Answer:
The 9th term for given sequence is 16.777
Therefore the 9th term is
.
Step-by-step explanation:
Given first three terms of a sequence are 100,80,64,...
Given
,
,
,...
Given sequence is of the form of Geometric sequence
Therefore it can be written as ![{\{a,ar,ar^2,...}\}](https://tex.z-dn.net/?f=%7B%5C%7Ba%2Car%2Car%5E2%2C...%7D%5C%7D)
therefore a=100 , ar=80 ,
,...
To find common ratio
![r=\frac{a_{2}}{a_{1}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Ba_%7B2%7D%7D%7Ba_%7B1%7D%7D)
![r=\frac{80}{100}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B80%7D%7B100%7D)
![r=\frac{4}{5}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%7D%7B5%7D)
![r=\frac{a_{3}}{a_{2}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Ba_%7B3%7D%7D%7Ba_%7B2%7D%7D)
![r=\frac{64}{80}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B64%7D%7B80%7D)
![r=\frac{4}{5}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%7D%7B5%7D)
Therefore ![r=\frac{4}{5}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%7D%7B5%7D)
The nth term of the geometric sequence is
![a_{n}=ar^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%3Dar%5E%7Bn-1%7D)
To find the 9th tem for the given geometric sequence is
![a_{n}=ar^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%3Dar%5E%7Bn-1%7D)
put n=9, a=100 and ![r=\frac{4}{5}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%7D%7B5%7D)
![a_{9}=100(\frac{4}{5})^{9-1}](https://tex.z-dn.net/?f=a_%7B9%7D%3D100%28%5Cfrac%7B4%7D%7B5%7D%29%5E%7B9-1%7D)
![=100(\frac{4}{5})^{8}](https://tex.z-dn.net/?f=%3D100%28%5Cfrac%7B4%7D%7B5%7D%29%5E%7B8%7D)
![=100(\frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5})](https://tex.z-dn.net/?f=%3D100%28%5Cfrac%7B4%7D%7B5%7D%5Ctimes%20%5Cfrac%7B4%7D%7B5%7D%5Ctimes%20%5Cfrac%7B4%7D%7B5%7D%5Ctimes%20%5Cfrac%7B4%7D%7B5%7D%5Ctimes%20%5Cfrac%7B4%7D%7B5%7D%5Ctimes%20%5Cfrac%7B4%7D%7B5%7D%5Ctimes%20%5Cfrac%7B4%7D%7B5%7D%5Ctimes%20%5Cfrac%7B4%7D%7B5%7D%29)
![=100(\frac{256\times 256}{625\times 625})](https://tex.z-dn.net/?f=%3D100%28%5Cfrac%7B256%5Ctimes%20256%7D%7B625%5Ctimes%20625%7D%29)
![=100(\frac{65536}{390625})](https://tex.z-dn.net/?f=%3D100%28%5Cfrac%7B65536%7D%7B390625%7D%29)
![=100(0.16777})](https://tex.z-dn.net/?f=%3D100%280.16777%7D%29)
![=16.777](https://tex.z-dn.net/?f=%3D16.777)
Therefore ![a_{9}=16.777](https://tex.z-dn.net/?f=a_%7B9%7D%3D16.777)
The 9th term is 16.777
Answer:
480 times
Step-by-step explanation:
per second=120
4 seconds=?
120 x 4 = 480
Answer:
x = 6/5
Step-by-step explanation:
x = 6/5
Sorry I am not the best at explaining for math but I know it is the right answer.
Answer:
11
Step-by-step explanation:
Answer:
15 degrees?
Step-by-step explanation: