The answer fam is.......... 22
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)
Answer:
To find the length of a horizontal line segment, find the difference between the x-coordinates. Subtract the smaller from the larger.
Answer: Devaughn's age is 48 and Sydney's age is 24
Step-by-step explanation:
72 divided by 3 gives you 24.
24+24 is 48 which is Devaughn's age.48-72 gives you 24 which is Sydney's age
Yes, you have the right answer for part 1.
But for the second part it should be A. Because if it is a square, it has to be both a rectangle and a rhombus, that is the only way to prove it.
We know it is a rhombus because we are given a right angle. And rhombus' diagonals are the perpendicular bisector of each other. we know the diagonals are both perpendicular bisectors because the segments divided are congruent, and it created a right angle. Therefore, it is a rhombus.
We know it is a rectangle because we know rectangles' diagonals are congruent. We can see all four segments are congruent, so "if congruent segments are added to congruent segments, then the sum is congruent". So the diagonals are congruent, showing it is also a rectangle.
So when a figure is both a rectangle and a rhombus, it is a square.
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