Answers
The next term in the sequence is obtained by subtracting 4 from the previous term:
13 = 17 - 4
9 = 13 - 4
5 = 9 - 4
and so on.
Recursively, we can describe the n-th term in the sequence (denoted a(n)) as a function of the (n - 1)-th term:
a(n) = a(n - 1) - 4
starting with a(1) = 17. So we have, for instance,
a(2) = a(1) - 4 = 17 - 4 = 13
We want to find an explicit formula for a(n), meaning we want a way to determine the n-th term only as a function of n, and not any other known term in the sequence. We can iteratively apply the recursive rule above:
a(n) = a(n - 1) - 4
a(n - 1) = a(n - 2) - 4
→ a(n) = (a(n - 2) - 4) - 4 = a(n - 2) - 2×4
a(n - 2) = a(n - 3) - 4
→ a(n) = (a(n - 3) - 4) - 2×4 = a(n - 3) - 3×4
a(n - 3) = a(n - 4) - 4
→ a(n) = (a(n - 4) - 4) - 3×4 = a(n - 4) - 4×4
and so on, down to
a(n) = a(1) - (n - 1)×4
The first term is a(1) = 17, so
a(n) = 17 - 4 (n - 1) = 21 - 4n
Related Questions
A right cone has a radius of 13 cm and a slant height of 20 cm. Find its surface area.
Question 12 options:
A)
10,618.6 cm2
B)
816.8 cm2
C)
1,347.7 cm2
D)
3,539.5 cm2
Answers
Answer:
[tex]A=1347.7\ cm^2[/tex]
Step-by-step explanation:
Given that,
Radius of a cone, r = 13 cm
Slant height of the cone, l = 20 cm
We need to find the surface area of the cone. The formula for the surface area of the cone is given by :
[tex]A=\pi rl +\pi r^2[/tex]
Put all the values,
[tex]A=\pi r(l + r)\\\\A=\pi \times 13(20 + 13)\\\\A=1347.7\ cm^2[/tex]
So, the surface area of the cone is [tex]1347.7\ cm^2[/tex].
Use long division to solve for n. 6,588 ÷ 4 = n
Answers
Answer:
n = 1647
Step-by-step explanation:
Answer:
n = 1647
Step-by-step explanation:
If 4 movie tickets cost $28, how much would it cost to buy 9 movie tickets
Answers
Answer:
$63
Step-by-step explanation:
First, divide 28 by 4 to get 7
Now we know that one ticket cost $7.
Do 7 times 9 to get 63
9 tickets costs $63
9 movie tickets would cost $63.
Since 4 movie tickets cost $28, you can divide 28 by 4 to get 7. From here, you can multiply 7 by 9 to get 63.
May I have brainliest please? :)
What is 57/7 ?
Division
Answers
Answer:
8.142
Step-by-step explanation:
Answer: You can decide to choose any of these but they're all the same!
8 R 1
Decimal form:
8.1 (if you round it to the nearest tenths).
8.14 (if you round it to the nearest hundredths).
8.143 (if you round it to the nearest thousandths).
Step-by-step explanation:
When you begin the division, you have to think of what is the highest number that is less than 57 that is a multiple of 7, that number is 56. 56/7 is 8 which is where I got the 8.
57 - 56 = 1 which is the remainder.
If you want to write it in decimal form, you divide the 1 by 7 and since you'll get a decimal number with 0.14.. you had that number to 8, which gives you your answer in decimal form!
Hope that helped!
4xr=14 pls i need help.
Answers
Answer: x =7/2 or r = 7/2 so this means there the same.
Step-by-step explanation:
_________
[tex] \: [/tex]
4 × r = 14
4r = 14
r = 14/4
r = 7/2
r = 3½ or 3,5
The sugar is sold at & 5.4 per kg at
At what price should it be sold per kg to com
a profit of 20%
Answers
the sugar is sold at rupees 5.4 per kg at a loss of 10% at what price should it be sold per kg to earn a profit of 20%
Answer:
7.2 rupees
Step-by-step explanation:
Given that at a loss of 10 percent which is 90% price, we have sugar sold at 5.4 rupees per k.g
Hence, at 100 percent we have => 5.4 × (100 ÷ 90 )= 6 rupees per kg.
Therefore, at 100 percent, where we have 6 rupees per kg, to make a profit of 20% we have
6 rupees per kg x 120% = 6 × 1.2 = 7.2 rupees per kg.
Hence, the final answer is 7.2 rupees per kg to make a profit of 20%.
A line passes through the points (-1, -8) and (3, 12). Compute the slope of
the line. Show your steps. *
Your answer
This is a required question
A line passes through the points (-1, -8) and (3, 12). Write the equation for
the line that passes through these points in the form y=mx + b. (Hint: you
already computed m in the previous problem.) *
Answers
Answer:
y = 5x - 3
Step-by-step explanation:
The Slope of a Line
Suppose it's given a line that passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the formula:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The equation of the line in slope-intercept form is:
y=mx+b
Where:
m = slope
b = y-intercept.
We are given the points (-1,-8) and (3,12). Compute the slope:
[tex]\displaystyle m=\frac{12+8}{3+1}=\frac{20}{4}=5[/tex]
The equation of the line now has one known value:
y = 5x + b
Let's use the point (3,12) to find the value of b:
12 = 5(3) + b = 15 + b
Solving for b:
b = 12 - 15 = -3
The required equation of the line is:
y = 5x - 3
When 3a? – 7a+ 6 is subtracted from 4a? - 3a +4,
the result is
Answers
Step-by-step explanation:
(3a-7a+6)-(4a-3a+4)
(-4a+6)-(1a+4)
Add the remaining a's together, as well as the 6 and 4.
you get,
-3a+10
Is this a function?
Answers
Find the x-intercepts for y = -7x2 + 4x + 9 using the quadratic formula. Choose all
correct answers.
Answers
Plz help me will put Brainiest
The maximum weight allowed per car on The Wildcat carnival ride is 297 pounds. Your friend weighs 99 pounds.
able to ride in a car together, how much can you weigh? Write and solve an inequality.
X + 99 S 198, at most 297 pounds
X + 99 5 297, at most 198 pounds
X-99 < 297, at most 99 pounds
x + 198 5 297, at most 99 pounds
Answers
Answer:
161 + 60 inequality-lessthanorequalto 221; at most 161 pounds
221 - 60 =161
Step-by-step explanation:
my teacher would like you to solve this using fraction ex:(345/x=727/2355) (just a heads up!!) please help :)
Answers
Answer:
84
Step-by-step explanation: (edited)
52% problems are pointless i.e. 48% are NOT pointless.
Recall that 1% = 1/100.
Therefore 48% = 48/100 = 12/25.
Let x be the number of problems that are not pointless.
x/175 = 12/25
x = 84
Answer:
84
Step-by-step explanation:
According to the question
175×48%
175×48/100
7×48/4
7×12
84
can someone fact check this to make sure its correct
Answers
All your answers look good!
Answer:
looks good
Step-by-step explanation:
The graph y = 1/2x^2 - x - 4 is shown below. State the coordinate of the zero(s):
Answers
Answer:
Zeros → (-2, 0) and (4, 0)
Step-by-step explanation:
Equation of the graph has been given as,
y = [tex]\frac{1}{2}x^{2} -x-4[/tex]
For zeros of the function,
y = 0
Therefore, [tex]\frac{1}{2}x^{2} -x-4=0[/tex]
By solving the equation algebraically,
x² - 2x - 8 = 0
x² - 4x + 2x - 8 = 0
x(x - 4) + 2(x - 4) = 0
(x + 2)(x - 4) = 0
x = -2, 4
Therefore, coordinates of the zeros will be (-2, 0) and (4, 0).
Let's confirm the zeros (x-intercepts) from the graph attached,
Coordinates of the x-intercepts are,
(-2, 0) and (4, 0)
The data shows the number of salad wraps sold on each day for two weeks at a sandwich shop.
Week 1: 15, 13, 14, 14, 13, 12, 13
Week 2: 18, 3, 15, 15, 16, 14, 16
Which statement about the data is true?
a. The mean of Week 1 data is a good estimate of the sandwich shop's daily sales.
b. The mean of Week 2 data is a good estimate of the sandwich shop's daily sales.
c. Both the mean of Week 1 data and the mean of Week 2 data are good estimates of the sandwich shop's daily sales.
d. Neither the mean of Week 1 data nor the mean of Week 2 data is a good estimate of the sandwich shop's daily sales.
Answers
Answer:
Did you find the answer?
Step-by-step explanation:
please help a.s.a.p!!!
Answers
Answer: I believe the answer is 2,3, and 4. If not, then it is just 2 and 4.
Step-by-step explanation:
(Giving brainliest to correct answer)
Congruence
Answers
Answer:
SAS
Step-by-step explanation:
you are given two congruent sides
and since the right angle is a vertical angle, you can one congruent angle between the triangles
The two dot plots compare ages of girls and boys in a pottery class.
Which group has a greater median?
Answers
Answer:
you didn't post a picture :/
SOMEONE PLEASE HELP!!! THIS IS MY LAST QUESTION!!!
Answers
Answer:
The answer to the question provided is 30.
Step-by-step explanation:
[tex] \frac{18}{27} = \frac{20}{x} \\ \\ \frac{540}{18} = \frac{18x}{18} \\ \\30 = x[/tex]
Happy to help!
=====================================================
Explanation:
Due to the parallel lines, we have two similar triangles. So the sides are proportional.
18/27 = 20/x
2/3 = 20/x
2x = 3*20
2x = 60 .... cross multiply
x = 60/2
x = 30
---------------
Another way you can approach it is to say
18/(18+27) = 20/(20+x)
18/45 = 20/(20+x)
2/5 = 20/(20+x)
2(20+x) = 5*20
40+2x = 100
2x = 100-40
2x = 60
x = 60/2
x = 30
What is the least common multiple of 40 and 30
Answers
Answer:
120
Step-by-step explanation:
Hi please help me answer this :)
Explain answer
Will give braisnlt
Answers
Answer:
There are no solutions
Step-by-step explanation:
No intersections or points that apply for the equations.
Any intersection between both lines is a solution. As these lines are parallel they have no solution. If they met at any point, 90 degree or not, there is solution, the solution will be a point. If they are on the same line, hitting all the same points, the solutions are infinite.
Find the value of x. 1) m angle2=3x-6 120° 2 B) 10 D) 6 A) 12 C) -11
Answers
If there are 27 students in one class,
how many are there in 5 classes?
Answers
Answer:
the answer I got is 135 if you multiply 27 times 5
If two parents, one with brown eyes (a dominant trait) and the other with blue eyes (the recessive trait) produce one twin boy with blue eyes, what is the probability that a fraternal twin will transmit the blue eye allele to his or her offspring
Answers
Answer:
50 percent
Step-by-step explanation:
It is given that one of the parent with a dominant trait have brown eyes and the other parent with a recessive trait has blue eyes. They produce a twin boy with eyes that is blue in color. So the probability of the fraternal twin to transmit his allele of blue eye to his or her offspring is 50 percent.
And also the probability of the offspring to pass the allele on to his or her offspring is 50 %.
The product rule is used : 0.5 x 0.5 = 0.25 or 25%.
Complete the following table using the equation: y = -2x+5
Answers
Answer:
what table could you explain
Step-by-step explanation:
Sample Response: They are both correct because there is more than one way to write a multivariable polynomial in standard form. Marcus has the exponents on the x variable in descending order from the highest degree to the lowest degree. Ariel has the exponents on the y variable in descending order from the highest degree to the lowest degree.
Answers
Answer:
They are both correct because there is more than one way to write a multivariable polynomial in standard form. Marcus has the exponents on the x variable in descending order from the highest degree to the lowest degree. Ariel has the exponents on the y variable in descending order from the highest degree to the lowest degree.
Step-by-step explanation:
coochie man
I need this it’s due today
Answers
a=9
hope this helps and have a wonderful day :)
i think the answer is 9
Step-by-step explanation:
step 1. simplify both sides of the equation
step 2. add 17 to both sides
step 3. multiply both sides by 3
answer a =9
Solve this inequality for x.
Answers
______________________________
1.) Multiply both sides of the equation by 5:[tex]81[/tex] × [tex]5=405[/tex][tex]55[/tex] × [tex]5=275[/tex]- Since 5 is positive, the inequality direction remains the same.
Inequality at the end of Step 1:
[tex]405-(1[/tex] × [tex]5+1)[/tex] ≤ [tex]275[/tex]2.) Solve the parenthesis:Multiply 1 and 5 to get 5.Add 5 and 1 to get 6.- We turn the fraction into parenthesis by multiplying because a fraction is originally is dividing, so we have to do the opposite, which in this case is multiplying.
Inequality at the end of Step 2:
[tex]405-6x[/tex] ≤ [tex]275[/tex]3.) Subtract 405 from both sides:[tex]405-405=[/tex] Cancels Out[tex]275-405=-130[/tex]- We do this to get 1 number/variable on each side.
Inequality at the end of Step 3:
[tex]-6x[/tex] ≤ [tex]-130[/tex]4.) Divide both sides by −6:[tex]-6x[/tex] ÷ [tex]-6=x[/tex][tex]-130[/tex] ÷ [tex]-6=\frac{-130}{-6}[/tex]- Since −6 is negative, the inequality direction is changed.
Inequality at the end of Step 3:
[tex]x[/tex] ≥ [tex]\frac{-130}{-6}[/tex]5.) Reduce the fraction [tex]\bold{\frac{-130}{-6}}[/tex] to lowest terms by extracting and canceling out −2:[tex]-130[/tex] ÷ [tex]-2=65[/tex][tex]-6[/tex] ÷ [tex]3[/tex]- Extracting and cancelling out just means dividing. So we just divide the numerator and denominator by -2.
Inequality at the end of Step 5:
[tex]x[/tex] ≥ [tex]\frac{65}{3}[/tex]6.) Turn the fraction into a mixed number:[tex]\frac{65}{3}=21\frac{2}{3}[/tex]- You can figure this out by dividing 65 by 3 which gives you a decimal, then turn the decimal into a fraction.
______________________________
Noah fills a soap dispenser from a big bottle that contains 2 1/3 liters of liquid soap. That amount of soap will fill 3 1/2 dispenser. How many liters of soap fit into one dispenser
Answers
Answer:
i have no more money to buy a candle shop full of dogs with cats and people
Step-by-step explanation:
ur mae
Answer:
None
Step-by-step explanation:
What is the decimal equivalent of the fraction 2?
0 2.125
0 2.4
O 2.1
O 2.18
Answers
Answer:
2 .1 because its closes to two