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.

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step-by-step explanation: