Which of the following functions generates the sequence 0, 2, 4, 6, ...?

F(n) = 2n – 2

Step-by-step explanation:

The sequence 0, 2, 4, 6

First, let us determine if the sequence is arithmetic progression (A.P) or geometric progression (G.P)

This is illustrated:

Let us calculate the common difference (d)

Common difference (d) = 2nd term – first term

Common difference (d) = 3rd term – 2nd term

=> 2 – 0 = 2

=> 4 – 2 = 2

The common difference (d) = 2.

Common ratio (r) = 2nd term /1st term

Common ratio (r) = 3rd term /2nd term

=> 2/0 = undefined

=> 4/2 = 2

There is no common ratio.

Since we have a common difference, therefore the sequence is arithmetic progression.

Now, let us obtain an expression for the sequence.

This can be obtained by using the arithmetic progression formula as shown below:

F(n) = a + (n – 1)d

a is the first term

n is the number of term

d is the common difference.

The sequence 0, 2, 4, 6

The first term (a) = 0

Common difference (d) = 2

F(n) = a + (n – 1)d

F(n) = 0 + (n – 1)2

F(n) = 2n – 2

be more specific

step-by-step explanation:

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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