are given:
Initial Velocity = 65 m/s
Final Velocity = 25 m/s
Time t = 10 seconds
We need to find acceleration.
The formula used to find acceleration is: [tex]Acceleration=\frac{Final\:Velocity-Initial\:Velocity}{Time}[/tex]
Putting value in the formula and finding acceleration:
[tex]Acceleration=\frac{Final\:Velocity-Initial\:Velocity}{Time}\\Acceleration=\frac{25-65}{10}\\Acceleration=\frac{-40}{10}\\Acceleration=-4\:ms^{-2}[/tex]
So, acceleration of object is -4 ms⁻²
9y-7=29
Prove y=4
Solve the problem
9y - 7 = 29
=> 9y = 29 + 7 [Transferring 7 to R.H.S.]
=> 9y = 36
=> y = 36/9 [Transferring 9 to R.H.S.]
=> y = 4
Hence proved.
Answer:
Here
Step-by-step explanation:
Question 1
1 pts
Two bottled waters and three bags of chips cost $4.75, One bottled water and two bags
of chips cost $2.75.How much do the chips cost?
(write answer without dollar sign, ex: $3.25 becomes 3.25)
x to the 2nd power minus 6 equals 1
Answer:
2.646
Step-by-step explanation:
You have to 6 to the 1 and then take the square root of the number which is seven leaving you with 2.646
Answer:
x = ±√7
Step-by-step explanation:
Symbolically, we have x^2 - 6 = 1, and so x^2 = 7, so that x = ±√7
Geometry
Is Dn (triangle DEF) = triangle D'E'F' an enlargement or a reduction? What is the scale factor n of the dilation?
Answer:
A. Enlargement, 1.5
Step-by-step explanation:
Comparing the two triangles, it would be observed that ΔD'E'F' is larger than ΔDEF. This implies that ΔDEF has been multiplied by a scale factor.
To determine the scale factor used, consider the side DE and D'E' of the two triangles:
scale factor = [tex]\frac{D'E'}{DE}[/tex]
= [tex]\frac{6}{4}[/tex]
scale factor = 1.5
Therefore, ΔDEF was enlarged to ΔD'E'F' using a scale factor of 1.5. Then the correct option is A.
Sam writes on a white board the positive integers from 1 to 6 inclusive, once each, She then writes p
additional fives and q sevens on the board. The mean of all the numbers on the board is then 5.3.
What is the smallest possible value of q?
Answer: The smallest possible value of q is 9.
Step-by-step explanation:
If we have the set of N numbers:
{x₁, x₂, x₃, ..., xₙ}
The mean of this set is:
M = (x₁ + x₂ + x₃ + ... + xₙ)/N
Now, in this case our set is:
{1, 2, 3, 4, 5, 6, p times 5, q times 7}
Then we have a total of:
6 + q + p numbers.
The mean of this set will be:
Mean = 5.3 = (1 + 2 + 3 + 4 + 5 + 6 + p*5 + q*7)/(6 + p + q)
This is the equation that we will use now.
First, we can simplify this as:
5.3 = (21 + p*5 + q*7)/(6 + p + q)
Now we can pass the denominator in the right to the other side as:
5.3*(6 + p + q) = (21 + p*5 + q*7)
31.8 + p*5.3 + q*5.3 = 21 + p*5 + q*7
Now we want to isolate the variable p in one side of the equation.
p*5.3 - p*5 = 21 - 31.8 + q*7 - q*5.3
p*0.3 = q*1.7 - 10.8
p = (q*1.7 - 10.8)/0.3 = q*(1.7/0.3) - 36
p = q*(1.7/0.3) - 36
p = q*(17/10)*(10/3) - 36
p = q*(17/3) - 36
Now we can see that the denominator is 3, so q should be a multiple of 3.
We want to start with the smallest multiples of 3, but if we use q = 3, then we will have a negative value of p (the same happens if we use 1 = 6)
We do not want that, then we need to use q = 9
p = 9*(17/3) - 36
p = 3*17 - 36
p = 15
Then we have;
9 times the number 7
15 times the number 5 (plus one, because it was already on the first 6 numbers that Sam wrote)
The smallest possible value of q is 9.
Now we want to get the smallest possible value of q.
Remember, p and q need to be positive numbers.
Why is angle 1 congruent with angle C In the diagram?
O they are exterior angles to the triangle
O they are corresponding angles
O they are interior angles to the triangle
O they are vertical angles
Answer:
They are vertical angles.
Step-by-step explanation:
Angle 1 would be congruent with C because they are vertical.
Solve the equation below.
2 (x - 4) - 4x = -10
Answer:
x=2
4-8=-4
-4(-4)=-16
-16-(-4)=-10
ok what next helppp i need 2
Answer:
3-2
Step-by-step explanation
help me!
Define the opposite and the absolute value of -15.
The opposite of -15 is -15. The absolute value of -15 is -15.
The opposite of -15 is -15. The absolute value of -15 is 15.
The opposite of -15 is 15. The absolute value of -15 is 15.
The opposite of -15 is 15. The absolute value of -15 is -15.
Answer:
The opposite of -15 is 15. The absolute value of -15 is 15.
Ansbsbxuhsbxbwaszbwihxbiybxcscbyqsbciasbhicbxshbabxh
Step-by-step explanation:
I need help Finding the perimeter of a towel that measures 2 feet by 34 foot
Answer:
72 feet
Step-by-step explanation:
multiply 34 by 2 (because there is 2 sides), and multiply 2 by 2 (because there is 2 sides), and you'll get 68 and 4. add them together, and you'll get 72.
A class writes the equation n + n + 1 + n + 2 = 87 to solve the following problem.
The sum of 3 consecutive odd integers is 87. Find the three integers.
What error did they make?
Answer:
n + n+2 + m+4 = 87
I got this answer.....hope it may helpful
can someone help me with this
Answer:
1] x=4.21
2] 52.5
3] 3.82
4] 38.73
5] 32.005
6] 31.21
Step-by-step explanation:
A biology class examined some flowers in a local meadow. The students saw 88 perennial
flowers and 12 annual flowers. What percentage of the flowers were perennials?
Answer:
88%
Step-by-step explanation:
how many months give you 27 years
Answer:
324 Months
Step-by-step explanation:
Answer:
324 months according to goggle.
Each of a company's 546 employees earns $790 each week. What is the total
amount the company pays all its employees for 4 weeks?
Answer:
$1,725,360
Step-by-step explanation:
For this, you would just multiply every number: [tex]employees×weekly salary×weeks[/tex] which is [tex]546×790×4=1,725,360[/tex].
Answer:
I think all u need to do is mulitply thoses numbers just use calulator
Step-by-step explanation:
hope it helped
Adult tickets for the school musical are sold for $3.50 and student tickets are sold for $2.50 on a given night 425 tickets were sold for $ 1237.50. Wrote a system of linear equations for the problem
Answer:
3.5x + 2.50y = 1237.50
425 = x + y
Step-by-step explanation:
number of adult tickets: x
number of student tickets: y
3.5x + 2.50y = 1237.50
( value of adult ticket [3.50]* number of adult tickets [x]) + (value of student ticket [2.50] * number of student tickets [y]) = total value (1237.50)
425 = x + y
(number of adult tickets [x]) + (number of student tickets [y]) = total (425)
