A geometric sequence is shown on the graph below. What is the formula for the nth term of the sequence?

remember, an=a1(r)^(n-1) where a1=first term or where n=1 and r=commmon ratio a2/a1=r so if you have the graph, find the y value coresponding to x=1 and that is a1 find the y value coresponding to x=2 and taht is a2, do a2/a1 to get r

so like I was saying

well, each term is 1/2 of the previous
20/40=1/2
so r=1/2
and a1=40
so
[tex]a_n=40(\frac{1}{2})^{n-1}[/tex] is da equation

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bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 2 · 2022-02-08T07:18:47+01:00

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

The formula for the nth term of the sequence given in the graph is,

[tex]a_n=40\times\dfrac{1}{2}^{(n-1)}[/tex]

What is geometric sequence?

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

It can be given as,

[tex]a_n=a_1\times r^{(n-1)}[/tex]

Here, [tex]a_1[/tex] is the first term of the sequence and [tex]r[/tex] is the common ratio.

Given information-

The series given in the problem is,

40, 20, 10, 5, 2.5.

Here the first term is ,

[tex]a_1=40[/tex]

Common ratio is,

[tex]r=\dfrac{20}{40} =\dfrac{1}{2}\\r=\dfrac{10}{20} =\dfrac{1}{2}\\r=\dfrac{5}{10} =\dfrac{1}{2}[/tex]

Thus the common ratio of the given geometric sequence is 1/2.

Thus put the values in the above formula to find the nth term as,

[tex]a_n=40\times\dfrac{1}{2}^{(n-1)}[/tex]

Hence the formula for the nth term of the sequence given in the graph is,

[tex]a_n=40\times\dfrac{1}{2}^{(n-1)}[/tex]

Learn more about the geometric sequence here;

https://brainly.com/question/1509142