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3 years ago

First five term for An=n^2-2n

Mathematics

1 answer:

densk [106]3 years ago

6 0

First 5 terms are: -1,0,3,8,15

Step-by-step explanation:

we will put n=1,2,3,4,5 to find first 5 terms of the sequence

Explicit formula for sequence is:

$a_n = n^2-2n$

Putting n=1

$a_1 = (1)^2-2(1)\\= 1-2\\= -1$

Putting n=2

$a_2 = (2)^2-2(2)\\= 4 - 4 \\=0$

Putting n=3

$a_3 = (3)^2-2(3)\\= 9-6\\= 3$

Putting n=4

$a_4 = (4)^2 - 2(4)\\= 16-8 \\= 8$

Putting n=5

$a_5 = (5)^2-2(5)\\= 25 - 10\\= 15$

Hence,

First 5 terms are: -1,0,3,8,15

Keywords: Arithmetic sequence, Common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

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ale4655 [162]

Answer:

The required equation is:

$y = -\frac{3}{2}x+9$

Step-by-step explanation:

To find the equation of a line, the slope and y-intercept is required.

The slope can be found by finding the slope of given line segment. A the perpendicular bisector of a line is perpendicular to the given line, the product of their slopes will be -1 and it will pass through the mid-point of given line segment.

Given points are:

$(x_1,y_1) = (8,10)\\(x_2,y_2) = (-4,2)$

We will find the slope of given line segment first

$m = \frac{y_2-y_1}{x_2-x_1}\\= \frac{2-10}{-4-8}\\=\frac{-8}{-12}\\=\frac{2}{3}$

Let m_1 be the slope of perpendicular bisector then,

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Now the mid-point

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We have to find equation of a line with slope -3/2 passing through (2,6)

The equation of line in slope-intercept form is given by:

$y = m_1x+b$

Putting the value of slope

$y= -\frac{3}{2}x+b$

Putting the point (2,6) to find the y-intercept

$6 = -\frac{3}{2}(2)+b\\6 = -3+b\\b = 6+3 =9$

The equation is:

$y = -\frac{3}{2}x+9$

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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