In which situation below would you want to use the Explicit Formula instead of the Recursive Formula?

A. Find the 4th term when the first term is 7 and the common difference is -2.
B.Find the 7th term when the first term is -1 and the common difference is 10.
C.Find the 106th term when the first term is 2 and the common difference is 5.
D.Find the 11th term when the first term is -3 and the common difference is 4.

Answers

Answer 1

9514 1404 393

Answer:

  all of them, possibly excepting the 4th term

Step-by-step explanation:

The recursive formula is good if you have terms near the one of interest. It might be used for the 4th term, but that would require that you compute the three previous terms:

  7, 5, 3, 1 . . . . requires 3 subtractions

It can be about as easy to calculate ...

  a4 = 7 -2(3) = 1 . . . . requires two* subtractions and a multiplication

__

However, for the 7th, 11th, and 106th terms, it is impractical to list all previous terms. The explicit formula is a better choice.

A.  a4 = 7 -2(3) = 1

B.  a7 = -1 +10(6) = 59

C.  a106 = 2 +5(105) = 527

D.  a11 = -3 +4(10) = 37

_____

* The explicit formula is ...

  an = a1 +d(n -1)

The operations identified in this formula (in the order required by the Order of Operations) are subtraction, multiplication, and addition. For a negative common difference, that amounts to two subtractions and a multiplication.

For manual evaluation, the work involved in using the recursive or explicit formulas for the 4th term is about the same, if the arithmetic is easily done mentally (as here).


Related Questions


Draw a diagram to represent each of these situations. Then write an addition expression that represents the final temperature.


The temperature was 80 ℉ in Arizona and then fell 20 ℉ during the night.






The temperature was -13 ℉ in Minneapolis and then rose 9 ℉ in the morning.






The temperature was -5 ℉ in Denver and then fell 8 ℉ by the morning.

Answers

Answer:

1) 80+(-20)

2) -13+9

3) -5+(8)

I don't quite know how to explain

Just think about 1) 60 is the new temperature, in order to have an addition problem we're going to have to use negative numbers. Since we had to subtract 20, in order to use addition it would be 80+(-20).

A seamstress needs to cut 15 pieces of ribbon
A7
B35
C135
D8100

Answers

B kdkdjendncjcjdcjndmrmfmfciv

8. Madison can complete two skirts in 15 days. How long will it take her to
complete eight skirts?

Answers

Answer:

60 days

Step-by-step explanation:

2:15

x4    x4

8:60

Ajar contains 5 purple, 6 yellow, 8 green, and
5 orange jelly beans. What is the probability
of selecting a yellow jelly bean followed by a
purple one, without replacement?

Answers

Answer:

5 out of 24 percent chance

Step-by-step explanation:

A new health drink has 160% of the recommended daily allowance (RDA) for a certain vitamin. The RDA for this vitamin is 50 MG. How many milligrams of the vitamins are in the drink? Please help me I need help fast!

Answers

Answer:

5

Step-by-step explanation:

5+5+5-10

Answer:80

Step-by-step explanation:

That’s just what it corrected me as, but it’s right

often considered the slope, this is the comparison of two different quantities that are changing

Answers

Answer:

I believe that would be the rate..

Step-by-step explanation:

3. Marta can buy a 6-pack of 15-ounce cans of broth for $11.29 or three
32-ounce containers for $10.97. Which is the better buy? (Example 1)

Answers

Answer:

the second one

Step-by-step explanation:

if you were to divide the price by ounces the first one would be .1254444444444444 per ounce while the second one would be .1142708333333333 per ounce so the second one is better.

at a basketball game at team made 58 successful shots they were a combination of one and two point shots the team scored 98 points in all right and solve a system of equations to find out the number of each type of shot

Answers

Answer:

There were 18 1 point goals and 40 2 point goals

Step-by-step explanation:

Let the number of one point shots be x and the number of two point shots be y

Total number of shot is 58

x + y = 58 ••••(i)

Then;

Total of 1 point is 1 * x = x

Total of 2 points is 2 * y = 2y

x + 2y = 98 ••••••(ii)

x = 98-2y

Put this in 1

98-2y + y = 58

-y = 58-98

y = 40

x = 58-40

x = 18

Select the correct answer from each drop-down menu.
Use the remainder theorem to verify this statement.
(x+5) is a factor of the function f(x) = x^3 + 3x^2 - 25x - 75
1. Find the (product, quotient, difference, sum) of f(x) and x + 5
2. The (quotient, remainder, sum, discriminant) of this operation is 0
3. Therefore, (x+5) is (not a factor, the opposite, a factor, the simplified form) of function f
4. So f ([-75, 5, -5, 75)] = 0

Answers

1. quotient

2.remainder

3. a factor

4. 5

Step-by-step explanation:

i just took the test

The expression (x + 5) is a factor of given function f(x).

So the remainder of the function will be zero.

Remainder theorem:

The given function is,

                      [tex]f(x) = x^3 + 3x^2 - 25x - 75[/tex]

We have to check (x + 5) is a factor of the given function.

Equate (x + 5) is equal to 0.

           x + 5 = 0

                 x = -5

Substitute x = -5 in given equation.

          [tex]f(-5)=(-5)^3+3(-5)^2-25(-5)-75\\\\f(-5)=-125+75+125-75\\\\f(-5)=0[/tex]

Since f(-5) = 0. Therefore, (x + 5) is a factor of given function f(x).

Learn more about the remainder theorem here:

https://brainly.com/question/13328536

Please hurry What is 4/15 divided by -3/5

Answers

Answer: -1 1/3 I believe

Answer:

-4/9

Step-by-step explanation:

=4/15 * -(5/3)

=-20/45

=-4/9

I'm writing a short story and I'm stuck on what should happen next. could you give me some ideas?

"M-Mr. Jacks!¨ Kate exclaimed, she turned her head to face him. His back was facing the sun and all she could see was the dark outline of his body. Kate stood up frantically, ¨You made it!¨ she was so excited. She noticed it was only him and wondered how everyone else was. “Did anyone else make it out?¨ she asked. He just stood there, no response. Instead, he walked closer, close enough for kate to actually see him. It wasn't Mr. Jacks. Standing there was a shadowy humanoid figure, it's presence gave her chills. Kate stepped back in fear. The shadow tilted it's head in an unnerving matter then lunged at her.  ¨Ack!” Kate exclaimed, barely dodging it's attack. Although it ripped her shirt she was fine. W-what the heck, Kate thought. It lunged at her again, completely missing. Terrified, Kate started running, whatever this thing was she knew that she did not want to be caught up in it's attack. The shadow started chasing after her, it's form shifted, the legs got longer and the fingers were transformed into long dagger-like weapons. Oh no. oh no no no no. She thought and started running even faster Kate was running for a long time and was running out of breath, while the shadow was gaining on her. Well this is it i guess. She thought, breathing heavily. There's nothing i can do. Tears started forming in her eyes, even though this might be her last moments she had a smile on her face. At least this is better than starving to death in that bubble. Then all of a sudden Kate heard a gunshot. She looked behind her and this beautiful african american girl stood there, finger on the trigger. Another shot was fired and the shadow fell to the ground, shiveled up on the floor. The girl had short puffed hair, cold dark eyes, and had scars that covered her body.  ¨Are you alright?¨ she called out. Kate fell to her knees and sighed in relief. Oh thank god. The girl walked over to her, ¨whats your name hon?¨ she asked. Kate looked up and replied, ¨My names kate and do you mean if i'm physically or mentally alright?¨ Which made the girl chuckle. ¨you seem fine to me¨ she said. ¨The names Alyiah.¨

I'll give extra points after and I'll mark brainiest​

Answers

Answer:

Either they converse s little more like if Kate asks "You came just at the right time! When did you get here?" or Alyiah says something like "Now come with me, I'm taking you to somewhere safe"

Step-by-step explanation:

This story sounds super cool, keep it up !!!

What is the slope for the following two points: (-1,2) and (5,-3) Your answer​

Answers

Answer:

I got -5/6

Step-by-step explanation:

Y2-Y1/X1-X2

So -3-2/5-(-1) =-5/6

I hope this is the right answer  :)

Which of the following is a correct interpretation of the expression -3 - 5​

Answers

Answer:

c

Step-by-step explanation:

Answer:

c.

Step-by-step explanation:

What is the height of the building in miles? Express the answer as a fraction in simplest form.

Answers

what building is it talking about

Answer:

3/22, a mile is 5,280ft so you put 720 over 5,280(720/5,280) and simplify it to get 3/22

Step-by-step explanation:

2. Suppose that 1% of the women in a certain population have breast cancer and that each of
these women undergoes a mammogram to test for breast cancer. According to one study, the
probability that a woman without breast cancer gets a positive test result is 0.121. The
probability that a woman with breast cancer gets a negative result is 0.0015. Select one woman
from this population at random.
(a) Express the provided information using probability notation.
(b) Display the provided information using a tree diagram. Then calculate the probabilities of
each of the four possible outcomes.
(c) Calculate the probability that a randomly selected woman from this population tests
positive.
(d) Given that the test result is positive, what is the probability that the woman actually has
breast cancer?

Answers

The correct answer would be D I think

Leo saves $43 a month for a new iPhone. About how much will he save during one year? (Estimate)

Answers

I think that Leo saves $512 in a year

in greek myth Icarus's story is a story about...



envy

lies

greed

pride

Answers

Answer: Look at the key words in his story!

Step-by-step explanation: For Envy look for words like: Jealousy , Hate , etc

Greed: MORE, not that, etc

Pride: More positive words

Lies: Words that show he is lying

Answer:

Pride

Step-by-step explanation:

The reason I chose this answer was because I felt like he took so much pride in his father's work that he thought there would be no flaw and that he could do anything with the wings.

PLEASE HELP MEH!!!!!!!!!:

Answers

Answer:

A

Step-by-step explanation:

Point slope form

x, y

[tex](y-x)= (slope)(x-y)[/tex]

So its

[tex]y-6=\frac{1}{2}(x+3)[/tex]

So option 1.

Hope this helps plz hit the crown :D

Answer:

B

Step-by-step explanation:

y=mx +b

y= 1/2x = b

y intercept (0,-6)

Need some help with this, 2 answer problem! Please help

Answers

Answer:

Part 1. Use x = 1.

Part 2. Use x = 0

Step-by-step explanation:

If x = 1, you have

[tex]\frac{9^1}{5^1} = \frac{9}{5}\\[/tex] , which is greater than 1.

If x = 0, you have

[tex]\frac{9^0}{5^0} = \frac{1}{1} = 1[/tex], which is NOT greater than 1.

3х + 8 + 10cjdidjdjdhdjdj

Answers

Answer:

3x+18

Step-by-step explanation:

Answer:

3 ( x + 6)

Step-by-step explanation:

3x + 8 + 10

add numbers together

3x + 18

factor out the 3 from the expression

3 (x + 6)

not sure about all the letters ? but hope this helps nn

Ed's new car has a value of $23,500, but it is expected to depreciate at a rate of 7.5% per year. What is the value of Ed's car after 7 years? Round to the nearest dollar, as needed.
$0
$142,162
$13,616
$14,720

Answers

Answer:

$13,616

Step-by-step explanation:

For each year we will have to constantly decrease it by 7.5%

23,500 - 7.5%

= 21,737.5

= 21,737.5 - 7.5%

= 20,107.1875

= 20,107.1875 - 7.5%

= 18599.1484375

= 18599.1484375 - 7.5%

= 17204.2123047

= 17204.2123047 - 7.5%

= 15913.8963818

= 15913.8963818 - 7.5%

= 14720.3541532

= 14720.3541532 - 7.5%

= 13616.3275917

Definitively we will get the answer $13,616

504-288
whats the answer pls?

Answers

Answer:

216 is the answer :) uwu

PLEASE LORD HELP MEEEEEEE i need to find the ordered pairs (a.k.a. find the x and y value of the equations


PLEASE HELP MEEEE I'M DYINGGGGG

Answers

Answer:

I am not 100 percent sure, it's been a long time since I've done this type of math but I think that these are the answers

Step-by-step explanation:

1. x= -3, y=-3

2. x= 5, y= -2

3. x= -3, y = -7

4. x=2, y= 1

5. x=0, y= -4

Which term best describes the graph of y = x – 1?

Answers

Answer:what ww said

Step-by-step explanation:

Answer:

Increasing

Step-by-step explanation:

Because im smart lol

Please helpppp!!! I think it's easy but I dont understand

Answers

2/3 is the slope for the graph

what is y=-4/3x-4 in standard form

Answers

Answer:

4x + 3y = - 12

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Given

y = - [tex]\frac{4}{3}[/tex] x - 4 ( multiply through by 3 to clear the fraction )

3y = - 4x - 12 ( add 4x to both sides )

4x + 3y = - 12 ← in standard form

Carrie and Alex are playing hide and seek Alex stands at the house to count Carrie runs 25 m west and finds nowhere to hide. She Continues 60 m north to the tree

Answers

Answer:

65m

Step-by-step explanation:

Since we are not asked what to find, we can as well calculate the displacement of Carrie.

Displacement will be gotten using Pythagoras theorem;

Given

direction through west x = -25m

direction through north y = 60m

Required

Displacement d

According to the theorem;

d² = x²+y²

d² = (-25)²+(60)²

d² = 625 + 3600

d² = 4225

d = √4225

d = 65 m

Hence the displacement of Carrie is 65m

A soccer ball on the ground was kicked with an initial velocity of 35 ft/sec at an elevation angle of 40º. Create a set of parametric equations to model the path of the soccer ball. Approximately how far away did the soccer ball hit the ground?


19 feet

26 feet

38 feet

52 feet

Answers

Answer:

38 feet.

Step-by-step explanation:

From the question given above, the following data were obtained:

Initial velocity (u) = 35 ft/s

Angle of projection (θ) = 40º

Acceleration due to gravity (g) = 9.8 m/s²

Range (R) =?

Next, we shall convert 9.8 m/s² to ft/s². This can be obtained as follow:

0.3048 m/s² = 1 ft/s²

Therefore,

9.8 m/s² = 9.8 m/s² × 1 ft/s²/ 0.3048 m/s²

9.8 m/s² = 32.15 ft/s²

Thus, 9.8 m/s² is equivalent to 32.15 ft/s².

Finally, we shall determine how far away the soccer ball hit the ground (i.e range) as shown below:

Initial velocity (u) = 35 ft/s

Angle of projection (θ) = 40º

Acceleration due to gravity (g) = 32.15 ft/s²

Range (R) =?

R = u² × Sine 2θ / g

R = 35² × Sine (2×40) / 32.15

R = 1225 × Sine 80/ 32.15

R = 1225 × 0.9848 / 32.15

R = 37.5 ≈ 38 feet.

Thus, the soccer ball hit the ground 38 feet away.

Answer:

The anwser is C.

Step-by-step explanation:

To prove a conjecture is true, you must prove it true for all cases. It only takes ONE false example to show that a conjecture is NOT true. This false example is a COUNTEREXAMPLE. Find a counterexample to show that each conjecture is false?

Answers

Answer:

the answer should be conjecture sum hehehe

Step-by-step explanation:

this is a veryyyy hard questionnnnnnn

2. Which example does NOT show the
commutative property of addition?
A. 4 + x = x + 4
B. ab = ba

C. a+b = b + a
D. 3x + 4y = 4y + 3x

Answers

Answer:

The answer is A....im pretty sure

Step-by-step explanation:

Answer:

I think it would be b.ab=ba but I'm, not 100% sure

Step-by-step explanation:

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