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3 years ago

Find an explicit formula for the arithmetic sequence 170,85,0,-85..., d(n)=

Mathematics

1 answer:

irinina [24]3 years ago

8 0

Answer:

d(n) = 85 * ( 3 - n )

Step-by-step explanation:

Let's find the common difference of the terms (if any).

The common difference is = 85 - 170 = 0 - 85 = -85 - 0 = -85

For an arithmatic sequence with first term a, common difference d,

nth term = a + ( n - 1 ) * d

So, d(n) = 170 + ( n - 1 ) * (-85)

= 255 - 85n

= 85 ( 3 - n )

[ If there's any mistake, please inform me ]

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3 years ago

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ioda

Answer:

Some have multiple choices. See below for additional comments.

a) iii
b) i
c) v
d) ii
e) iv

Step-by-step explanation:

i -- slope-intercept form. Shows the slope and the y-intercept

ii -- slope-intercept form. Shows the slope and the x-intercept

iii -- intercept form. Shows both the x- and y-intercepts

iv -- standard form.

v -- point-slope form. Shows the slope and one point on the line.

vi -- another point-slope form. Shows the slope and one point on the line

With the above forms in mind, ...

a) both intercepts are best shown in form iii

b) the slope is shown in forms i, ii, v, vi. Form i is the most uncluttered.

c) points are shown in forms v and vi. Form v may be least confusing.

d) the sign can be readily determined in form ii.

e) testing the given point is easily done using forms ii and iv. Form iv may be the best for this.

_____

<em>Additional comments</em>

Since each of these forms of the equation has utility in different situations, it can be worthwhile to learn the different forms. For example, I like the standard form for making perpendicular lines, though any of the "slope-" forms can be useful for that, too. The useful form to start with will be the one that best relates to the information given. (For two points given, there is a "2-point form" not shown here.)

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