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2 years ago

5

Write an explicit formula for an, the nth term of the sequence 11, 20, 29

1 answer:

photoshop1234 [79]2 years ago

7 0

On = 38 - 9n
Step-by-step explanation:
Note the common difference d between
consecutive terms
d= 20 - 29 = 11 - 20 = - 9
This indicates the sequence is arithmetic with n
th term
On
= apt (n - 1)d
where a, is the first term and d the common
difference
Here a, = 29 and d=- 9, thus
An = 29 - 9 (n - 1) = 29 - 9n + 9 = 38 - 9n

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Answer:

Step-by-step explanation:

n = sample size = 5

a) Let us determine the sum

$\sum x_i= 100+200+300+400+490=1490$

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$S_x_y = \sum x_i y_i -\frac{(\sum x_i)(\sum y_i) }{n} \\\\$

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The estimate b of the slope β is the ratio of $S_x_y$ and $S_x_x$

$b = \frac{S_x_y}{S_x_x}$

$\frac{64386}{96080} = 0.67$

The mean is the sum of all value divide by number of values

$\bar x= \frac{\sum x_i}{n} \\\\= \frac{100+200+300+400+490}{5} \\\\= \frac{1490}{5} = 298$

$\bar y= \frac{\sum y_i}{n} \\\\= \frac{237+350+419+465+507}{5} \\\\= \frac{1978}{5} = 395.6$

The estimate a of the intercept is

$a = \bar y - b \bar x$

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General least square equation;

$\bar y = \alpha + \beta x$

replace alpha by a = 3 and beta by b = 0.67 in general least equation

y = a + bx

195.9 + 0.67x

b)

<em>Scatter plot is shown in the attached file</em>

x is on the horizontal axis

y is n the vertical axis

The degree of freedom of regression is 1

because we use one variable s predictor variable

$d_f_R = 1$

The degree of freedom of error is the sample size n decrease by 2

$d_f_E =n-2= 5 - 2=3$

Total df is equal to the sum of seperate degree of freedom dfR and dfE

total df = 1 +3 4

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Total SS =Syy= 45007.2

SSE + Total SS = SSR

= 45007.2 - 43146.9296

= 1860.2705

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