Answer:
The next fraction in the given geometric sequence is ![\frac{40}{243}](https://tex.z-dn.net/?f=%5Cfrac%7B40%7D%7B243%7D)
Therefore ![a_5=\frac{40}{243}](https://tex.z-dn.net/?f=a_5%3D%5Cfrac%7B40%7D%7B243%7D)
Step-by-step explanation:
Given geometric sequence is
![\frac{5}{6}, \frac{5}{9}, \frac{10}{27}, \frac{20}{81}, \ldots](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B6%7D%2C%20%5Cfrac%7B5%7D%7B9%7D%2C%20%5Cfrac%7B10%7D%7B27%7D%2C%20%5Cfrac%7B20%7D%7B81%7D%2C%20%5Cldots)
To find the 5th term of the given geometric sequence:
Let
etc.
First find the common ratio
![r=\frac{a_2}{a_1}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Ba_2%7D%7Ba_1%7D)
![=\frac{\frac{5}{9}}{\frac{5}{6}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Cfrac%7B5%7D%7B9%7D%7D%7B%5Cfrac%7B5%7D%7B6%7D%7D)
![=\frac{5}{9}\times \frac{6}{5}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%7D%7B9%7D%5Ctimes%20%5Cfrac%7B6%7D%7B5%7D)
Therefore ![r=\frac{2}{3}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B2%7D%7B3%7D)
![r=\frac{a_3}{a_2}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Ba_3%7D%7Ba_2%7D)
![=\frac{\frac{10}{27}}{\frac{5}{9}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Cfrac%7B10%7D%7B27%7D%7D%7B%5Cfrac%7B5%7D%7B9%7D%7D)
![=\frac{10}{27}\times \frac{9}{5}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B10%7D%7B27%7D%5Ctimes%20%5Cfrac%7B9%7D%7B5%7D)
Therefore ![r=\frac{2}{3}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B2%7D%7B3%7D)
Therefore the common ratio ![r=\frac{2}{3}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B2%7D%7B3%7D)
The nth term of geometric sequence is ![a_n=a_1r^{n-1}](https://tex.z-dn.net/?f=a_n%3Da_1r%5E%7Bn-1%7D)
Put
and
in the above equation we get
![a_5=\frac{5}{6}(\frac{2}{3})^{5-1}](https://tex.z-dn.net/?f=a_5%3D%5Cfrac%7B5%7D%7B6%7D%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B5-1%7D)
![=\frac{5}{6}(\frac{2}{3})^4](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%7D%7B6%7D%28%5Cfrac%7B2%7D%7B3%7D%29%5E4)
![=\frac{5}{6}(\frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}\times \frac{2}{3})](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%7D%7B6%7D%28%5Cfrac%7B2%7D%7B3%7D%5Ctimes%20%5Cfrac%7B2%7D%7B3%7D%5Ctimes%20%5Cfrac%7B2%7D%7B3%7D%5Ctimes%20%5Cfrac%7B2%7D%7B3%7D%29)
![=\frac{5}{3}(\frac{8}{81})](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%7D%7B3%7D%28%5Cfrac%7B8%7D%7B81%7D%29)
![a_5=\frac{40}{243}](https://tex.z-dn.net/?f=a_5%3D%5Cfrac%7B40%7D%7B243%7D)
Therefore ![a_5=\frac{40}{243}](https://tex.z-dn.net/?f=a_5%3D%5Cfrac%7B40%7D%7B243%7D)
Therefore the next fraction in the given geometric sequence is ![\frac{40}{243}](https://tex.z-dn.net/?f=%5Cfrac%7B40%7D%7B243%7D)
60*0.08 Multiply the price of the sweater by 0.08, or 8%
4.8 solution
60-4.8 Subtract discount from original price
55.2 solution
7/100=a/55.2 construct formula to find sales tax
a=3.864 solution
55.2+3.864 add solution to discounted price
59.064 solution
$59.06 round down to 59.06
It will be less than 60 dollars because, according to the work shown, 59.06<60.
Answer:
The slope of line q is
.
Step-by-step explanation:
We know that line p has a slope of
, and that line p and line q are parallel. Parallel lines always have the same slope. Thus, the slope of line q must be
as well.
Answer:
C
Step-by-step explanation:
Only C is a polynomial function. It is recognizable as such by the positive, integer power x^4. The others have negative powers, which eliminates them.