Answer:
The common ratio is [tex]r=\pm\frac{1}{3}[/tex].
Step-by-step explanation:
Given : The second term in a geometric sequence is 12. The fourth term in the same sequence is 4/3.
To find : What is the common ratio in this sequence?
Solution :
The nth term of G.P is [tex]a_n=ar^{n-1}[/tex]
The second term in a geometric sequence is 12.
i.e. [tex]a_2=ar^{2-1}[/tex]
[tex]12=ar[/tex] .....(1)
The four term in a geometric sequence is [tex]\frac{4}{3}[/tex].
i.e. [tex]a_4=ar^{4-1}[/tex]
[tex]\frac{4}{3}=ar^3[/tex] .....(2)
Divide (1) and (2),
[tex]\frac{\frac{4}{3}}{12}=\frac{ar^3}{ar}[/tex]
[tex]\frac{1}{9}=r^2[/tex]
[tex]\sqrt{\frac{1}{9}}=r[/tex]
[tex]\pm\frac{1}{3}=r[/tex]
Therefore, the common ratio is [tex]r=\pm\frac{1}{3}[/tex].
