Respuesta :
For a geometric sequence, the ratio between the third and second term is the same as the ratio between the fourth and third term.
Thus, we can say: [tex]12x = r[/tex] and [tex]r \cdot x = \frac{4}{3}[/tex]
[tex]12x = \frac{4}{\frac{3}{x}}}[/tex]
[tex]12x = \frac{4}{3x}[/tex]
[tex]36x^{2} = 4[/tex]
[tex]9x^{2} = 1[/tex]
[tex]x^{2} = \frac{1}{9}[/tex]
[tex]x^{2} = \pm \frac{1}{3}[/tex]
Hence, the common ratio for this sequence is: [tex]r = \pm \frac{1}{3}[/tex]
Thus, we can say: [tex]12x = r[/tex] and [tex]r \cdot x = \frac{4}{3}[/tex]
[tex]12x = \frac{4}{\frac{3}{x}}}[/tex]
[tex]12x = \frac{4}{3x}[/tex]
[tex]36x^{2} = 4[/tex]
[tex]9x^{2} = 1[/tex]
[tex]x^{2} = \frac{1}{9}[/tex]
[tex]x^{2} = \pm \frac{1}{3}[/tex]
Hence, the common ratio for this sequence is: [tex]r = \pm \frac{1}{3}[/tex]
Answer:
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.
