The second term in a geometric sequence is 12. the fourth term in the same sequence is 4/3. what is the common ratio in this sequence?

1/3

Step-by-step explanation:

Given:-

For the geometric sequence:

- 2nd Term = 12

- 4th Term = 4 / 3

Find:-

What is the common ratio in this sequence?

Solution:-

- A geometric sequence is categorized by two parameters which are:

                                  a : First Term

                                  r : Common ratio.

- The general (nth) term in a geometric sequence is given by the following relation.

                           Term = a * ( r ) ^ ( n - 1 )

Where,                n = Term number

- We will develop two equations for the given two terms as follows:

                           12 = a * ( r ) ^ ( 2 - 1 ) = a * ( r )

                           4/3 = a * ( r ) ^ ( 4 - 1 ) = a * ( r )^3

- Now divide the two equations and solve for common ratio (r):

                           12*3 / 4 = 1 / r^2

                           9 =  1 / r^2

                           r = √(1 /9) = 1 / 3

- The common ratio (r) is equal to 1 / 3.

g(x) is the negative form of f(x)? because whenever its the negative form it reflects its self over the x axis. idk if this is right though.

step-by-step explanation:

the solution is x=1

step-by-step explanation:

we are given our   equation as

let's assume

left side function is

right side function is

now, we can draw graph

and then we can get intersection point

the intersection point will be solution

so, the solution is

x=1