What is the recursive rule for this geometric sequence? 2, 12, 18, 132, ... Enter your answers in the boxes. an= _ ⋅an−1
2 answers:
The recursive rule for a
geometric sequence allow you to find the previous term of an n'th position.
Common Ratio: 6
Recursive Rule Formula:
Please mark as Brainliest, thank you.
Answer: ![a_{n+1}=6a_n](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%3D6a_n)
Step-by-step explanation:
The given geometric sequence= 2, 12, 18,132,..........
Here the first term
= 2
The second term
=12
The third term
=18
The fourth term
=132 and so on
We know that the common ratio in geometric series is
![r=\frac{a_{n+1}}{a_n}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Ba_%7Bn%2B1%7D%7D%7Ba_n%7D)
Here, ![r=\frac{12}{2}=\frac{18}{12}=\frac{132}{18}=6](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B12%7D%7B2%7D%3D%5Cfrac%7B18%7D%7B12%7D%3D%5Cfrac%7B132%7D%7B18%7D%3D6)
Thus The recursive rule for this geometric sequence is
![6=\frac{a_{n+1}}{a_n}](https://tex.z-dn.net/?f=6%3D%5Cfrac%7Ba_%7Bn%2B1%7D%7D%7Ba_n%7D)
![\Rightarrow\ a_{n+1}=6a_n](https://tex.z-dn.net/?f=%5CRightarrow%5C%20a_%7Bn%2B1%7D%3D6a_n)
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