A sequence is recursively defined by f(1)=3,f(n)=2* f(n-1) for n >=2. Write the equation for the nth term

Answers

Answer 1

Given:

[tex]f(1)=3,f(n)=2\times f(n-1)[/tex]         ...(i)

For [tex]n\geq 2[/tex].

To find:

The nth term for the given recursive formula.

Solution:

The given recursive formula is of the form of

[tex]f(n)=r\times f(n-1)[/tex]            ...(ii)

It is the recursive formula of a GP, where r is common ratio.

On comparing (i) and (ii), we get

[tex]r=2[/tex]

Now,

First term: [tex]a=f(1)=3[/tex]

Common difference: [tex]r=2[/tex]

nth term of a GP is

[tex]f(n)=ar^{n-1}[/tex]

Putting a=3 and r=2, we get

[tex]f(n)=3(2)^{n-1}[/tex]

Therefore, the equation for the nth term is [tex]f(n)=3(2)^{n-1}[/tex].


Related Questions

Help on this please

Answers

Answer:

I got 25

I really hope that helps

Answer:

I got B. 25

Step-by-step explanation:

B is your answer

A container has 12 1/2 cups of pancake mix. A serving uses exactly 1 1/2
cups
• How many full servings are in the container?
• How many cups of pancake mix are left over?
Enter each answer on a separate line.

Answers

Answer:

8 full servings

Step-by-step explanation:

1/2 cup of mix left

A ranch hand herded his cattle to some grazing land. Then he began riding back to the ranch, which is due west, at 7 kilometers per hour. Simultaneously, the cows began moving away from him, too, headed due east at 2 kilometers per hour. How long did it take for the herd and the ranch hand to be 4 kilometers apart?

Answers

Answer:

4 kilometrs

Step-by-step explanation:

if you add the 2 to another 2 you get four

Answer:

4 kilometres

Hope this helped!

the crowd at a sporting event is estimated to be 2,500 people. the exact attendance is 2,486 people. what is the percentage error?

Answers

Answer:

0.56%

Step-by-step explanation:

Percentage error

[tex] = \frac{2500 - 2486}{2500} \times 100 \\ \\ = \frac{1400}{2500} \\ \\ = 0.56\%[/tex]

The crowd at a sporting event is estimated to be 2,500 people, the exact attendance is 2,486 people, the percentage error is, 0.56%

What is the percentage?

The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.

Formula for percentage;

Percentage = (present quantity/whole quantity)×100

Given that,

The crowd estimated to be 2,500 people

The exact attendance is 2,486 people

Percentage error = ?

Percentage error = (estimated value- exact value)/estimated value×100

Percentage error =   (2,500 - 2,486) /2500×100

                             =  0.56%

So, the percentage error is 0.56%

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What is 11% of 600?

80
45
60
66

Answers

Answer:

66 is the answer to your question

Answer:

66

Step-by-step explanation:

11 % = 0.11

600 × 0.11 = 66


What is the slope of the line that passes through the points (-2,3) and (-14, -5)?
Write your answer in simplest form

Answers

Slope = 2/3 (positive 2/3)
You use the formula Y2-Y1/X2-X1 in order to get the slope

What is the equation to a line with a slope of -3 and a y-intercept of 8?

Answers

Answer:

y=-3x+8

Step-by-step explanation:

y=mx+b

(m=slope and b=y-intercept)

Answer:

Step-by-step explanation:

let’s use this equation y = mx + b

where m = slope

and b = y intercept

since slope is -3, m = -3

and since y intercept is 8, b = 8

so the equation is

y = -3x +8

2.
Work out 5.9 + 3.172

Answers

Answer:

9.072

Step-by-step explanation:

Answer:

9.072

Step-by-step explanation:

For this problem, we will simply use the property of 0 and addition to accumulate a sum.

Note, any digit not shown to the right of a decimal can be written with a zero. So 5.9 can be rewritten as 5.900.

Let's perform the addition.

5.900

+ 3.172

-----------

9.072

Using the idea of zeros to the right of the decimal, we are able to trivially complete this sum.

Hence, the answer is 9.072.

Cheers.

WHICH OF THE FOLLOWING IS TRUE FOR THIS SITUATION?

Answers

B (sorry if wrong) hope this helps
It’s D

Check the graph, they both are at 4 inches by 6 weeks so that’s the right answer

A field is in the shape of a Rectangle. The width
of the rectangle is x yards. The length of the
rectangle is 3 more than the width. Write an
expression for the perimeter of the field.

Answers

Answer:

4x+6

Step-by-step explanation:

The perimeter of the field can be obtained by calculating the distance around the field.

in this case, we know that the shape of the field is a rectangle.

The perimeter of a rectangle can be obtained by using the formula

[tex]2(l+b)[/tex]

The width of the rectangle is given as x yards

The length of the rectangle is given as x +3 yards

Therefore, an expression to determine the perimeter of the rectangle can be given as

[tex]2(x+3+x)\\=2(2x+3)\\=4x+6[/tex]

If f(x)= (2x +5)and g(x) = (2x2−5x+3), find f(x) · g(x) (please help)

A. 4x3 − 31x + 154x3 − 31x + 15

B.4x3 − 20x2 +19x + 154x3 − 20x2 +19x + 15

C.4x3 − 19x + 154x3 − 19x + 15

D.4x3 + 20x2 − 19x +15

Answers

Answer: 4x³-19x+15

Step-by-step explanation:

We are given f(x) and g(x). Since we need to find f(x)·g(x), we multiply f(x) and g(x).

[tex](2x+5)(2x^2-5x+3)[/tex]                               [distribute by FOIL]

[tex]4x^3-10x^2+6x+10x^2-25x+15[/tex]           [combine like terms]

[tex]4x^3-19x+15[/tex]

Now we know [tex]4x^3-19x+15[/tex] is the correct answer.

Select all of the correct solutions for the following equation
52
2y = 18
a
o ad oo
(5,3)
(4,1)
(3,3)
c
None of the above

Answers

Answer:

Your answer is (4,1).

Step-by-step explanation:

5x - 2y = 18

5(4) - 2(1) = 18

20 - 2 = 18

18 = 18 (Which means it's correct)

Let me know if you need anymore help!

Explain when it is appropriate to use a benchmark percent in solving a problem.

Answers

Answer:

The most common benchmark percents are 0%, 10%, 25%, 50%, 75% and 100%.

These benchmark values are sometimes used when estimating a solution involving percentages.

Real-World Example

If an item costs $36.00 and there is a 7% sales tax, the benchmark of 10% can be used to mentally estimate the sales tax of the item.

10% of 36, done mentally, is 3.6.

Since 7% is a bit less than 10%, the sales tax will be a bit less than $3.60.Step-by-step explanation:

At Carly's Pancake House there are 39 dirty coffee mugs and 21 clean coffee mugs. What
percentage of the coffee mugs at the pancake house are dirty?

Answers

Answer:

65%

Step-by-step explanation:

What you need to do is add both the clean and the dirty mugs together to get a total amount of mugs (60) and then divide 39 by 60 because you are dividing the mugs that you want to find the percentage of by the total amount of mugs. The equation would look like this:

39/60=0.65

therefore, the answer is 65%

Please help i dont get this!

Answers

Answer:

The other one is -8 this is because the point on the graph is multiplied by 2

Step-by-step explanation:

PLEASE HELP FAST What is the answer for this I will give brainless an extra points for correct answer I appreciate it

Answers

Answer:

-3

Step-by-step explanation:

the answer is negative 3, because when x is two, y is three

Answer:

f(2) = -3

Step-by-step explanation:

This is the answer because:

1) The question is basically asking what the y-cordinate is.

2) In order to find the y-cordinate, look at the graph and find where 2 is on the x-axis. Then, see wheree the y-coordinate is on the same line a the x-cordinate which is 2.  

3) When you line up the cordinates, you can see that where x is 2, y is -3.

Therefore, the answer is -3.

Hope this helps! :D

John runs the same amount each day (r). If he runs for 4 days this week write an expression to represent the amount he ran this week.

Answers

Answer:

[tex]r \cdot 4 = z[/tex]

Step-by-step explanation:

An expression means that we don't know enough to create an equation. So, this means we will mostly be using variables.

John runs r amount every day. We need to create an expression for if he runs r amount for 4 days.

[tex]r \cdot 4 = z[/tex]

r = how much he runs per day

4 = how many days he runs

z = how much he runs this week

This is your expression!

Answer:

r * 4 = a

Step-by-step explanation:

If John runs the same amount everyday (r) for the past four days, we can multiply 4 by r

r * 4

We don't have enough information to write the answer to the expression so in its place we can put a variable. (In this case, I chose a)

r * 4 = a

So a possible expression for this problem is r *4 = a

Hope this helps! Have a great day! :)

Help me pleaseee on this plss

Answers

Answer:

a(n)= -4n-6

Step-by-step explanation:

If you plug the number of the sequence in as n in the equation (1=-10, 2=-14, etc.) and then plug the actual number (-10, -14, etc.) in as the a(n), for each of the equations, the only one that works with all four is the first one.

a(7x + 3) = b + 14x what are the values of a and b

Answers

Answer:

a= 2

b=6

Step-by-step explanation:

Follow me Please

Ellen needs to make b batches of blueberry scones this weekend for her family's brunch party. She needs 2 cartons of blueberries for each batch, and each carton costs $4. Pick all the expressions that represent how much Ellen will spend on blueberries.

Answers

Answer:

Ellen will spend

$4(2b) on blueberries

Where b = number of batches of Blueberry scones she wants to make

Step-by-step explanation:

From the above question:.

Ellen needs to make b batches of blueberry scones this weekend for her family's brunch party.

Since she needs 2 cartons of blueberries for each batch, and each carton costs $4

1 batch = 2 cartons of blueberries

b batches =

Cross Multiply

b × 2 cartons

= 2b cartons of blueberries.

We also know that:

1 carton blueberries = $4

2b cartons of blueberries = x

Cross Multiply

x = 2b × $4

Therefore, Ellen will spend :

$4(2b) on blueberries

there are between 25 and 43 students in a class
the ratio of boys to girls is 5 : 7
how many students are in the class?

Answers

Answer:

36

Step-by-step explanation:

Since the sum of the ratios is 5+7=12 the total number of students must be divisible by 12

The only number within the given range is 36

The number of students should be in the class should be considered as the 36.

Calculation of the number of students:

Since

there are between 25 and 43 students in a class

the ratio of boys to girls is 5 : 7

So here the total ratio should be like

= 5 + 7

= 12

So here the number of students should be divisible by 12

So, it should be 36

Learn more about ratio here: https://brainly.com/question/13111469

Ten(10) adults and 3 children attend a local concert for $59. Four(4) adults and 3
children attend the same concert for $29. How much does it cost for each to attend?

Answers

Answer:

$5 per adult and $3 per kid

Step-by-step explanation:

5x10=50

3x3=9

50+9=59

4x5=20

3x3=9

20+9=29

Does anyone know the answer to this problem?

Answers

Answer:

15

Step-by-step explanation:

3^2 + sqrt4 + 4

3^2 = 9

sqrt4 = 2

(9)+(2)+(4)=15

therefore, the answer is 15

Please help I'll give you brainliest and a lot of points

Answers

Answer:

about 50

Step-by-step explanation:

they a move up 5 minutes eace half mile

dont come at me if it is wrong :)

could u plz answer this
2x-7=13
3x+4=25​

Answers

Answer:

x=10

Step-by-step explanation:

NEED HELP ASAP PLEASE!

Answers

Answer:-2

Step-by-step explanation:

-y+2x=-1 needs to be changed to y=-2x-1 so that you can set the two equation equal to each other in order to solve for x. That makes it -2x-1=1/2x+4

-4= -4

-2x-5 = 1/2x

+2x = +2x

-5 = 2.5x

div. 2.5 div. 2.5

X= -2

Check: y= -2(-2)-1 Y=3

y=1/2(-2)+4 Y=3

It takes Andre 4 minutes to swim 5 laps.

How many laps PER MINUTE is that? (round to two decimal places if needed)
can someone also show there work?

Answers

=> 4 minutes.........5 laps |:4
=> 1 minute....1,25 laps
=> 1,25 laps per minute

PLEASE HELP ME FIND X!!!!!!!!!! 50 POINTS

Answers

Answer:

96 this should help it it does. you are welcome if it does not do not get mad at me

Step-by-step explanation:

i just did it

In the system of equations, b is a constant. If the system has infinitely many solutions, what is the value of b?

Answers

Answer:

The value of b is 9.5

Step-by-step explanation:

If a system of equations has infinitely  many solutions, that means the two equations are equal

If the system of equations ax + by = c, dx + ey = f, then

a = d ⇒ coefficients of xb = e ⇒ coefficients of yc = f ⇒ numerical terms

Let us use this fact to solve the question

3x - y = 19 ⇒ (1)

1.5x - 0.5 y = b ⇒ (2)

∵ This system of equations has infinitely many solutions

∴ The coefficients of x must be equal

∴ The coefficients of y must be equal

∴ The numerical terms must be equal

→ Multiply equation (2) by 2 to make the coefficients of x and y on it

  equal the coefficients of x and y in equation (1)

∵ 2(1.5x) - 2(0.5y) = 2(b)

3x - y = 2b ⇒ (3)

→ By comparing equations (1) and (3), 19 must equal 2b

∵ 2b = 19

→ Divide both sides by 2

b = 9.5

The value of b is 9.5

Which of the scatterplots have no correlation? Check all that apply.

On a graph, points curve up and down.
On a graph, points are grouped together to form a horizontal cluster.
On a graph, points are grouped together to form a vertical cluster.
On a graph, points are grouped together and decrease.
On a graph, points are scattered over the graph.

Answers

Answer:

2, 3, and 5

Step-by-step explanation:

got it right on test.

The scatterplots (B), (C), and (E) have no correlation. which is the correct answer would be options (B), (C), and (E)

What is the Scatter plot?

The variables in the scatter plot made from the data are described by the independent variable, time, which is graphed along the horizontal axis.

When analyzing data with more than two variables, a scatter plot is used, which has a separate vertical axis for each variable.

According to the given option,

The second has no slope, therefore there is no correlation.

The third has a zero average slope with no upward or descending trend; no correlation.

The fifth has a general increasing tendency and will have a non-zero correlation.

Thus, the scatterplots (B), (C), and (E) have no correlation.

Hence, the correct answer would be options (B), (C), and (E),

Learn more about the Scatter plot here:

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