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3 years ago

What is the explicit formula for this sequence?

Mathematics

1 answer:

kati45 [8]3 years ago

6 0

<em>Greetings from Brasil...</em>

With the recursive formula, lets build the sequence:

A1 = 4

A2 = A1 - 7

A3 = A2 - 7

A4 = A3 - 7

A5 = A4 - 7

(...)

But pay attention to A3....

A3 = A2 - 7 but A2 = A1 - 7 , so rewriting A3

A3 = (A1 - 7) - 7 ⇒ A3 = A1 + 2.(- 7)

A4 = A3 - 7 ⇒ A4 = [(A1 - 7) - 7] - 7 = A1 + 3.(- 7)

A5 = {[(A1 - 7) - 7] - 7} - 7 = A5 + 4.(- 7)

You might be interested in

Solve for all values of x by factoring.<br> X^2 +2x-36=2x

steposvetlana [31]

Answer: 26 and 2

Step-by-step explanation: because it makes sense

4 0

3 years ago

How to get midpoint in a graph with 2 endpoints

Flura [38]

Answer:

You can find the midpoint of a line segment given 2 endpoints, (x1, y1) and (x2, y2). Add each x-coordinate and divide by 2 to find x of the midpoint. Add each y-coordinate and divide by 2 to find y of the midpoint. It's important to note that a midpoint is the middle point on a line segment.

In order to see the midpoint formula in use, let's look at an example.

Question:

Determine the midpoint of the line segment with the given endpoints.

A(3, 7), B(9, 1)A(3,7),B(9,1)

Solution:

We can use the formula for midpoint to determine the midpoint: M= (x1 + x2/2 , y1+y2/2)

First, plug the x and y value into the formula:

M=(3+9/2 , 7+1/2)

Then, we can calculate the midpoint:

(6, 4)

3 0

3 years ago

when nicky tried to solve an equation using properties of equality, she ended up with the equation -3=-3. what equation mioght s

kicyunya [14]

Answer:

<em>There are infinitely many solutions.</em>

Step-by-step explanation:

<u>Equations</u>

Suppose Nicky was trying to solve the equation

2(x - 1) - 1 = 3(x + 1) - 6 - x

Operating:

2x - 2 - 1 = 3x + 3 - 6 - x

2x - 3 = 2x - 3

Subtracting 2x:

-3 = -3

This equation is true regardless of the value of x, thus x can have any value. There are infinitely many solutions.

The same result could have come with these equations:

4x - 3 = -3 + 4x

4(x - 1) + 1 = 4(x + 1) - 7

7 0

3 years ago

Given that y= 2* (power of X)

svetoff [14.1K]

A)
y=2^x

4^x=2^(2x)=y²

solution:
y=2^x hence y²=4^x

chek:
x=5 ⇒ y=2⁵=32
4⁵=1024
y₂=32²=1024

b)
8(4^x)-9(2^x)+1=0
8(2^(2x)-9(2^x)+1=0

2^x=t

8t²-9t+1=0
We solve the quadratic.
t₁=1/8 ⇒2^x=1/8
2^x=1/2³
2^x=2⁻³
x=-3

t₂=1 ⇒ 2^x=1 ⇒x=0

Solutions:
x=-3
x=0

5 0

3 years ago

15 points please help me ASAP

gayaneshka [121]

The distance between the means is equal to 4.
The mean absolute deviation (MAD) for player A is equal to 2.
The mean absolute deviation (MAD) for player B is equal to 2.
Distance between the means = two (2) times the MAD.
There is some overlap and the distance between the means is between 1 times the MAD and 5 times the MAD.

<h3>What is a number line?</h3>

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

A line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

A mean is also referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the distance between the means of both players A and B is given by:

Distance = Mean of player B - Mean of player A

Distance = 10 - 6

Distance = 4.

The mean absolute deviation (MAD) for player A is given by:

MAD A = 1/11[2(3 - 6) + 2(4 - 6) + (5 - 6) + (6 - 6) + (7 - 6) + 2(8 - 6) + 2(9 - 6)]

MAD A = 1/11[2(3) + 2(2) + (1) + (0) + (1) + 2(2) + 2(3)]

MAD A = 1/11[6 + 4 + 1 + 0 + 1 + 4 + 6]

MAD A = 1/11 × [22]

MAD A = 22/11

MAD A = 2.

Also, the mean absolute deviation (MAD) for player B is given by:

MAD B = 1/11[2(7 - 10) + 2(8 - 10) + (9 - 10) + (10 - 10) + (11 - 10) + 2(12 - 10) + 2(13 - 10)]

MAD B = 1/11[2(3) + 2(2) + (1) + (0) + (1) + 2(2) + 2(3)]

MAD B = 1/11[6 + 4 + 1 + 0 + 1 + 4 + 6]

MAD B = 1/11 × [22]

MAD B = 22/11

MAD B = 2.

Therefore, distance between the means = two (2) times the MAD.

Distance = Means × MAD

4 = 2 × 2.

In conclusion, we can infer and logically deduce that there is some overlap and the distance between the means of both players A and B is between one (1) times the MAD and five (5) times the MAD.

Read more on line plot here: brainly.com/question/8989301

#SPJ1

6 0

1 year ago