All categories

3 years ago

Find the third, fourth, and fifth terms of the sequence defined by

Mathematics

2 answers:

statuscvo [17]3 years ago

7 0

By the recursive definition,

$a_3=2a_2-a_1=2\cdot9-4=14$

$a_4=2a_3-a_2=2\cdot14-9=19$

$a_5=2a_4-a_3=2\cdot19-14=24$

$a_6=2a_5-a_4=2\cdot24-19=29$

olga_2 [115]3 years ago

7 0

Answer:

a3=14, a4=19, a5=24

Step-by-step explanation:

Put the numbers where the symbols are and do the arithmetic.

a3 = 2(a2) -(a1) = 2(9) -4 = 14

a4 = 2(a3) -(a2) = 2(14) -9 = 19

a5 = 2(a4) -(a3) = 2(19) -14 = 24

a6 = 2(a5) -(a4) = 2(24) -19 = 29

_____

With a little work, you can show that this is an arithmetic sequence with a common difference of a2-a1 = 5.

Let d = a[2] -a[1]

Of course, the second term is that difference added to the first:

a[2] = a[1] + (a[2] -a[1]) = a[1] +d

The third term is ...

a[3] = 2a[2] -a[1] = a[2] +(a[2] -a[1]) = a[2] +d

a[4] = 2a[3] -a[2] = a[3] +(a[3] -a[2]) = a[3] -(a[2] +d) -a[2] = a[3] +d

You might be interested in

5/8 - 1/6 in simplest form

anzhelika [568]

First, you got to answer the question. The answer is 11/24, since 11 is a prime number that's your answer.

8 0

3 years ago

Read 2 more answers

I will mark you brainliest!!!! What is the slope of this line?

katen-ka-za [31]

Answer:

Step-by-step explanation:

Rise over Run

4 0

3 years ago

HELP ASAP!!! Find the missing value. V=758.16 L=13 W=? H=7.2

ella [17]

Answer: 8.1

Step-by-step explanation:

758.16 ÷ 13 =58.32

58.32 ÷ 7.2 = 8.1

Check: 8.1 ×13 ×7.2=758.16

6 0

3 years ago

Read 2 more answers

Consider the given data. x 0 2 4 6 9 11 12 15 17 19 y 5 6 7 6 9 8 8 10 12 12 Use the least-squares regression to fit a straight

levacccp [35]

Answer:

See below

Step-by-step explanation:

By using the table 1 attached (See Table 1 attached)

We can perform all the calculations to express both, y as a function of x or x as a function of y.

Let's make first the line relating y as a function of x.

y as a function of x

(y=response variable, x=explanatory variable)

$\bf y=m_{yx}x+b_{yx}$

where

$\bf m_{yx}$ is the slope of the line

$\bf b_{yx}$ is the y-intercept

In this case we use these formulas:

$\bf m_{yx}=\frac{(\sum y)(\sum x)^2-(\sum x)(\sum xy)}{n\sum x^2-(\sum x)^2}$

$\bf b_{yx}=\frac{n\sum xy-(\sum x)(\sum y)}{n(\sum x^2)-(\sum x)^2}$

n = 10 is the number of observations taken (pairs x,y)

Note: Be careful not to confuse

$\bf \sum x^2$ with $\bf (\sum x)^2$

Performing our calculations we get:

$\bf m_{yx}=\frac{(83)(95)^2-(95)(923)}{10*1277-(95)^2}=176.6061$

$\bf b_{yx}=\frac{10*923-(95)(83)}{10(1277)-(95)^2}=0.3591$

So the equation of the line that relates y as a function of x is

In order to compute the standard error $\bf S_{yx}$ , we must use Table 2 (See Table 2 attached) and use the definition

$\bf s_{yx}=\sqrt{\frac{(y-y_{est})^2}{n}}$

and we have that standard error when y is a function of x is

$\bf s_{yx}=\sqrt{\frac{39515985}{10}}=1987.8628$

Now, to find the line that relates x as a function of y, we simply switch the roles of x and y in the formulas.

So now we have:

x as a function of y

(x=response variable, y=explanatory variable)

$\bf x=m_{xy}y+b_{xy}$

where

$\bf m_{xy}$ is the slope of the line

$\bf b_{xy}$ is the x-intercept

In this case we use these formulas:

$\bf m_{xy}=\frac{(\sum x)(\sum y)^2-(\sum y)(\sum xy)}{n\sum y^2-(\sum y)^2}$

$\bf b_{xy}=\frac{n\sum xy-(\sum x)(\sum y)}{n(\sum y^2)-(\sum y)^2}$

n = 10 is the number of observations taken (pairs x,y)

Note: Be careful not to confuse

$\bf \sum y^2$ with $\bf (\sum y)^2$

Remark: If you wanted to draw this line in the classical style (the independent variable on the horizontal axis), you would have to swap the axis X and Y)

Computing our values, we get

$\bf m_{xy}=\frac{(95)(83)^2-(83)(923)}{10*743-(83)^2}=1068.1072$

$\bf b_{xy}=\frac{10*923-(95)(83)}{10(743)-(83)^2}=2.4861$

and the line that relates x as a function of y is

To find the standard error $\bf S_{xy}$ we use Table 3 (See Table 3 attached) and the formula

$\bf s_{xy}=\sqrt{\frac{(x-x_{est})^2}{n}}$

and we have that standard error when y is a function of x is

$\bf s_{xy}=\sqrt{\frac{846507757}{10}}=9200.5856$

In both cases the correlation coefficient r is the same and it can be computed with the formula:

$\bf r=\frac{\sum xy}{\sqrt{(\sum x^2)(\sum y^2)}}$

Remark: This formula for r is only true if we assume the correlation is linear. The formula does not hold for other kind of correlations like parabolic, exponential,..., etc.

Computing the correlation coefficient :

$\bf r=\frac{923}{\sqrt{(1277)(743)}}=0.9478$

5 0

4 years ago

What quadrants is the points (2,-3)?

zheka24 [161]

Answer:

Quadrant 4

there are four quantdrants, A is on the fourth one

4 0

3 years ago