20 plz ! which sequence is modeled by the graph below? coordinate plane showing the points 1, 6; 2, 0.6; and 3, 0.06 a) an = 6(−10)n − 1 b) an = 0.6(10)n − 1 c) an = 6(one tenth)n − 1 d) an = one tenth(6)n − 1

option c   is correct

step-by-step explanation:

we will find what type of   sequence is the order of the coordinates:

, and

common difference states that the difference between two numbers in an arithmetic sequence.

then;

and

since, the common differences are not equal;

hence, the sequence is not arithmetic sequence.

geometric sequence states that a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio

now, find the common ratio;

and

therefore, the common ratio is .

this implies that the sequence is geometric sequence.

now, the general form for a geometric series:

where r is the common ratio and is the initial value.              

since the common ratio of the geometric sequence is r =  

now, substitute the value of r and   in [1]; we get

therefore, the given sequence is modeled by the graph is geometric sequence

i.e,

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!