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.)
Find Cos b in the triangle
Answer:
3/5
Step-by-step explanation:
SOHCAHTOA
Cos- adjacent/hypotenuse
adjacent side: 3
hypotenuse: 5
adj/hyp: 3/5
Good night everyone
Also
should I
A. Go to bed
B. clean my room
C. Cry
c. is looking like the best option right now
Answer:
A
Step-by-step explanation:
8 hours of sleep is healthy
Answer:
clean your room then go to bed. you will feel proud of yourself after you do
f(n) = 3(n+ 1). Find f(-2)
Answer:
-6 +3= -3
Step-by-step explanation:
An ice cream shop is choosing a milk delivery service. The Spotted Cow charges $2.80 per gallon, plus a $2 delivery fee. Dairy Farms charges $2.10 per gallon, plus a $10 delivery fee. If the ice cream shop uses 20 gallons a milk per week, which service is a better deal? Group of answer choices
Answer:
The Dairy Farm is better deal.
Step-by-step explanation:
Given that:
Per gallon charges of the Spotted Cow = $2.80
Delivery fee = $2
Let,
x be the gallons of milk.
S(x) = 2.80x + 2
Putting x = 20
S(20) = 2.80(20) + 2 = 56 + 2
S(20) = $58
Per gallon charges of the Dairy Farms = $2.10
Delivery fee = $10
D(x) = 2.10x + 10
Putting x = 20
D(20) = 2.10(20) + 10 = 42 + 10
D(20) = $52
Hence,
The Dairy Farm is better deal.
Can someone could explain the part of simplifying rational expressions where it is x is not equal to a number. I've had a hard time understanding how to get that answer. The picture is an example in my notes.
Answer:
yeah it is bcoz if x is -1 then x+1 will be
-1+1 which is 0 and ur whole equation will say
now thats a lot of damage
Find the measure of each interior angle.
Answer:
d) m<J = 115, m<K = 130, m<M = 50, m<N = 65
Step-by-step explanation:
The sum of interior angles in this rectangle is equal to 360
if we add all the given angles 7x + 10 = 360 subtract 10 from both sides
7x = 350 divide both sides by 7
x = 50 to find the measure of each angle replace x with 50
DOES ANYONE KNOW WHAT THE CORRDINTS ARE??!!
Answer:
-7 and -5
Step-by-step explanation:
It is where the parabola intercepts the x axis which is -7 and -5
What is 0.0000000053 in standard form?
Answer:
5.3
Step-by-step explanation:
3x - 8 = 4(x+5) plz plz plz solve it
Answer:
=−28
Step-by-step explanation:
If 20 is 40% of a value,what is that value
Answer:
50, 20 is 40 %
to get from 40 % to 100% you multiply by 2.5
20 times 2.5 is 50
50 is 100%
Step-by-step explanation:
hope this helps have a good day :) ❤
I need help quick because it’s timed.
[tex]5x {}^{2} + 2x - 3 - px - p[/tex]
Answer:
5x² + 2x - 3 - px - p
= 5x² + 5x - 3x - 3 - p(x + 1)
= 5x(x + 1) - 3(x + 1) - p(x + 1)
= (x + 1)(5x - 3 - p)
Which value of y makes the inequality 3y^2+2(y-5)>8 true
A y=0
B y= -1
C y= -2
D y= -3
Answer:
Conclusion:
As y = -3 MAKES the inequality TRUE.
Therefore, option D i.e. y = -3 is true.
Step-by-step explanation:
Given the inequality
3y² + 2(y - 5) > 8
For y = 0
substitute y = 0 in the inequality
3y² + 2(y - 5) > 8
3(0)² + 2(0 - 5) > 8
3(0) + 2(-5) > 8
0 - 10 > 8
-10 > 8
FALSE!
-10 can not be greater than 8.
Hence, y = 0 does not make the inequality true.
For y = -1
substitute y = -1 in the inequality
3y² + 2(y - 5) > 8
3(-1)² + 2(-1 - 5) > 8
3(1) + 2(-6) > 8
3 - 12 > 8
-9 > 8
FALSE!
-9 can not be greater than 8.
Hence, y = 1 does not make the inequality true.
For y = -2
substitute y = -2 in the inequality
3y² + 2(y - 5) > 8
3(-2)² + 2(-2 - 5) > 8
3(4) + 2(-7) > 8
12 - 14 > 8
-2 > 8
FALSE!
-2 can not be greater than 8.
Hence, y = -2 does not make the inequality true.
For y = -3
substitute y = -3 in the inequality
3y² + 2(y - 5) > 8
3(-3)² + 2(-3 - 5) > 8
3(9) + 2(-8) > 8
27 - 16 > 8
11 > 8
TRUE!
11 is indeed greater than 8.
Hence, y = -3 MAKES the inequality TRUE.
Conclusion:
As y = -3 MAKES the inequality TRUE.
Therefore, option D i.e. y = -3 is true.
Answer:
D
Step-by-step explanation:
Increase 386.3 by 4%
Given:
Increase 386.3 by 4%.
To find:
The value for given statement.
Solution:
We have,
Initial value = 386.3
Increasing rate = 4%
The increased value is
[tex]\text{New value}=\text{Initial value + Increasing rate }\times \text{Initial value}[/tex]
[tex]\text{New value}=386.3+\dfrac{4}{100}\times 386.3[/tex]
[tex]\text{New value}=386.3+15.452 [/tex]
[tex]\text{New value}=401.752[/tex]
Therefore, the required value is 401.752.
34=16+x helpppppp please due in 30 minutes
Answer:
34-16=18
so x = 18
Step-by-step explanation:
Answer:
x = 18
Step-by-step explanation:
Subtract 16 from both sides to get x by itself. 34 - 16 = 18. 18 = x
A box of a dozen fruit tarts costs $15. How much money does 1 fruit tart cost?
1 dozen = 12 so 15/12 is 1.25
which means 1 fruit tart is $1.25
Find the length of the hypotenuse, c in this triangle
Answer:
c = 5cm
Step-by-step explanation:
a^2 + b^2 = c^2
4^2 + 3^2 = c^2
16 + 9 = c^2
25 = c^2
do the square root of 25 and c to solve for c
the square root of c^2 is c
therefore, c= 5cm
Pls help!!!!!!!!!!!!!!!!!!!!
Answer:
16x - 9 is the expression
Step-by-step explanation:
2x + 2x = 4x co effecients with the same variables can be added then I multiplied 4x by 4x which would 16x then later got the expression (16x - 9).
Mae has a number cube with 6 sides that are numbered 1 through 6. What is the probability that Mae will roll an odd number?
A
1 out of 3
B
1 out of 6
с
3 out of 6
D
5 out of 6
Answer:
C) [tex]P(E) = \frac{3}{6}[/tex]
The probability that Mae will roll an odd number
[tex]P(E) = \frac{3}{6}[/tex]
Step-by-step explanation:
Step(i):-
Given that Mae has a number cube with 6 sides that are numbered 1 through 6.
n(S) = { 1,2,3,4,5,6,} = 6
Let 'E ' be the event of odd numbers
Mae will roll an odd number
n(E) = {1, 3, 5} = 3
Step(ii):-
The probability that Mae will roll an odd number
[tex]P(E) = \frac{n(E)}{n(S)} = \frac{3}{6}[/tex]
[tex]P(E) = \frac{3}{6}[/tex]
What is x?
4x(2x+6)=8x²(23-5)
pls, help for the first person to answer I will give them a brainlist.
Answer:
x= 3/17
Step-by-step explanation:
4x(2x+6) =8x^2(23-5)
8x^2 +24x = 144 x^2
24x = 136 x^2
24= 136 x
x=24/136
x=3/17
1/2y=25
Help please
Answer:
=> 25 x 2 = 50
Step-by-step explanation:
3x + 16 = 136
(3 seconds per item, plus 16 seconds to process payment, equals 136 seconds total.)
Subtract 16 from each side. Then divide both sides by 3.
Answer:
x = 40
Step-by-step explanation:
how do you solve y=3-x
2x+y=6
Answer:
x=3 y=0
Step-by-step explanation:
This is called system of innequalities
we know y= 3-x and we substitute that into 2x+y=6 and we get
2x+3-x=6 we solve and get x=3
then we substitute x into the first equation and we get y=3-3 and get 0
x=3 y=0
Helena wants to find the perimeter of the graphed quadrilateral ABCD.
Which side will require the use of the distance formula to find the length?
side AB
side BC
side CD
side DA
Round the fraction to the nearest whole number. 3 1/2
Answer:
4
Step-by-step explanation:
3 1/2= 3.5
5 rounds up, so it'll be 4
Answer:
4 hope this helps
I don’t get it please can I have help :)
Answer:
[tex] {7}^{2} \times \sqrt[3]{7}\\ = {7}^{2} \times {7}^{ \frac{1}{3} } \\ = {7}^{(2 + \frac{1}{3}) } \\ = {7}^{ \frac{(6 + 1)}{3}} \\ = \boxed{{7}^{ \frac{7}{3}}}✓[/tex]
7⁷/³ is the right answer.WHO's BIRTHDAY was on 24 January?
my bday was yesterday
mentors can u please not remove this because i want this to be here and I WILL be VERy HApy
happy belated birthday!
1. Many nonmetals are weak and
2. The property of an element to be beaten into sheets is
known as
3. The total space occupied by an object is
5.
is a gas and is an
Answer:
44
Step-by-step explanation:
i did 4 + 40 = 44 :)))))
Helpppppppppp plzzzzz
so do all the question like this types
thankyou for your question
What is the value of (x)?
Answer:
1
Step-by-step explanation:
Answer:
x=1
Step-by-step explanation: