PART A
The geometric sequence is defined by the equation
![a_{n}=3^{3-n}](https://tex.z-dn.net/?f=a_%7Bn%7D%3D3%5E%7B3-n%7D)
To find the first three terms, we put n=1,2,3
When n=1,
![a_{1}=3^{3-1}](https://tex.z-dn.net/?f=a_%7B1%7D%3D3%5E%7B3-1%7D)
![a_{1}=3^{2}](https://tex.z-dn.net/?f=a_%7B1%7D%3D3%5E%7B2%7D)
![a_{1}=9](https://tex.z-dn.net/?f=a_%7B1%7D%3D9)
When n=2,
![a_{2}=3^{3-2}](https://tex.z-dn.net/?f=a_%7B2%7D%3D3%5E%7B3-2%7D)
![a_{2}=3^{1}](https://tex.z-dn.net/?f=a_%7B2%7D%3D3%5E%7B1%7D)
![a_{2}=3](https://tex.z-dn.net/?f=a_%7B2%7D%3D3)
When n=3
![a_{3}=3^{3-3}](https://tex.z-dn.net/?f=a_%7B3%7D%3D3%5E%7B3-3%7D)
![a_{3}=3^{0}](https://tex.z-dn.net/?f=a_%7B3%7D%3D3%5E%7B0%7D)
![a_{1}=1](https://tex.z-dn.net/?f=a_%7B1%7D%3D1)
The first three terms are,
![9,3,1](https://tex.z-dn.net/?f=9%2C3%2C1)
PART B
The common ratio can be found using any two consecutive terms.
The common ratio is given by,
![r= \frac{a_{2}}{a_{1}}](https://tex.z-dn.net/?f=%20r%3D%20%5Cfrac%7Ba_%7B2%7D%7D%7Ba_%7B1%7D%7D%20)
![r = \frac{3}{9}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B3%7D%7B9%7D%20)
![r = \frac{1}{3}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20)
PART C
To find
![a_{11}](https://tex.z-dn.net/?f=a_%7B11%7D)
We substitute n=11 into the equation of the geometric sequence.
![a_{11} = {3}^{3 - 11}](https://tex.z-dn.net/?f=a_%7B11%7D%20%3D%20%7B3%7D%5E%7B3%20-%2011%7D%20)
This implies that,
![a_{11} = {3}^{ - 8}](https://tex.z-dn.net/?f=a_%7B11%7D%20%3D%20%7B3%7D%5E%7B%20-%208%7D%20)
![a_{11} = \frac{1}{ {3}^{8} }](https://tex.z-dn.net/?f=a_%7B11%7D%20%3D%20%5Cfrac%7B1%7D%7B%20%7B3%7D%5E%7B8%7D%20%7D%20)