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.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

no

step-by-step explanation:

answer