Answer:
IDK why diden't it finish its dinner?
Step-by-step explanation:
Answer:
(3,7)
Step-by-step explanation:
Answer:
See the attached!
Step-by-step explanation:
Answer:
Data 3 has the greater spread in 90 and 100 while Data 4 has a greater spread in 80
Step-by-step explanation:
Hope this Helped
Answer:
The equation is:
![S=\frac{a_n*r-a_1}{r-1}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7Ba_n%2Ar-a_1%7D%7Br-1%7D)
![S=\frac{\frac{16}{243}*\frac{2}{3}-\frac{1}{3}}{\frac{2}{3}-1}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7B%5Cfrac%7B16%7D%7B243%7D%2A%5Cfrac%7B2%7D%7B3%7D-%5Cfrac%7B1%7D%7B3%7D%7D%7B%5Cfrac%7B2%7D%7B3%7D-1%7D)
The sum is:
![S=\frac{211}{243}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7B211%7D%7B243%7D)
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If the sequence is infinite, the formula is:
![S = \frac{a_1}{1-r}](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7Ba_1%7D%7B1-r%7D)
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Step-by-step explanation:
We must calculate the radius of the geometric series
![r =\frac{a_{n+1}}{a_n}\\\\r=\frac{\frac{2}{9}}{\frac{1}{3}}\\\\r=\frac{2}{3}](https://tex.z-dn.net/?f=r%20%3D%5Cfrac%7Ba_%7Bn%2B1%7D%7D%7Ba_n%7D%5C%5C%5C%5Cr%3D%5Cfrac%7B%5Cfrac%7B2%7D%7B9%7D%7D%7B%5Cfrac%7B1%7D%7B3%7D%7D%5C%5C%5C%5Cr%3D%5Cfrac%7B2%7D%7B3%7D)
The first term of the series is: ![a_1=\frac{1}{3}](https://tex.z-dn.net/?f=a_1%3D%5Cfrac%7B1%7D%7B3%7D)
The last term of the series is: ![a_n=\frac{16}{243}](https://tex.z-dn.net/?f=a_n%3D%5Cfrac%7B16%7D%7B243%7D)
If the sequence is finite then the formula is:
![S=\frac{a_n*r-a_1}{r-1}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7Ba_n%2Ar-a_1%7D%7Br-1%7D)
![S=\frac{\frac{16}{243}*\frac{2}{3}-\frac{1}{3}}{\frac{2}{3}-1}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7B%5Cfrac%7B16%7D%7B243%7D%2A%5Cfrac%7B2%7D%7B3%7D-%5Cfrac%7B1%7D%7B3%7D%7D%7B%5Cfrac%7B2%7D%7B3%7D-1%7D)
![S=\frac{211}{243}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7B211%7D%7B243%7D)
If the sequence is infinite then by definition as the radius are
then the formula for the sum of the geometric sequence is:
![S = \frac{a_1}{1-r}\\\\S = \frac{\frac{1}{3}}{1-\frac{2}{3}}\\\\S =1](https://tex.z-dn.net/?f=S%20%3D%20%5Cfrac%7Ba_1%7D%7B1-r%7D%5C%5C%5C%5CS%20%3D%20%5Cfrac%7B%5Cfrac%7B1%7D%7B3%7D%7D%7B1-%5Cfrac%7B2%7D%7B3%7D%7D%5C%5C%5C%5CS%20%3D1)